On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > > On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > > > On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> > > > > > On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > > > > >
> > > > > > > sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> > > > > > >
> > > > > > > Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > > > > >
> > > > > > > Where the sqrt of -1 is the second half of the equation above --
> > > > > > > (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> > > > > > > Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > > > > > A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> > > > > > > going in the positive and the mirror image going into the negative.
> > > > > > > Just enter the above equation into Wolfram Alpha using any number.
> > > > > > > pi(in this case),e , golden ratio, the primes etc. giving the same results.
> > > > > > >
> > > > > > > Just having some fun. ;-)!!!
> > > > > > Check this out:
> > > > > >
> > > > > > https://youtu.be/d0vY0CKYhPY
> > > > > >
> > > > > > ;^)
> > > > > Interesting.
> > > > > The many different crazy places pi will appear.
> > > > > I just used pi as one of the ---> oo numbers that work in this equation.
> > > > >
> > > > > I did this plot in the third quadrant where each new frame was a continuation of
> > > > > the last frame. So the parabolic curve keeps slightly increasing the distance from the
> > > > > -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> > > > > reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> > > > > and y=0. Where x+y=x^2
> > > > > A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> > > > > x + y=x^2 from the first quadrant.
> > > > > That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> > > > > Duplicating the same part of the parabola in the first quadrant --
> > > > > x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> > > > > but only equal too -1 in the third quadrant.
> > > > > Negative integer points of -x\-y in the parabola in the third quadrant --
> > > > > -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > > Explaining this plot in the third quadrant---
> > > > The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> > > > opposed to the first quadrant where x\y is the plus quadrant.
> > > >
> > > > These points on the parabola in the third quadrant of the Cartesian coordinate
> > > > system start @ y=-0.5 and x=0
> > > > So the first y=-0.5 is not in the -y calculations below but that part of the
> > > > parabola that falls only in the third quadrant.
> > > > Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> > > > and in it's mirror image flipped state reflex's only that part of the parabola
> > > > falling in the 3rd quadrant .
> > > >
> > > > (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> > > > the square root of -1 where -x+-y= -1
> > > > (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > > > (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> > > > (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> > > > (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > > (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2.8786796565...
> > > > (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3.6547921201...
> > > > (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > > (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> > > > (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> > > > (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > > ...
> > > >
> > > > A certain way to do the squaring and square root function in the third negative
> > > > quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> > > > Where n can be any number that will represent the two plotted points
> > > > on the reversed mirror image of the parabola -x+-y.
> > > >
> > > > Just a novel way to express negative values.
> > > What is interesting is that----
> > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> > > The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> > > the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> > > and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> > > This is probably true for all numbers.
> > I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> > becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> > when summed -x+-y = -pi .
> >
> > The same with e and any other number.
> There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
>
> Dan

(r)=ratio and (n) = any number.

Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n

Neat huh?

Dan

On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > > On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > > On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > > > On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > > > > On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> > > > > > > On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > > > > > >
> > > > > > > > sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > >
> > > > > > > > Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > > > > > >
> > > > > > > > Where the sqrt of -1 is the second half of the equation above --
> > > > > > > > (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> > > > > > > > Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > > > > > > A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> > > > > > > > going in the positive and the mirror image going into the negative.
> > > > > > > > Just enter the above equation into Wolfram Alpha using any number.
> > > > > > > > pi(in this case),e , golden ratio, the primes etc. giving the same results.
> > > > > > > >
> > > > > > > > Just having some fun. ;-)!!!
> > > > > > > Check this out:
> > > > > > >
> > > > > > > https://youtu.be/d0vY0CKYhPY
> > > > > > >
> > > > > > > ;^)
> > > > > > Interesting.
> > > > > > The many different crazy places pi will appear.
> > > > > > I just used pi as one of the ---> oo numbers that work in this equation.
> > > > > >
> > > > > > I did this plot in the third quadrant where each new frame was a continuation of
> > > > > > the last frame. So the parabolic curve keeps slightly increasing the distance from the
> > > > > > -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> > > > > > reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> > > > > > and y=0. Where x+y=x^2
> > > > > > A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> > > > > > x + y=x^2 from the first quadrant.
> > > > > > That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> > > > > > Duplicating the same part of the parabola in the first quadrant --
> > > > > > x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> > > > > > but only equal too -1 in the third quadrant.
> > > > > > Negative integer points of -x\-y in the parabola in the third quadrant --
> > > > > > -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > > > Explaining this plot in the third quadrant---
> > > > > The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> > > > > opposed to the first quadrant where x\y is the plus quadrant.
> > > > >
> > > > > These points on the parabola in the third quadrant of the Cartesian coordinate
> > > > > system start @ y=-0.5 and x=0
> > > > > So the first y=-0.5 is not in the -y calculations below but that part of the
> > > > > parabola that falls only in the third quadrant.
> > > > > Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> > > > > and in it's mirror image flipped state reflex's only that part of the parabola
> > > > > falling in the 3rd quadrant .
> > > > >
> > > > > (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> > > > > the square root of -1 where -x+-y= -1
> > > > > (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > > > > (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> > > > > (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> > > > > (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > > > (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2..8786796565...
> > > > > (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3..6547921201...
> > > > > (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > > > (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> > > > > (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> > > > > (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > > > ...
> > > > >
> > > > > A certain way to do the squaring and square root function in the third negative
> > > > > quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> > > > > Where n can be any number that will represent the two plotted points
> > > > > on the reversed mirror image of the parabola -x+-y.
> > > > >
> > > > > Just a novel way to express negative values.
> > > > What is interesting is that----
> > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> > > > The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> > > > the first quadrant where x+y =x^2 then add 1 to the above ratio 2..458777240...+1= 3.4587772407...
> > > > and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> > > > This is probably true for all numbers.
> > > I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> > > becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> > > when summed -x+-y = -pi .
> > >
> > > The same with e and any other number.
> > There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> > where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427.... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> > 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> > 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> > So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >
> > Dan
> (r)=ratio and (n) = any number.
>
> Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
>
> Neat huh?
>
> Dan

I finally have the proof.
Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.

Enter below into Wolfram alpha---
-x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant..
It took awhile but I finally presented it the right way for Wolfram.

Pick any value for n and you will see why n=0--->oo.

On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> > On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > > On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > > > On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > > > On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > > > > On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > > > > > On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> > > > > > > > On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > > > > > > >
> > > > > > > > > sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > >
> > > > > > > > > Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > > > > > > >
> > > > > > > > > Where the sqrt of -1 is the second half of the equation above --
> > > > > > > > > (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > > Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> > > > > > > > > Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > > > > > > > A mirror image of the x + y= x^2 plot starting at y=-..25 part of the parabola
> > > > > > > > > going in the positive and the mirror image going into the negative.
> > > > > > > > > Just enter the above equation into Wolfram Alpha using any number.
> > > > > > > > > pi(in this case),e , golden ratio, the primes etc. giving the same results.
> > > > > > > > >
> > > > > > > > > Just having some fun. ;-)!!!
> > > > > > > > Check this out:
> > > > > > > >
> > > > > > > > https://youtu.be/d0vY0CKYhPY
> > > > > > > >
> > > > > > > > ;^)
> > > > > > > Interesting.
> > > > > > > The many different crazy places pi will appear.
> > > > > > > I just used pi as one of the ---> oo numbers that work in this equation.
> > > > > > >
> > > > > > > I did this plot in the third quadrant where each new frame was a continuation of
> > > > > > > the last frame. So the parabolic curve keeps slightly increasing the distance from the
> > > > > > > -y axis. This part of the curve starts @ x=0 and -y= -0.5.. An exact duplicate of its'
> > > > > > > reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> > > > > > > and y=0. Where x+y=x^2
> > > > > > > A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> > > > > > > x + y=x^2 from the first quadrant.
> > > > > > > That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> > > > > > > Duplicating the same part of the parabola in the first quadrant --
> > > > > > > x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> > > > > > > but only equal too -1 in the third quadrant.
> > > > > > > Negative integer points of -x\-y in the parabola in the third quadrant --
> > > > > > > -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > > > > Explaining this plot in the third quadrant---
> > > > > > The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> > > > > > opposed to the first quadrant where x\y is the plus quadrant.
> > > > > >
> > > > > > These points on the parabola in the third quadrant of the Cartesian coordinate
> > > > > > system start @ y=-0.5 and x=0
> > > > > > So the first y=-0.5 is not in the -y calculations below but that part of the
> > > > > > parabola that falls only in the third quadrant.
> > > > > > Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> > > > > > and in it's mirror image flipped state reflex's only that part of the parabola
> > > > > > falling in the 3rd quadrant .
> > > > > >
> > > > > > (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> > > > > > the square root of -1 where -x+-y= -1
> > > > > > (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > > > > > (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> > > > > > (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2..1291713067...
> > > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> > > > > > (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > > > > (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2.8786796565...
> > > > > > (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3.6547921201...
> > > > > > (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > > > > (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> > > > > > (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> > > > > > (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > > > > ...
> > > > > >
> > > > > > A certain way to do the squaring and square root function in the third negative
> > > > > > quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> > > > > > Where n can be any number that will represent the two plotted points
> > > > > > on the reversed mirror image of the parabola -x+-y.
> > > > > >
> > > > > > Just a novel way to express negative values.
> > > > > What is interesting is that----
> > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> > > > > The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> > > > > the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> > > > > and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> > > > > This is probably true for all numbers.
> > > > I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> > > > becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> > > > when summed -x+-y = -pi .
> > > >
> > > > The same with e and any other number.
> > > There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> > > where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> > > 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> > > 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> > > So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> > >
> > > Dan
> > (r)=ratio and (n) = any number.
> >
> > Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> > Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> > quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> >
> > Neat huh?
> >
> > Dan
> I finally have the proof.
> Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
>
> Enter below into Wolfram alpha---
> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> It took awhile but I finally presented it the right way for Wolfram.
>
> Pick any value for n and you will see why n=0--->oo.

On Thursday, July 7, 2022 at 8:56:41 AM UTC-7, Dan joyce wrote:
> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> > On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> > > On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > > > On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > > > > On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > > > > On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > > > > > On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > > > > > > On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> > > > > > > > > On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > > > > > > > >
> > > > > > > > > > sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > > >
> > > > > > > > > > Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > > > > > > > >
> > > > > > > > > > Where the sqrt of -1 is the second half of the equation above --
> > > > > > > > > > (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > > > Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> > > > > > > > > > Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > > > > > > > > A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> > > > > > > > > > going in the positive and the mirror image going into the negative.
> > > > > > > > > > Just enter the above equation into Wolfram Alpha using any number.
> > > > > > > > > > pi(in this case),e , golden ratio, the primes etc. giving the same results.
> > > > > > > > > >
> > > > > > > > > > Just having some fun. ;-)!!!
> > > > > > > > > Check this out:
> > > > > > > > >
> > > > > > > > > https://youtu.be/d0vY0CKYhPY
> > > > > > > > >
> > > > > > > > > ;^)
> > > > > > > > Interesting.
> > > > > > > > The many different crazy places pi will appear.
> > > > > > > > I just used pi as one of the ---> oo numbers that work in this equation.
> > > > > > > >
> > > > > > > > I did this plot in the third quadrant where each new frame was a continuation of
> > > > > > > > the last frame. So the parabolic curve keeps slightly increasing the distance from the
> > > > > > > > -y axis. This part of the curve starts @ x=0 and -y= -0..5. An exact duplicate of its'
> > > > > > > > reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> > > > > > > > and y=0. Where x+y=x^2
> > > > > > > > A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> > > > > > > > x + y=x^2 from the first quadrant.
> > > > > > > > That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> > > > > > > > Duplicating the same part of the parabola in the first quadrant --
> > > > > > > > x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> > > > > > > > but only equal too -1 in the third quadrant.
> > > > > > > > Negative integer points of -x\-y in the parabola in the third quadrant --
> > > > > > > > -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > > > > > Explaining this plot in the third quadrant---
> > > > > > > The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> > > > > > > opposed to the first quadrant where x\y is the plus quadrant.
> > > > > > >
> > > > > > > These points on the parabola in the third quadrant of the Cartesian coordinate
> > > > > > > system start @ y=-0.5 and x=0
> > > > > > > So the first y=-0.5 is not in the -y calculations below but that part of the
> > > > > > > parabola that falls only in the third quadrant.
> > > > > > > Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> > > > > > > and in it's mirror image flipped state reflex's only that part of the parabola
> > > > > > > falling in the 3rd quadrant .
> > > > > > >
> > > > > > > (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> > > > > > > the square root of -1 where -x+-y= -1
> > > > > > > (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1..41886117...
> > > > > > > (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> > > > > > > (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> > > > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> > > > > > > (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > > > > > (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2.8786796565...
> > > > > > > (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3.6547921201...
> > > > > > > (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > > > > > (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> > > > > > > (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> > > > > > > (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > > > > > ...
> > > > > > >
> > > > > > > A certain way to do the squaring and square root function in the third negative
> > > > > > > quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> > > > > > > Where n can be any number that will represent the two plotted points
> > > > > > > on the reversed mirror image of the parabola -x+-y.
> > > > > > >
> > > > > > > Just a novel way to express negative values.
> > > > > > What is interesting is that----
> > > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> > > > > > The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> > > > > > the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> > > > > > and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> > > > > > This is probably true for all numbers.
> > > > > I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> > > > > becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> > > > > when summed -x+-y = -pi .
> > > > >
> > > > > The same with e and any other number.
> > > > There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> > > > where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> > > > 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> > > > 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> > > > So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> > > >
> > > > Dan
> > > (r)=ratio and (n) = any number.
> > >
> > > Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> > > Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> > > quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> > >
> > > Neat huh?
> > >
> > > Dan
> > I finally have the proof.
> > Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
> >
> > Enter below into Wolfram alpha---
> > -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> > The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> > From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> > It took awhile but I finally presented it the right way for Wolfram.
> >
> > Pick any value for n and you will see why n=0--->oo.
> When -x = -pi in the third quadrant then, to find the the negative square of
> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
>
> The ratio of -y/-x = 4.3007475966...
> Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> x^2 = 28.0979250837...
> y = x^2 - x= 5.3007475966... = 22.797177487...
> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
>
> The same procedure (added values to a number) will work with any number in
> the negative -x\-y third quadrant. Then cross checking with the first quadrant
> x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> adding 1 to the ratio and then x=r applied to the first quadrant.
>
> This is not imaginary but using real numbers in just 2 dimensions depicting
> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> quadrant the parabola is flipped from the up to the down position and then
> flipped over to the left.
> Is this the only way to give a square root of a negative number without using
> imaginary (i)?
>
> The math works but the negative squares and square roots are probably not the
> correct meaning of all this?
>
> Any thoughts?

On 7/7/2022 8:56 AM, Dan joyce wrote:
> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
>>>>>>>>>>
>>>>>>>>>> sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>
>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
>>>>>>>>>>
>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
>>>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
>>>>>>>>>> going in the positive and the mirror image going into the negative.
>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any number.
>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the same results.
>>>>>>>>>>
>>>>>>>>>> Just having some fun. ;-)!!!
>>>>>>>>> Check this out:
>>>>>>>>>
>>>>>>>>> https://youtu.be/d0vY0CKYhPY
>>>>>>>>>
>>>>>>>>> ;^)
>>>>>>>> Interesting.
>>>>>>>> The many different crazy places pi will appear.
>>>>>>>> I just used pi as one of the ---> oo numbers that work in this equation.
>>>>>>>>
>>>>>>>> I did this plot in the third quadrant where each new frame was a continuation of
>>>>>>>> the last frame. So the parabolic curve keeps slightly increasing the distance from the
>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
>>>>>>>> reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
>>>>>>>> and y=0. Where x+y=x^2
>>>>>>>> A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
>>>>>>>> x + y=x^2 from the first quadrant.
>>>>>>>> That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
>>>>>>>> but only equal too -1 in the third quadrant.
>>>>>>>> Negative integer points of -x\-y in the parabola in the third quadrant --
>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
>>>>>>> Explaining this plot in the third quadrant---
>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
>>>>>>>
>>>>>>> These points on the parabola in the third quadrant of the Cartesian coordinate
>>>>>>> system start @ y=-0.5 and x=0
>>>>>>> So the first y=-0.5 is not in the -y calculations below but that part of the
>>>>>>> parabola that falls only in the third quadrant.
>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
>>>>>>> and in it's mirror image flipped state reflex's only that part of the parabola
>>>>>>> falling in the 3rd quadrant .
>>>>>>>
>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
>>>>>>> the square root of -1 where -x+-y= -1
>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2.8786796565...
>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3.6547921201...
>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
>>>>>>> ...
>>>>>>>
>>>>>>> A certain way to do the squaring and square root function in the third negative
>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
>>>>>>> Where n can be any number that will represent the two plotted points
>>>>>>> on the reversed mirror image of the parabola -x+-y.
>>>>>>>
>>>>>>> Just a novel way to express negative values.
>>>>>> What is interesting is that----
>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
>>>>>> This is probably true for all numbers.
>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
>>>>> becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
>>>>> when summed -x+-y = -pi .
>>>>>
>>>>> The same with e and any other number.
>>>> There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
>>>>
>>>> Dan
>>> (r)=ratio and (n) = any number.
>>>
>>> Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
>>> quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
>>>
>>> Neat huh?
>>>
>>> Dan
>> I finally have the proof.
>> Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
>>
>> Enter below into Wolfram alpha---
>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
>> The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
>> It took awhile but I finally presented it the right way for Wolfram.
>>
>> Pick any value for n and you will see why n=0--->oo.
>
> When -x = -pi in the third quadrant then, to find the the negative square of
> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
>
> The ratio of -y/-x = 4.3007475966...
> Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> x^2 = 28.0979250837...
> y = x^2 - x= 5.3007475966... = 22.797177487...
> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
>
> The same procedure (added values to a number) will work with any number in
> the negative -x\-y third quadrant. Then cross checking with the first quadrant
> x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> adding 1 to the ratio and then x=r applied to the first quadrant.
>
> This is not imaginary but using real numbers in just 2 dimensions depicting
> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> quadrant the parabola is flipped from the up to the down position and then
> flipped over to the left.
> Is this the only way to give a square root of a negative number without using
> imaginary (i)?
>
> The math works but the negative squares and square roots are probably not the
> correct meaning of all this?
>
> Any thoughts?

On Thursday, July 7, 2022 at 5:42:37 PM UTC-4, Chris M. Thomasson wrote:
> On 7/7/2022 8:56 AM, Dan joyce wrote:
> > On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> >> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> >>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> >>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> >>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> >>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> >>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> >>>>>>>>>>
> >>>>>>>>>> sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>
> >>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> >>>>>>>>>>
> >>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> >>>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> >>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> >>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> >>>>>>>>>> going in the positive and the mirror image going into the negative.
> >>>>>>>>>> Just enter the above equation into Wolfram Alpha using any number.
> >>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the same results.
> >>>>>>>>>>
> >>>>>>>>>> Just having some fun. ;-)!!!
> >>>>>>>>> Check this out:
> >>>>>>>>>
> >>>>>>>>> https://youtu.be/d0vY0CKYhPY
> >>>>>>>>>
> >>>>>>>>> ;^)
> >>>>>>>> Interesting.
> >>>>>>>> The many different crazy places pi will appear.
> >>>>>>>> I just used pi as one of the ---> oo numbers that work in this equation.
> >>>>>>>>
> >>>>>>>> I did this plot in the third quadrant where each new frame was a continuation of
> >>>>>>>> the last frame. So the parabolic curve keeps slightly increasing the distance from the
> >>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> >>>>>>>> reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> >>>>>>>> and y=0. Where x+y=x^2
> >>>>>>>> A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> >>>>>>>> x + y=x^2 from the first quadrant.
> >>>>>>>> That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> >>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> >>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> >>>>>>>> but only equal too -1 in the third quadrant.
> >>>>>>>> Negative integer points of -x\-y in the parabola in the third quadrant --
> >>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> >>>>>>> Explaining this plot in the third quadrant---
> >>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> >>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> >>>>>>>
> >>>>>>> These points on the parabola in the third quadrant of the Cartesian coordinate
> >>>>>>> system start @ y=-0.5 and x=0
> >>>>>>> So the first y=-0.5 is not in the -y calculations below but that part of the
> >>>>>>> parabola that falls only in the third quadrant.
> >>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> >>>>>>> and in it's mirror image flipped state reflex's only that part of the parabola
> >>>>>>> falling in the 3rd quadrant .
> >>>>>>>
> >>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> >>>>>>> the square root of -1 where -x+-y= -1
> >>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> >>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> >>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> >>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> >>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2..8786796565...
> >>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3..6547921201...
> >>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> >>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> >>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> >>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> >>>>>>> ...
> >>>>>>>
> >>>>>>> A certain way to do the squaring and square root function in the third negative
> >>>>>>> quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> >>>>>>> Where n can be any number that will represent the two plotted points
> >>>>>>> on the reversed mirror image of the parabola -x+-y.
> >>>>>>>
> >>>>>>> Just a novel way to express negative values.
> >>>>>> What is interesting is that----
> >>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> >>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> >>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> >>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> >>>>>> This is probably true for all numbers.
> >>>>> I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> >>>>> becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> >>>>> when summed -x+-y = -pi .
> >>>>>
> >>>>> The same with e and any other number.
> >>>> There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> >>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> >>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> >>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> >>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >>>>
> >>>> Dan
> >>> (r)=ratio and (n) = any number.
> >>>
> >>> Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> >>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> >>> quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> >>>
> >>> Neat huh?
> >>>
> >>> Dan
> >> I finally have the proof.
> >> Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
> >>
> >> Enter below into Wolfram alpha---
> >> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> >> The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> >> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> >> It took awhile but I finally presented it the right way for Wolfram.
> >>
> >> Pick any value for n and you will see why n=0--->oo.
> >
> > When -x = -pi in the third quadrant then, to find the the negative square of
> > -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> > quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >
> > The ratio of -y/-x = 4.3007475966...
> > Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> > x^2 = 28.0979250837...
> > y = x^2 - x= 5.3007475966... = 22.797177487...
> > Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
> >
> > The same procedure (added values to a number) will work with any number in
> > the negative -x\-y third quadrant. Then cross checking with the first quadrant
> > x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> > adding 1 to the ratio and then x=r applied to the first quadrant.
> >
> > This is not imaginary but using real numbers in just 2 dimensions depicting
> > the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> > quadrant the parabola is flipped from the up to the down position and then
> > flipped over to the left.
> > Is this the only way to give a square root of a negative number without using
> > imaginary (i)?
> >
> > The math works but the negative squares and square roots are probably not the
> > correct meaning of all this?
> >
> > Any thoughts?
> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> component, then convert back to rectangular form, and we have 0-1i.
> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>
> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> purely real because the imaginary part is zero. ;^)
>
> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>
> This creates the borders of the four quadrants of a unit circle.
>
> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> the point 0-1i.
>
> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>
> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> Keep in mind that the radius of the imaginary unit is one.
>
> With polar form in mind:
>
> 1+0i + PI = -1+0i
>
> Also:
>
> 1+0i + PI/2 = 0+1i = the imaginary unit.

On Thursday, July 7, 2022 at 3:23:31 PM UTC-4, mitchr...@gmail.com wrote:
> On Thursday, July 7, 2022 at 8:56:41 AM UTC-7, Dan joyce wrote:
> > On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> > > On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> > > > On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > > > > On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > > > > > On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > > > > > On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > > > > > > On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > > > > > > > On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> > > > > > > > > > On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > > > > > > > > >
> > > > > > > > > > > sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > > > >
> > > > > > > > > > > Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > > > > > > > > >
> > > > > > > > > > > Where the sqrt of -1 is the second half of the equation above --
> > > > > > > > > > > (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> > > > > > > > > > > Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> > > > > > > > > > > Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > > > > > > > > > A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> > > > > > > > > > > going in the positive and the mirror image going into the negative.
> > > > > > > > > > > Just enter the above equation into Wolfram Alpha using any number.
> > > > > > > > > > > pi(in this case),e , golden ratio, the primes etc. giving the same results.
> > > > > > > > > > >
> > > > > > > > > > > Just having some fun. ;-)!!!
> > > > > > > > > > Check this out:
> > > > > > > > > >
> > > > > > > > > > https://youtu.be/d0vY0CKYhPY
> > > > > > > > > >
> > > > > > > > > > ;^)
> > > > > > > > > Interesting.
> > > > > > > > > The many different crazy places pi will appear.
> > > > > > > > > I just used pi as one of the ---> oo numbers that work in this equation.
> > > > > > > > >
> > > > > > > > > I did this plot in the third quadrant where each new frame was a continuation of
> > > > > > > > > the last frame. So the parabolic curve keeps slightly increasing the distance from the
> > > > > > > > > -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> > > > > > > > > reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> > > > > > > > > and y=0. Where x+y=x^2
> > > > > > > > > A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> > > > > > > > > x + y=x^2 from the first quadrant.
> > > > > > > > > That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> > > > > > > > > Duplicating the same part of the parabola in the first quadrant --
> > > > > > > > > x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> > > > > > > > > but only equal too -1 in the third quadrant.
> > > > > > > > > Negative integer points of -x\-y in the parabola in the third quadrant --
> > > > > > > > > -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > > > > > > Explaining this plot in the third quadrant---
> > > > > > > > The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> > > > > > > > opposed to the first quadrant where x\y is the plus quadrant.
> > > > > > > >
> > > > > > > > These points on the parabola in the third quadrant of the Cartesian coordinate
> > > > > > > > system start @ y=-0.5 and x=0
> > > > > > > > So the first y=-0.5 is not in the -y calculations below but that part of the
> > > > > > > > parabola that falls only in the third quadrant.
> > > > > > > > Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> > > > > > > > and in it's mirror image flipped state reflex's only that part of the parabola
> > > > > > > > falling in the 3rd quadrant .
> > > > > > > >
> > > > > > > > (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> > > > > > > > the square root of -1 where -x+-y= -1
> > > > > > > > (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > > > > > > > (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> > > > > > > > (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> > > > > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> > > > > > > > (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > > > > > > (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2.8786796565...
> > > > > > > > (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3.6547921201...
> > > > > > > > (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > > > > > > (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> > > > > > > > (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> > > > > > > > (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > > > > > > ...
> > > > > > > >
> > > > > > > > A certain way to do the squaring and square root function in the third negative
> > > > > > > > quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> > > > > > > > Where n can be any number that will represent the two plotted points
> > > > > > > > on the reversed mirror image of the parabola -x+-y.
> > > > > > > >
> > > > > > > > Just a novel way to express negative values.
> > > > > > > What is interesting is that----
> > > > > > > (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> > > > > > > The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> > > > > > > the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> > > > > > > and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> > > > > > > This is probably true for all numbers.
> > > > > > I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> > > > > > becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> > > > > > when summed -x+-y = -pi .
> > > > > >
> > > > > > The same with e and any other number.
> > > > > There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> > > > > where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286.... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> > > > > 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> > > > > 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> > > > > So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> > > > >
> > > > > Dan
> > > > (r)=ratio and (n) = any number.
> > > >
> > > > Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> > > > Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> > > > quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> > > >
> > > > Neat huh?
> > > >
> > > > Dan
> > > I finally have the proof.
> > > Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
> > >
> > > Enter below into Wolfram alpha---
> > > -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> > > The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> > > From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> > > It took awhile but I finally presented it the right way for Wolfram.
> > >
> > > Pick any value for n and you will see why n=0--->oo.
> > When -x = -pi in the third quadrant then, to find the the negative square of
> > -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> > quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >
> > The ratio of -y/-x = 4.3007475966...
> > Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> > x^2 = 28.0979250837...
> > y = x^2 - x= 5.3007475966... = 22.797177487...
> > Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
> >
> > The same procedure (added values to a number) will work with any number in
> > the negative -x\-y third quadrant. Then cross checking with the first quadrant
> > x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> > adding 1 to the ratio and then x=r applied to the first quadrant.
> >
> > This is not imaginary but using real numbers in just 2 dimensions depicting
> > the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> > quadrant the parabola is flipped from the up to the down position and then
> > flipped over to the left.
> > Is this the only way to give a square root of a negative number without using
> > imaginary (i)?
> >
> > The math works but the negative squares and square roots are probably not the
> > correct meaning of all this?
> >
> > Any thoughts?
> There is nothing to derive from the math that is imaginary.

On Thursday, July 7, 2022 at 5:42:37 PM UTC-4, Chris M. Thomasson wrote:
> On 7/7/2022 8:56 AM, Dan joyce wrote:
> > On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> >> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> >>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> >>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> >>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> >>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> >>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> >>>>>>>>>>
> >>>>>>>>>> sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>
> >>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> >>>>>>>>>>
> >>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> >>>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> >>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> >>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> >>>>>>>>>> going in the positive and the mirror image going into the negative.
> >>>>>>>>>> Just enter the above equation into Wolfram Alpha using any number.
> >>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the same results.
> >>>>>>>>>>
> >>>>>>>>>> Just having some fun. ;-)!!!
> >>>>>>>>> Check this out:
> >>>>>>>>>
> >>>>>>>>> https://youtu.be/d0vY0CKYhPY
> >>>>>>>>>
> >>>>>>>>> ;^)
> >>>>>>>> Interesting.
> >>>>>>>> The many different crazy places pi will appear.
> >>>>>>>> I just used pi as one of the ---> oo numbers that work in this equation.
> >>>>>>>>
> >>>>>>>> I did this plot in the third quadrant where each new frame was a continuation of
> >>>>>>>> the last frame. So the parabolic curve keeps slightly increasing the distance from the
> >>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> >>>>>>>> reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> >>>>>>>> and y=0. Where x+y=x^2
> >>>>>>>> A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> >>>>>>>> x + y=x^2 from the first quadrant.
> >>>>>>>> That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> >>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> >>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> >>>>>>>> but only equal too -1 in the third quadrant.
> >>>>>>>> Negative integer points of -x\-y in the parabola in the third quadrant --
> >>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> >>>>>>> Explaining this plot in the third quadrant---
> >>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> >>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> >>>>>>>
> >>>>>>> These points on the parabola in the third quadrant of the Cartesian coordinate
> >>>>>>> system start @ y=-0.5 and x=0
> >>>>>>> So the first y=-0.5 is not in the -y calculations below but that part of the
> >>>>>>> parabola that falls only in the third quadrant.
> >>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> >>>>>>> and in it's mirror image flipped state reflex's only that part of the parabola
> >>>>>>> falling in the 3rd quadrant .
> >>>>>>>
> >>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> >>>>>>> the square root of -1 where -x+-y= -1
> >>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> >>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> >>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> >>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> >>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2..8786796565...
> >>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3..6547921201...
> >>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> >>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> >>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> >>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> >>>>>>> ...
> >>>>>>>
> >>>>>>> A certain way to do the squaring and square root function in the third negative
> >>>>>>> quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> >>>>>>> Where n can be any number that will represent the two plotted points
> >>>>>>> on the reversed mirror image of the parabola -x+-y.
> >>>>>>>
> >>>>>>> Just a novel way to express negative values.
> >>>>>> What is interesting is that----
> >>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> >>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> >>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> >>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> >>>>>> This is probably true for all numbers.
> >>>>> I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> >>>>> becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> >>>>> when summed -x+-y = -pi .
> >>>>>
> >>>>> The same with e and any other number.
> >>>> There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> >>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> >>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> >>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> >>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >>>>
> >>>> Dan
> >>> (r)=ratio and (n) = any number.
> >>>
> >>> Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> >>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> >>> quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> >>>
> >>> Neat huh?
> >>>
> >>> Dan
> >> I finally have the proof.
> >> Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
> >>
> >> Enter below into Wolfram alpha---
> >> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> >> The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> >> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> >> It took awhile but I finally presented it the right way for Wolfram.
> >>
> >> Pick any value for n and you will see why n=0--->oo.
> >
> > When -x = -pi in the third quadrant then, to find the the negative square of
> > -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> > quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >
> > The ratio of -y/-x = 4.3007475966...
> > Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> > x^2 = 28.0979250837...
> > y = x^2 - x= 5.3007475966... = 22.797177487...
> > Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
> >
> > The same procedure (added values to a number) will work with any number in
> > the negative -x\-y third quadrant. Then cross checking with the first quadrant
> > x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> > adding 1 to the ratio and then x=r applied to the first quadrant.
> >
> > This is not imaginary but using real numbers in just 2 dimensions depicting
> > the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> > quadrant the parabola is flipped from the up to the down position and then
> > flipped over to the left.
> > Is this the only way to give a square root of a negative number without using
> > imaginary (i)?
> >
> > The math works but the negative squares and square roots are probably not the
> > correct meaning of all this?
> >
> > Any thoughts?
> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> component, then convert back to rectangular form, and we have 0-1i.
> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>
> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> purely real because the imaginary part is zero. ;^)
>
> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>
> This creates the borders of the four quadrants of a unit circle.
>
> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> the point 0-1i.
>
> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>
> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> Keep in mind that the radius of the imaginary unit is one.
>
> With polar form in mind:
>
> 1+0i + PI = -1+0i
>
> Also:
>
> 1+0i + PI/2 = 0+1i = the imaginary unit.

On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
> On 7/7/2022 8:56 AM, Dan joyce wrote:
>> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
>>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
>>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
>>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
>>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
>>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
>>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
>>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
>>>>>>>>> Thomasson wrote:
>>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
>>>>>>>>>>>
>>>>>>>>>>> sqrt(-1) =
>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>>
>>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
>>>>>>>>>>>
>>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
>>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
>>>>>>>>>>> coordinate system
>>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
>>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
>>>>>>>>>>> of the parabola
>>>>>>>>>>> going in the positive and the mirror image going into the
>>>>>>>>>>> negative.
>>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
>>>>>>>>>>> number.
>>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
>>>>>>>>>>> same results.
>>>>>>>>>>>
>>>>>>>>>>> Just having some fun. ;-)!!!
>>>>>>>>>> Check this out:
>>>>>>>>>>
>>>>>>>>>> https://youtu.be/d0vY0CKYhPY
>>>>>>>>>>
>>>>>>>>>> ;^)
>>>>>>>>> Interesting.
>>>>>>>>> The many different crazy places pi will appear.
>>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
>>>>>>>>> equation.
>>>>>>>>>
>>>>>>>>> I did this plot in the third quadrant where each new frame was
>>>>>>>>> a continuation of
>>>>>>>>> the last frame. So the parabolic curve keeps slightly
>>>>>>>>> increasing the distance from the
>>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
>>>>>>>>> exact duplicate of its'
>>>>>>>>> reverse mirror image of the side of the parabola in the first
>>>>>>>>> quadrant starting @ x=1
>>>>>>>>> and y=0. Where x+y=x^2
>>>>>>>>> A whole different calculation is required in the third quadrant
>>>>>>>>> for x + y=x^2 to duplicate
>>>>>>>>> x + y=x^2 from the first quadrant.
>>>>>>>>> That is where the third quadrant value of the sqrt -1 =
>>>>>>>>> ((sqrt6)-2)/2
>>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
>>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
>>>>>>>>> = 2 in the first quadrant.
>>>>>>>>> but only equal too -1 in the third quadrant.
>>>>>>>>> Negative integer points of -x\-y in the parabola in the third
>>>>>>>>> quadrant --
>>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
>>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
>>>>>>>> Explaining this plot in the third quadrant---
>>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
>>>>>>>> the minus quadrant
>>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
>>>>>>>>
>>>>>>>> These points on the parabola in the third quadrant of the
>>>>>>>> Cartesian coordinate
>>>>>>>> system start @ y=-0.5 and x=0
>>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
>>>>>>>> part of the
>>>>>>>> parabola that falls only in the third quadrant.
>>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
>>>>>>>> the first quadrant
>>>>>>>> and in it's mirror image flipped state reflex's only that part
>>>>>>>> of the parabola
>>>>>>>> falling in the 3rd quadrant .
>>>>>>>>
>>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
>>>>>>>> -y=-0.7752551287... -x here represents
>>>>>>>> the square root of -1 where -x+-y= -1
>>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
>>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
>>>>>>>> -1.9243247976...
>>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
>>>>>>>> -2.1291713067...
>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>>> -2.2332969077...
>>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
>>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
>>>>>>>> -2.8786796565...
>>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
>>>>>>>> -3.6547921201...
>>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
>>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
>>>>>>>> -5.2613872124...
>>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
>>>>>>>> -6.0845240525... .
>>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
>>>>>>>> ...
>>>>>>>>
>>>>>>>> A certain way to do the squaring and square root function in the
>>>>>>>> third negative
>>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
>>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
>>>>>>>> Where n can be any number that will represent the two plotted
>>>>>>>> points
>>>>>>>> on the reversed mirror image of the parabola -x+-y.
>>>>>>>>
>>>>>>>> Just a novel way to express negative values.
>>>>>>> What is interesting is that----
>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>> -2.2332969077... summed =pi
>>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
>>>>>>> pi but the ratio applied to
>>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
>>>>>>> 2.458777240...+1= 3.4587772407...
>>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
>>>>>>> same ratio between -x/-y and x/y.
>>>>>>> This is probably true for all numbers.
>>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
>>>>>> 3.4587772407... and this ratio
>>>>>> becomes the new x value in the first quadrant. Giving the same
>>>>>> ratio of -x/-y from the third quadrant that
>>>>>> when summed -x+-y = -pi .
>>>>>>
>>>>>> The same with e and any other number.
>>>>> There is a direct correlation between the first quadrant x\y where
>>>>> x^2 = x + y = x^2 and the third quadrant
>>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
>>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
>>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
>>>>> the ratio =4.4494897427... and this becomes the new x in the first
>>>>> quadrant where x+y=x^2 and the ratio y/x =
>>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
>>>>> subtract 2 from x in the first quadrant
>>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
>>>>> quadrant.
>>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
>>>>>
>>>>> Dan
>>>> (r)=ratio and (n) = any number.
>>>>
>>>> Then for all negative -n in the third quadrant --- -x=((((
>>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
>>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
>>>> the same valued (r) as in the negative third
>>>> quadrant but with a different value for (n) in the first quadrant as
>>>> x + y=((r+1) ^2) or x + y =x^2 =n
>>>>
>>>> Neat huh?
>>>>
>>>> Dan
>>> I finally have the proof.
>>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
>>> with the first positive (x\y) quadrant.
>>>
>>> Enter below into Wolfram alpha---
>>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
>>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
>>> The left side of the equation represents the 3rd quadrant (up too and
>>> including the third (,) above.
>>>  From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
>>> It took awhile but I finally presented it the right way for Wolfram.
>>>
>>> Pick any value for n and you will see why n=0--->oo.
>>
>> When -x = -pi in the third quadrant then, to find the the negative
>> square of
>> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
>> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
>> third
>> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
>>
>> The ratio of -y/-x = 4.3007475966...
>> Apply that to the first quadrant giving x = 4.3007475966... +1 =
>> 5.3007475966...
>> x^2 = 28.0979250837...
>> y = x^2 - x= 5.3007475966... = 22.797177487...
>> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
>> quadrant.
>>
>> The same procedure (added values to a number) will work with any
>> number in
>> the negative -x\-y third quadrant. Then cross checking with the first
>> quadrant
>> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
>> y/x after
>> adding 1 to the ratio and then x=r applied to the first quadrant.
>>
>> This is not imaginary but using real numbers in just 2 dimensions
>> depicting
>> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
>> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
>> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
>> third
>> quadrant the parabola is flipped from the up to the down position and
>> then
>> flipped over to the left.
>> Is this the only way to give a square root of a negative number
>> without using
>> imaginary (i)?
>>
>> The math works but the negative squares and square roots are probably
>> not the
>> correct meaning of all this?
>>
>> Any thoughts?
>
> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> component, then convert back to rectangular form, and we have 0-1i.
> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>
> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> purely real because the imaginary part is zero. ;^)
>
> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>
> This creates the borders of the four quadrants of a unit circle.
>
> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> the point 0-1i.
>
> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>
> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> Keep in mind that the radius of the imaginary unit is one.
>
> With polar form in mind:
>
> 1+0i + PI = -1+0i
>
> Also:
>
> 1+0i + PI/2 = 0+1i = the imaginary unit.

On Saturday, July 9, 2022 at 7:45:18 PM UTC-4, Chris M. Thomasson wrote:
> On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
> > On 7/7/2022 8:56 AM, Dan joyce wrote:
> >> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> >>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> >>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> >>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> >>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> >>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
> >>>>>>>>> Thomasson wrote:
> >>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> >>>>>>>>>>>
> >>>>>>>>>>> sqrt(-1) =
> >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>>
> >>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> >>>>>>>>>>>
> >>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> >>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
> >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
> >>>>>>>>>>> coordinate system
> >>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> >>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
> >>>>>>>>>>> of the parabola
> >>>>>>>>>>> going in the positive and the mirror image going into the
> >>>>>>>>>>> negative.
> >>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
> >>>>>>>>>>> number.
> >>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
> >>>>>>>>>>> same results.
> >>>>>>>>>>>
> >>>>>>>>>>> Just having some fun. ;-)!!!
> >>>>>>>>>> Check this out:
> >>>>>>>>>>
> >>>>>>>>>> https://youtu.be/d0vY0CKYhPY
> >>>>>>>>>>
> >>>>>>>>>> ;^)
> >>>>>>>>> Interesting.
> >>>>>>>>> The many different crazy places pi will appear.
> >>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
> >>>>>>>>> equation.
> >>>>>>>>>
> >>>>>>>>> I did this plot in the third quadrant where each new frame was
> >>>>>>>>> a continuation of
> >>>>>>>>> the last frame. So the parabolic curve keeps slightly
> >>>>>>>>> increasing the distance from the
> >>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
> >>>>>>>>> exact duplicate of its'
> >>>>>>>>> reverse mirror image of the side of the parabola in the first
> >>>>>>>>> quadrant starting @ x=1
> >>>>>>>>> and y=0. Where x+y=x^2
> >>>>>>>>> A whole different calculation is required in the third quadrant
> >>>>>>>>> for x + y=x^2 to duplicate
> >>>>>>>>> x + y=x^2 from the first quadrant.
> >>>>>>>>> That is where the third quadrant value of the sqrt -1 =
> >>>>>>>>> ((sqrt6)-2)/2
> >>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> >>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
> >>>>>>>>> = 2 in the first quadrant.
> >>>>>>>>> but only equal too -1 in the third quadrant.
> >>>>>>>>> Negative integer points of -x\-y in the parabola in the third
> >>>>>>>>> quadrant --
> >>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
> >>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> >>>>>>>> Explaining this plot in the third quadrant---
> >>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
> >>>>>>>> the minus quadrant
> >>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> >>>>>>>>
> >>>>>>>> These points on the parabola in the third quadrant of the
> >>>>>>>> Cartesian coordinate
> >>>>>>>> system start @ y=-0.5 and x=0
> >>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
> >>>>>>>> part of the
> >>>>>>>> parabola that falls only in the third quadrant.
> >>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
> >>>>>>>> the first quadrant
> >>>>>>>> and in it's mirror image flipped state reflex's only that part
> >>>>>>>> of the parabola
> >>>>>>>> falling in the 3rd quadrant .
> >>>>>>>>
> >>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
> >>>>>>>> -y=-0.7752551287... -x here represents
> >>>>>>>> the square root of -1 where -x+-y= -1
> >>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> >>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
> >>>>>>>> -1.9243247976...
> >>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
> >>>>>>>> -2.1291713067...
> >>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> >>>>>>>> -2.2332969077...
> >>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> >>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
> >>>>>>>> -2.8786796565...
> >>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
> >>>>>>>> -3.6547921201...
> >>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> >>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
> >>>>>>>> -5.2613872124...
> >>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
> >>>>>>>> -6.0845240525... .
> >>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> >>>>>>>> ...
> >>>>>>>>
> >>>>>>>> A certain way to do the squaring and square root function in the
> >>>>>>>> third negative
> >>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
> >>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
> >>>>>>>> Where n can be any number that will represent the two plotted
> >>>>>>>> points
> >>>>>>>> on the reversed mirror image of the parabola -x+-y.
> >>>>>>>>
> >>>>>>>> Just a novel way to express negative values.
> >>>>>>> What is interesting is that----
> >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> >>>>>>> -2.2332969077... summed =pi
> >>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
> >>>>>>> pi but the ratio applied to
> >>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
> >>>>>>> 2.458777240...+1= 3.4587772407...
> >>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
> >>>>>>> same ratio between -x/-y and x/y.
> >>>>>>> This is probably true for all numbers.
> >>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
> >>>>>> 3.4587772407... and this ratio
> >>>>>> becomes the new x value in the first quadrant. Giving the same
> >>>>>> ratio of -x/-y from the third quadrant that
> >>>>>> when summed -x+-y = -pi .
> >>>>>>
> >>>>>> The same with e and any other number.
> >>>>> There is a direct correlation between the first quadrant x\y where
> >>>>> x^2 = x + y = x^2 and the third quadrant
> >>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
> >>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
> >>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
> >>>>> the ratio =4.4494897427... and this becomes the new x in the first
> >>>>> quadrant where x+y=x^2 and the ratio y/x =
> >>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
> >>>>> subtract 2 from x in the first quadrant
> >>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
> >>>>> quadrant.
> >>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >>>>>
> >>>>> Dan
> >>>> (r)=ratio and (n) = any number.
> >>>>
> >>>> Then for all negative -n in the third quadrant --- -x=((((
> >>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> >>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
> >>>> the same valued (r) as in the negative third
> >>>> quadrant but with a different value for (n) in the first quadrant as
> >>>> x + y=((r+1) ^2) or x + y =x^2 =n
> >>>>
> >>>> Neat huh?
> >>>>
> >>>> Dan
> >>> I finally have the proof.
> >>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
> >>> with the first positive (x\y) quadrant.
> >>>
> >>> Enter below into Wolfram alpha---
> >>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
> >>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
> >>> The left side of the equation represents the 3rd quadrant (up too and
> >>> including the third (,) above.
> >>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> >>> It took awhile but I finally presented it the right way for Wolfram.
> >>>
> >>> Pick any value for n and you will see why n=0--->oo.
> >>
> >> When -x = -pi in the third quadrant then, to find the the negative
> >> square of
> >> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> >> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
> >> third
> >> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >>
> >> The ratio of -y/-x = 4.3007475966...
> >> Apply that to the first quadrant giving x = 4.3007475966... +1 =
> >> 5.3007475966...
> >> x^2 = 28.0979250837...
> >> y = x^2 - x= 5.3007475966... = 22.797177487...
> >> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
> >> quadrant.
> >>
> >> The same procedure (added values to a number) will work with any
> >> number in
> >> the negative -x\-y third quadrant. Then cross checking with the first
> >> quadrant
> >> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
> >> y/x after
> >> adding 1 to the ratio and then x=r applied to the first quadrant.
> >>
> >> This is not imaginary but using real numbers in just 2 dimensions
> >> depicting
> >> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> >> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> >> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
> >> third
> >> quadrant the parabola is flipped from the up to the down position and
> >> then
> >> flipped over to the left.
> >> Is this the only way to give a square root of a negative number
> >> without using
> >> imaginary (i)?
> >>
> >> The math works but the negative squares and square roots are probably
> >> not the
> >> correct meaning of all this?
> >>
> >> Any thoughts?
> >
> > Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> > component, then convert back to rectangular form, and we have 0-1i.
> > Adding PI to the polar form of 0-1i brings us right back to 0+1i.
> >
> > So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> > purely real because the imaginary part is zero. ;^)
> >
> > Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
> >
> > This creates the borders of the four quadrants of a unit circle.
> >
> > Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> > the point 0-1i.
> >
> > 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
> >
> > For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> > Keep in mind that the radius of the imaginary unit is one.
> >
> > With polar form in mind:
> >
> > 1+0i + PI = -1+0i
> >
> > Also:
> >
> > 1+0i + PI/2 = 0+1i = the imaginary unit.
> Argh!
>
> That has to be a mistake of mine! 0+1i plus PI = -1+0i. So, adding PI +
> PI / 2 to 0+1i has to be 0-1i... Right?

On Sunday, July 10, 2022 at 12:53:24 PM UTC-4, djoyce099 wrote:
> On Saturday, July 9, 2022 at 7:45:18 PM UTC-4, Chris M. Thomasson wrote:
> > On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
> > > On 7/7/2022 8:56 AM, Dan joyce wrote:
> > >> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> > >>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> > >>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > >>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > >>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > >>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > >>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > >>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
> > >>>>>>>>> Thomasson wrote:
> > >>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> > >>>>>>>>>>>
> > >>>>>>>>>>> sqrt(-1) =
> > >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> > >>>>>>>>>>>
> > >>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > >>>>>>>>>>>
> > >>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> > >>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
> > >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> > >>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
> > >>>>>>>>>>> coordinate system
> > >>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > >>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
> > >>>>>>>>>>> of the parabola
> > >>>>>>>>>>> going in the positive and the mirror image going into the
> > >>>>>>>>>>> negative.
> > >>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
> > >>>>>>>>>>> number.
> > >>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
> > >>>>>>>>>>> same results.
> > >>>>>>>>>>>
> > >>>>>>>>>>> Just having some fun. ;-)!!!
> > >>>>>>>>>> Check this out:
> > >>>>>>>>>>
> > >>>>>>>>>> https://youtu.be/d0vY0CKYhPY
> > >>>>>>>>>>
> > >>>>>>>>>> ;^)
> > >>>>>>>>> Interesting.
> > >>>>>>>>> The many different crazy places pi will appear.
> > >>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
> > >>>>>>>>> equation.
> > >>>>>>>>>
> > >>>>>>>>> I did this plot in the third quadrant where each new frame was
> > >>>>>>>>> a continuation of
> > >>>>>>>>> the last frame. So the parabolic curve keeps slightly
> > >>>>>>>>> increasing the distance from the
> > >>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
> > >>>>>>>>> exact duplicate of its'
> > >>>>>>>>> reverse mirror image of the side of the parabola in the first
> > >>>>>>>>> quadrant starting @ x=1
> > >>>>>>>>> and y=0. Where x+y=x^2
> > >>>>>>>>> A whole different calculation is required in the third quadrant
> > >>>>>>>>> for x + y=x^2 to duplicate
> > >>>>>>>>> x + y=x^2 from the first quadrant.
> > >>>>>>>>> That is where the third quadrant value of the sqrt -1 =
> > >>>>>>>>> ((sqrt6)-2)/2
> > >>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> > >>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
> > >>>>>>>>> = 2 in the first quadrant.
> > >>>>>>>>> but only equal too -1 in the third quadrant.
> > >>>>>>>>> Negative integer points of -x\-y in the parabola in the third
> > >>>>>>>>> quadrant --
> > >>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
> > >>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > >>>>>>>> Explaining this plot in the third quadrant---
> > >>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
> > >>>>>>>> the minus quadrant
> > >>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> > >>>>>>>>
> > >>>>>>>> These points on the parabola in the third quadrant of the
> > >>>>>>>> Cartesian coordinate
> > >>>>>>>> system start @ y=-0.5 and x=0
> > >>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
> > >>>>>>>> part of the
> > >>>>>>>> parabola that falls only in the third quadrant.
> > >>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
> > >>>>>>>> the first quadrant
> > >>>>>>>> and in it's mirror image flipped state reflex's only that part
> > >>>>>>>> of the parabola
> > >>>>>>>> falling in the 3rd quadrant .
> > >>>>>>>>
> > >>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
> > >>>>>>>> -y=-0.7752551287... -x here represents
> > >>>>>>>> the square root of -1 where -x+-y= -1
> > >>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > >>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
> > >>>>>>>> -1.9243247976...
> > >>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
> > >>>>>>>> -2.1291713067...
> > >>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> > >>>>>>>> -2.2332969077...
> > >>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > >>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
> > >>>>>>>> -2.8786796565...
> > >>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
> > >>>>>>>> -3.6547921201...
> > >>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > >>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
> > >>>>>>>> -5.2613872124...
> > >>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
> > >>>>>>>> -6.0845240525... .
> > >>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > >>>>>>>> ...
> > >>>>>>>>
> > >>>>>>>> A certain way to do the squaring and square root function in the
> > >>>>>>>> third negative
> > >>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
> > >>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
> > >>>>>>>> Where n can be any number that will represent the two plotted
> > >>>>>>>> points
> > >>>>>>>> on the reversed mirror image of the parabola -x+-y.
> > >>>>>>>>
> > >>>>>>>> Just a novel way to express negative values.
> > >>>>>>> What is interesting is that----
> > >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> > >>>>>>> -2.2332969077... summed =pi
> > >>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
> > >>>>>>> pi but the ratio applied to
> > >>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
> > >>>>>>> 2.458777240...+1= 3.4587772407...
> > >>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
> > >>>>>>> same ratio between -x/-y and x/y.
> > >>>>>>> This is probably true for all numbers.
> > >>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
> > >>>>>> 3.4587772407... and this ratio
> > >>>>>> becomes the new x value in the first quadrant. Giving the same
> > >>>>>> ratio of -x/-y from the third quadrant that
> > >>>>>> when summed -x+-y = -pi .
> > >>>>>>
> > >>>>>> The same with e and any other number.
> > >>>>> There is a direct correlation between the first quadrant x\y where
> > >>>>> x^2 = x + y = x^2 and the third quadrant
> > >>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
> > >>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
> > >>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
> > >>>>> the ratio =4.4494897427... and this becomes the new x in the first
> > >>>>> quadrant where x+y=x^2 and the ratio y/x =
> > >>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
> > >>>>> subtract 2 from x in the first quadrant
> > >>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
> > >>>>> quadrant.
> > >>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> > >>>>>
> > >>>>> Dan
> > >>>> (r)=ratio and (n) = any number.
> > >>>>
> > >>>> Then for all negative -n in the third quadrant --- -x=((((
> > >>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> > >>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
> > >>>> the same valued (r) as in the negative third
> > >>>> quadrant but with a different value for (n) in the first quadrant as
> > >>>> x + y=((r+1) ^2) or x + y =x^2 =n
> > >>>>
> > >>>> Neat huh?
> > >>>>
> > >>>> Dan
> > >>> I finally have the proof.
> > >>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
> > >>> with the first positive (x\y) quadrant.
> > >>>
> > >>> Enter below into Wolfram alpha---
> > >>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
> > >>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
> > >>> The left side of the equation represents the 3rd quadrant (up too and
> > >>> including the third (,) above.
> > >>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> > >>> It took awhile but I finally presented it the right way for Wolfram.
> > >>>
> > >>> Pick any value for n and you will see why n=0--->oo.
> > >>
> > >> When -x = -pi in the third quadrant then, to find the the negative
> > >> square of
> > >> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > >> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
> > >> third
> > >> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> > >>
> > >> The ratio of -y/-x = 4.3007475966...
> > >> Apply that to the first quadrant giving x = 4.3007475966... +1 =
> > >> 5.3007475966...
> > >> x^2 = 28.0979250837...
> > >> y = x^2 - x= 5.3007475966... = 22.797177487...
> > >> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
> > >> quadrant.
> > >>
> > >> The same procedure (added values to a number) will work with any
> > >> number in
> > >> the negative -x\-y third quadrant. Then cross checking with the first
> > >> quadrant
> > >> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
> > >> y/x after
> > >> adding 1 to the ratio and then x=r applied to the first quadrant.
> > >>
> > >> This is not imaginary but using real numbers in just 2 dimensions
> > >> depicting
> > >> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > >> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > >> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
> > >> third
> > >> quadrant the parabola is flipped from the up to the down position and
> > >> then
> > >> flipped over to the left.
> > >> Is this the only way to give a square root of a negative number
> > >> without using
> > >> imaginary (i)?
> > >>
> > >> The math works but the negative squares and square roots are probably
> > >> not the
> > >> correct meaning of all this?
> > >>
> > >> Any thoughts?
> > >
> > > Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> > > component, then convert back to rectangular form, and we have 0-1i.
> > > Adding PI to the polar form of 0-1i brings us right back to 0+1i.
> > >
> > > So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> > > purely real because the imaginary part is zero. ;^)
> > >
> > > Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
> > >
> > > This creates the borders of the four quadrants of a unit circle.
> > >
> > > Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> > > the point 0-1i.
> > >
> > > 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
> > >
> > > For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> > > Keep in mind that the radius of the imaginary unit is one.
> > >
> > > With polar form in mind:
> > >
> > > 1+0i + PI = -1+0i
> > >
> > > Also:
> > >
> > > 1+0i + PI/2 = 0+1i = the imaginary unit.
> > Argh!
> >
> > That has to be a mistake of mine! 0+1i plus PI = -1+0i. So, adding PI +
> > PI / 2 to 0+1i has to be 0-1i... Right?
> The only thing I came up with is --- 1+0i + pi^ei = 0+1i

On Sunday, July 10, 2022 at 1:17:53 PM UTC-4, djoyce099 wrote:
> On Sunday, July 10, 2022 at 12:53:24 PM UTC-4, djoyce099 wrote:
> > On Saturday, July 9, 2022 at 7:45:18 PM UTC-4, Chris M. Thomasson wrote:
> > > On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
> > > > On 7/7/2022 8:56 AM, Dan joyce wrote:
> > > >> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> > > >>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> > > >>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> > > >>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> > > >>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> > > >>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> > > >>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> > > >>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
> > > >>>>>>>>> Thomasson wrote:
> > > >>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> sqrt(-1) =
> > > >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> > > >>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
> > > >>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> > > >>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
> > > >>>>>>>>>>> coordinate system
> > > >>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> > > >>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
> > > >>>>>>>>>>> of the parabola
> > > >>>>>>>>>>> going in the positive and the mirror image going into the
> > > >>>>>>>>>>> negative.
> > > >>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
> > > >>>>>>>>>>> number.
> > > >>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
> > > >>>>>>>>>>> same results.
> > > >>>>>>>>>>>
> > > >>>>>>>>>>> Just having some fun. ;-)!!!
> > > >>>>>>>>>> Check this out:
> > > >>>>>>>>>>
> > > >>>>>>>>>> https://youtu.be/d0vY0CKYhPY
> > > >>>>>>>>>>
> > > >>>>>>>>>> ;^)
> > > >>>>>>>>> Interesting.
> > > >>>>>>>>> The many different crazy places pi will appear.
> > > >>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
> > > >>>>>>>>> equation.
> > > >>>>>>>>>
> > > >>>>>>>>> I did this plot in the third quadrant where each new frame was
> > > >>>>>>>>> a continuation of
> > > >>>>>>>>> the last frame. So the parabolic curve keeps slightly
> > > >>>>>>>>> increasing the distance from the
> > > >>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
> > > >>>>>>>>> exact duplicate of its'
> > > >>>>>>>>> reverse mirror image of the side of the parabola in the first
> > > >>>>>>>>> quadrant starting @ x=1
> > > >>>>>>>>> and y=0. Where x+y=x^2
> > > >>>>>>>>> A whole different calculation is required in the third quadrant
> > > >>>>>>>>> for x + y=x^2 to duplicate
> > > >>>>>>>>> x + y=x^2 from the first quadrant.
> > > >>>>>>>>> That is where the third quadrant value of the sqrt -1 =
> > > >>>>>>>>> ((sqrt6)-2)/2
> > > >>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> > > >>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
> > > >>>>>>>>> = 2 in the first quadrant.
> > > >>>>>>>>> but only equal too -1 in the third quadrant.
> > > >>>>>>>>> Negative integer points of -x\-y in the parabola in the third
> > > >>>>>>>>> quadrant --
> > > >>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
> > > >>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> > > >>>>>>>> Explaining this plot in the third quadrant---
> > > >>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
> > > >>>>>>>> the minus quadrant
> > > >>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> > > >>>>>>>>
> > > >>>>>>>> These points on the parabola in the third quadrant of the
> > > >>>>>>>> Cartesian coordinate
> > > >>>>>>>> system start @ y=-0.5 and x=0
> > > >>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
> > > >>>>>>>> part of the
> > > >>>>>>>> parabola that falls only in the third quadrant.
> > > >>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
> > > >>>>>>>> the first quadrant
> > > >>>>>>>> and in it's mirror image flipped state reflex's only that part
> > > >>>>>>>> of the parabola
> > > >>>>>>>> falling in the 3rd quadrant .
> > > >>>>>>>>
> > > >>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
> > > >>>>>>>> -y=-0.7752551287... -x here represents
> > > >>>>>>>> the square root of -1 where -x+-y= -1
> > > >>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> > > >>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
> > > >>>>>>>> -1.9243247976...
> > > >>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
> > > >>>>>>>> -2.1291713067...
> > > >>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> > > >>>>>>>> -2.2332969077...
> > > >>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> > > >>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
> > > >>>>>>>> -2.8786796565...
> > > >>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
> > > >>>>>>>> -3.6547921201...
> > > >>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> > > >>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
> > > >>>>>>>> -5.2613872124...
> > > >>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
> > > >>>>>>>> -6.0845240525... .
> > > >>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> > > >>>>>>>> ...
> > > >>>>>>>>
> > > >>>>>>>> A certain way to do the squaring and square root function in the
> > > >>>>>>>> third negative
> > > >>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
> > > >>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
> > > >>>>>>>> Where n can be any number that will represent the two plotted
> > > >>>>>>>> points
> > > >>>>>>>> on the reversed mirror image of the parabola -x+-y.
> > > >>>>>>>>
> > > >>>>>>>> Just a novel way to express negative values.
> > > >>>>>>> What is interesting is that----
> > > >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> > > >>>>>>> -2.2332969077... summed =pi
> > > >>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
> > > >>>>>>> pi but the ratio applied to
> > > >>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
> > > >>>>>>> 2.458777240...+1= 3.4587772407...
> > > >>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
> > > >>>>>>> same ratio between -x/-y and x/y.
> > > >>>>>>> This is probably true for all numbers.
> > > >>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
> > > >>>>>> 3.4587772407... and this ratio
> > > >>>>>> becomes the new x value in the first quadrant. Giving the same
> > > >>>>>> ratio of -x/-y from the third quadrant that
> > > >>>>>> when summed -x+-y = -pi .
> > > >>>>>>
> > > >>>>>> The same with e and any other number.
> > > >>>>> There is a direct correlation between the first quadrant x\y where
> > > >>>>> x^2 = x + y = x^2 and the third quadrant
> > > >>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
> > > >>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
> > > >>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
> > > >>>>> the ratio =4.4494897427... and this becomes the new x in the first
> > > >>>>> quadrant where x+y=x^2 and the ratio y/x =
> > > >>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
> > > >>>>> subtract 2 from x in the first quadrant
> > > >>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
> > > >>>>> quadrant.
> > > >>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> > > >>>>>
> > > >>>>> Dan
> > > >>>> (r)=ratio and (n) = any number.
> > > >>>>
> > > >>>> Then for all negative -n in the third quadrant --- -x=((((
> > > >>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> > > >>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
> > > >>>> the same valued (r) as in the negative third
> > > >>>> quadrant but with a different value for (n) in the first quadrant as
> > > >>>> x + y=((r+1) ^2) or x + y =x^2 =n
> > > >>>>
> > > >>>> Neat huh?
> > > >>>>
> > > >>>> Dan
> > > >>> I finally have the proof.
> > > >>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
> > > >>> with the first positive (x\y) quadrant.
> > > >>>
> > > >>> Enter below into Wolfram alpha---
> > > >>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
> > > >>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
> > > >>> The left side of the equation represents the 3rd quadrant (up too and
> > > >>> including the third (,) above.
> > > >>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> > > >>> It took awhile but I finally presented it the right way for Wolfram.
> > > >>>
> > > >>> Pick any value for n and you will see why n=0--->oo.
> > > >>
> > > >> When -x = -pi in the third quadrant then, to find the the negative
> > > >> square of
> > > >> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > > >> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
> > > >> third
> > > >> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> > > >>
> > > >> The ratio of -y/-x = 4.3007475966...
> > > >> Apply that to the first quadrant giving x = 4.3007475966... +1 =
> > > >> 5.3007475966...
> > > >> x^2 = 28.0979250837...
> > > >> y = x^2 - x= 5.3007475966... = 22.797177487...
> > > >> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
> > > >> quadrant.
> > > >>
> > > >> The same procedure (added values to a number) will work with any
> > > >> number in
> > > >> the negative -x\-y third quadrant. Then cross checking with the first
> > > >> quadrant
> > > >> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
> > > >> y/x after
> > > >> adding 1 to the ratio and then x=r applied to the first quadrant.
> > > >>
> > > >> This is not imaginary but using real numbers in just 2 dimensions
> > > >> depicting
> > > >> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > > >> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > > >> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
> > > >> third
> > > >> quadrant the parabola is flipped from the up to the down position and
> > > >> then
> > > >> flipped over to the left.
> > > >> Is this the only way to give a square root of a negative number
> > > >> without using
> > > >> imaginary (i)?
> > > >>
> > > >> The math works but the negative squares and square roots are probably
> > > >> not the
> > > >> correct meaning of all this?
> > > >>
> > > >> Any thoughts?
> > > >
> > > > Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> > > > component, then convert back to rectangular form, and we have 0-1i.
> > > > Adding PI to the polar form of 0-1i brings us right back to 0+1i.
> > > >
> > > > So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> > > > purely real because the imaginary part is zero. ;^)
> > > >
> > > > Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
> > > >
> > > > This creates the borders of the four quadrants of a unit circle.
> > > >
> > > > Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> > > > the point 0-1i.
> > > >
> > > > 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
> > > >
> > > > For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> > > > Keep in mind that the radius of the imaginary unit is one.
> > > >
> > > > With polar form in mind:
> > > >
> > > > 1+0i + PI = -1+0i
> > > >
> > > > Also:
> > > >
> > > > 1+0i + PI/2 = 0+1i = the imaginary unit.
> > > Argh!
> > >
> > > That has to be a mistake of mine! 0+1i plus PI = -1+0i. So, adding PI +
> > > PI / 2 to 0+1i has to be 0-1i... Right?
> > The only thing I came up with is --- 1+0i + pi^ei = 0+1i
> I would guess it is logical when e^pi(i)= -1 and then reversing the two -- pi^ei = 1
> I am probably wrong because Iam' not into the imaginary (i) but an interesting question.

On Thursday, July 7, 2022 at 2:42:37 PM UTC-7, Chris M. Thomasson wrote:
> On 7/7/2022 8:56 AM, Dan joyce wrote:
> > On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> >> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> >>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> >>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> >>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> >>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> >>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M. Thomasson wrote:
> >>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> >>>>>>>>>>
> >>>>>>>>>> sqrt(-1) = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>
> >>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> >>>>>>>>>>
> >>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> >>>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian coordinate system
> >>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> >>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part of the parabola
> >>>>>>>>>> going in the positive and the mirror image going into the negative.
> >>>>>>>>>> Just enter the above equation into Wolfram Alpha using any number.
> >>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the same results.
> >>>>>>>>>>
> >>>>>>>>>> Just having some fun. ;-)!!!
> >>>>>>>>> Check this out:
> >>>>>>>>>
> >>>>>>>>> https://youtu.be/d0vY0CKYhPY
> >>>>>>>>>
> >>>>>>>>> ;^)
> >>>>>>>> Interesting.
> >>>>>>>> The many different crazy places pi will appear.
> >>>>>>>> I just used pi as one of the ---> oo numbers that work in this equation.
> >>>>>>>>
> >>>>>>>> I did this plot in the third quadrant where each new frame was a continuation of
> >>>>>>>> the last frame. So the parabolic curve keeps slightly increasing the distance from the
> >>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An exact duplicate of its'
> >>>>>>>> reverse mirror image of the side of the parabola in the first quadrant starting @ x=1
> >>>>>>>> and y=0. Where x+y=x^2
> >>>>>>>> A whole different calculation is required in the third quadrant for x + y=x^2 to duplicate
> >>>>>>>> x + y=x^2 from the first quadrant.
> >>>>>>>> That is where the third quadrant value of the sqrt -1 = ((sqrt6)-2)/2
> >>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> >>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2 = 2 in the first quadrant.
> >>>>>>>> but only equal too -1 in the third quadrant.
> >>>>>>>> Negative integer points of -x\-y in the parabola in the third quadrant --
> >>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 , -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> >>>>>>> Explaining this plot in the third quadrant---
> >>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is the minus quadrant
> >>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> >>>>>>>
> >>>>>>> These points on the parabola in the third quadrant of the Cartesian coordinate
> >>>>>>> system start @ y=-0.5 and x=0
> >>>>>>> So the first y=-0.5 is not in the -y calculations below but that part of the
> >>>>>>> parabola that falls only in the third quadrant.
> >>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in the first quadrant
> >>>>>>> and in it's mirror image flipped state reflex's only that part of the parabola
> >>>>>>> falling in the 3rd quadrant .
> >>>>>>>
> >>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then -y=-0.7752551287... -x here represents
> >>>>>>> the square root of -1 where -x+-y= -1
> >>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> >>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y= -1.9243247976...
> >>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y= -2.1291713067...
> >>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077...
> >>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> >>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y= -2..8786796565...
> >>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y= -3..6547921201...
> >>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> >>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y= -5.2613872124...
> >>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y= -6.0845240525... .
> >>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> >>>>>>> ...
> >>>>>>>
> >>>>>>> A certain way to do the squaring and square root function in the third negative
> >>>>>>> quadrant where -x+-y= (-x^2) only by a special formula ((((sqrt(n*4+2))-2)/2)*-1 .
> >>>>>>> Where n can be any number that will represent the two plotted points
> >>>>>>> on the reversed mirror image of the parabola -x+-y.
> >>>>>>>
> >>>>>>> Just a novel way to express negative values.
> >>>>>> What is interesting is that----
> >>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y= -2.2332969077... summed =pi
> >>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed = pi but the ratio applied to
> >>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio 2.458777240...+1= 3.4587772407...
> >>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the same ratio between -x/-y and x/y.
> >>>>>> This is probably true for all numbers.
> >>>>> I should have stated, add 1 to the above ratio 2.458777240...+1= 3.4587772407... and this ratio
> >>>>> becomes the new x value in the first quadrant. Giving the same ratio of -x/-y from the third quadrant that
> >>>>> when summed -x+-y = -pi .
> >>>>>
> >>>>> The same with e and any other number.
> >>>> There is a direct correlation between the first quadrant x\y where x^2 = x + y = x^2 and the third quadrant
> >>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x= (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 = -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to the ratio =4.4494897427... and this becomes the new x in the first quadrant where x+y=x^2 and the ratio y/x =
> >>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also subtract 2 from x in the first quadrant
> >>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third quadrant.
> >>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >>>>
> >>>> Dan
> >>> (r)=ratio and (n) = any number.
> >>>
> >>> Then for all negative -n in the third quadrant --- -x=(((( sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> >>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r the same valued (r) as in the negative third
> >>> quadrant but with a different value for (n) in the first quadrant as x + y=((r+1) ^2) or x + y =x^2 =n
> >>>
> >>> Neat huh?
> >>>
> >>> Dan
> >> I finally have the proof.
> >> Joining the full negative Cartesian coordinate third quadrant (-x\-y) with the first positive (x\y) quadrant.
> >>
> >> Enter below into Wolfram alpha---
> >> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x, x=r+1,x+y=x^2,y/x=r, n=0--->oo
> >> The left side of the equation represents the 3rd quadrant (up too and including the third (,) above.
> >> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> >> It took awhile but I finally presented it the right way for Wolfram.
> >>
> >> Pick any value for n and you will see why n=0--->oo.
> >
> > When -x = -pi in the third quadrant then, to find the the negative square of
> > -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> > To check -pi^2 from above by finding the negative sqrt of -pi^2 in the third
> > quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >
> > The ratio of -y/-x = 4.3007475966...
> > Apply that to the first quadrant giving x = 4.3007475966... +1 = 5.3007475966...
> > x^2 = 28.0979250837...
> > y = x^2 - x= 5.3007475966... = 22.797177487...
> > Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third quadrant.
> >
> > The same procedure (added values to a number) will work with any number in
> > the negative -x\-y third quadrant. Then cross checking with the first quadrant
> > x\y of the Cartesian coordinate system matching the ratio of -y/-x and y/x after
> > adding 1 to the ratio and then x=r applied to the first quadrant.
> >
> > This is not imaginary but using real numbers in just 2 dimensions depicting
> > the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> > (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> > starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the third
> > quadrant the parabola is flipped from the up to the down position and then
> > flipped over to the left.
> > Is this the only way to give a square root of a negative number without using
> > imaginary (i)?
> >
> > The math works but the negative squares and square roots are probably not the
> > correct meaning of all this?
> >
> > Any thoughts?
> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> component, then convert back to rectangular form, and we have 0-1i.
> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>
> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> purely real because the imaginary part is zero. ;^)
>
> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>
> This creates the borders of the four quadrants of a unit circle.
>
> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> the point 0-1i.
>
> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>
> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> Keep in mind that the radius of the imaginary unit is one.
>
> With polar form in mind:
>
> 1+0i + PI = -1+0i
>
> Also:
>
> 1+0i + PI/2 = 0+1i = the imaginary unit.

On 7/9/2022 4:45 PM, Chris M. Thomasson wrote:
> On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
>> On 7/7/2022 8:56 AM, Dan joyce wrote:
>>> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
>>>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
>>>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
>>>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
>>>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
>>>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
>>>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
>>>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
>>>>>>>>>>>>
>>>>>>>>>>>> sqrt(-1) =
>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>>>
>>>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
>>>>>>>>>>>>
>>>>>>>>>>>> Where the sqrt of -1 is the second half of the equation
>>>>>>>>>>>> above --
>>>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
>>>>>>>>>>>> coordinate system
>>>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
>>>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25
>>>>>>>>>>>> part of the parabola
>>>>>>>>>>>> going in the positive and the mirror image going into the
>>>>>>>>>>>> negative.
>>>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
>>>>>>>>>>>> number.
>>>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving
>>>>>>>>>>>> the same results.
>>>>>>>>>>>>
>>>>>>>>>>>> Just having some fun. ;-)!!!
>>>>>>>>>>> Check this out:
>>>>>>>>>>>
>>>>>>>>>>> https://youtu.be/d0vY0CKYhPY
>>>>>>>>>>>
>>>>>>>>>>> ;^)
>>>>>>>>>> Interesting.
>>>>>>>>>> The many different crazy places pi will appear.
>>>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
>>>>>>>>>> equation.
>>>>>>>>>>
>>>>>>>>>> I did this plot in the third quadrant where each new frame was
>>>>>>>>>> a continuation of
>>>>>>>>>> the last frame. So the parabolic curve keeps slightly
>>>>>>>>>> increasing the distance from the
>>>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
>>>>>>>>>> exact duplicate of its'
>>>>>>>>>> reverse mirror image of the side of the parabola in the first
>>>>>>>>>> quadrant starting @ x=1
>>>>>>>>>> and y=0. Where x+y=x^2
>>>>>>>>>> A whole different calculation is required in the third
>>>>>>>>>> quadrant for x + y=x^2 to duplicate
>>>>>>>>>> x + y=x^2 from the first quadrant.
>>>>>>>>>> That is where the third quadrant value of the sqrt -1 =
>>>>>>>>>> ((sqrt6)-2)/2
>>>>>>>>>> Duplicating the same part of the parabola in the first
>>>>>>>>>> quadrant --
>>>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
>>>>>>>>>> = 2 in the first quadrant.
>>>>>>>>>> but only equal too -1 in the third quadrant.
>>>>>>>>>> Negative integer points of -x\-y in the parabola in the third
>>>>>>>>>> quadrant --
>>>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
>>>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
>>>>>>>>> Explaining this plot in the third quadrant---
>>>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y
>>>>>>>>> is the minus quadrant
>>>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
>>>>>>>>>
>>>>>>>>> These points on the parabola in the third quadrant of the
>>>>>>>>> Cartesian coordinate
>>>>>>>>> system start @ y=-0.5 and x=0
>>>>>>>>> So the first y=-0.5 is not in the -y calculations below but
>>>>>>>>> that part of the
>>>>>>>>> parabola that falls only in the third quadrant.
>>>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
>>>>>>>>> the first quadrant
>>>>>>>>> and in it's mirror image flipped state reflex's only that part
>>>>>>>>> of the parabola
>>>>>>>>> falling in the 3rd quadrant .
>>>>>>>>>
>>>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
>>>>>>>>> -y=-0.7752551287... -x here represents
>>>>>>>>> the square root of -1 where -x+-y= -1
>>>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y=
>>>>>>>>> -1.41886117...
>>>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
>>>>>>>>> -1.9243247976...
>>>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
>>>>>>>>> -2.1291713067...
>>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>>>> -2.2332969077...
>>>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
>>>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
>>>>>>>>> -2.8786796565...
>>>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
>>>>>>>>> -3.6547921201...
>>>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y=
>>>>>>>>> -4.4504902433
>>>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
>>>>>>>>> -5.2613872124...
>>>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
>>>>>>>>> -6.0845240525... .
>>>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
>>>>>>>>> ...
>>>>>>>>>
>>>>>>>>> A certain way to do the squaring and square root function in
>>>>>>>>> the third negative
>>>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
>>>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
>>>>>>>>> Where n can be any number that will represent the two plotted
>>>>>>>>> points
>>>>>>>>> on the reversed mirror image of the parabola -x+-y.
>>>>>>>>>
>>>>>>>>> Just a novel way to express negative values.
>>>>>>>> What is interesting is that----
>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>>> -2.2332969077... summed =pi
>>>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed
>>>>>>>> = pi but the ratio applied to
>>>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
>>>>>>>> 2.458777240...+1= 3.4587772407...
>>>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
>>>>>>>> same ratio between -x/-y and x/y.
>>>>>>>> This is probably true for all numbers.
>>>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
>>>>>>> 3.4587772407... and this ratio
>>>>>>> becomes the new x value in the first quadrant. Giving the same
>>>>>>> ratio of -x/-y from the third quadrant that
>>>>>>> when summed -x+-y = -pi .
>>>>>>>
>>>>>>> The same with e and any other number.
>>>>>> There is a direct correlation between the first quadrant x\y where
>>>>>> x^2 = x + y = x^2 and the third quadrant
>>>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
>>>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
>>>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
>>>>>> the ratio =4.4494897427... and this becomes the new x in the first
>>>>>> quadrant where x+y=x^2 and the ratio y/x =
>>>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
>>>>>> subtract 2 from x in the first quadrant
>>>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
>>>>>> quadrant.
>>>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
>>>>>>
>>>>>> Dan
>>>>> (r)=ratio and (n) = any number.
>>>>>
>>>>> Then for all negative -n in the third quadrant --- -x=((((
>>>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
>>>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
>>>>> the same valued (r) as in the negative third
>>>>> quadrant but with a different value for (n) in the first quadrant
>>>>> as x + y=((r+1) ^2) or x + y =x^2 =n
>>>>>
>>>>> Neat huh?
>>>>>
>>>>> Dan
>>>> I finally have the proof.
>>>> Joining the full negative Cartesian coordinate third quadrant
>>>> (-x\-y) with the first positive (x\y) quadrant.
>>>>
>>>> Enter below into Wolfram alpha---
>>>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
>>>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
>>>> The left side of the equation represents the 3rd quadrant (up too
>>>> and including the third (,) above.
>>>>  From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
>>>> It took awhile but I finally presented it the right way for Wolfram.
>>>>
>>>> Pick any value for n and you will see why n=0--->oo.
>>>
>>> When -x = -pi in the third quadrant then, to find the the negative
>>> square of
>>> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
>>> To check -pi^2 from above by finding the negative sqrt of -pi^2 in
>>> the third
>>> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
>>>
>>> The ratio of -y/-x = 4.3007475966...
>>> Apply that to the first quadrant giving x = 4.3007475966... +1 =
>>> 5.3007475966...
>>> x^2 = 28.0979250837...
>>> y = x^2 - x= 5.3007475966... = 22.797177487...
>>> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
>>> quadrant.
>>>
>>> The same procedure (added values to a number) will work with any
>>> number in
>>> the negative -x\-y third quadrant. Then cross checking with the first
>>> quadrant
>>> x\y of the Cartesian coordinate system matching the ratio of -y/-x
>>> and y/x after
>>> adding 1 to the ratio and then x=r applied to the first quadrant.
>>>
>>> This is not imaginary but using real numbers in just 2 dimensions
>>> depicting
>>> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
>>> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
>>> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
>>> third
>>> quadrant the parabola is flipped from the up to the down position and
>>> then
>>> flipped over to the left.
>>> Is this the only way to give a square root of a negative number
>>> without using
>>> imaginary (i)?
>>>
>>> The math works but the negative squares and square roots are probably
>>> not the
>>> correct meaning of all this?
>>>
>>> Any thoughts?
>>
>> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
>> component, then convert back to rectangular form, and we have 0-1i.
>> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>>
>> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that
>> is purely real because the imaginary part is zero. ;^)
>>
>> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>>
>> This creates the borders of the four quadrants of a unit circle.
>>
>> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can
>> plot the point 0-1i.
>>
>> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>>
>> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
>> Keep in mind that the radius of the imaginary unit is one.
>>
>> With polar form in mind:
>>
>> 1+0i + PI = -1+0i
>>
>> Also:
>>
>> 1+0i + PI/2 = 0+1i = the imaginary unit.

On 7/10/2022 10:53 AM, djoyce099 wrote:
> On Sunday, July 10, 2022 at 1:17:53 PM UTC-4, djoyce099 wrote:
>> On Sunday, July 10, 2022 at 12:53:24 PM UTC-4, djoyce099 wrote:
>>> On Saturday, July 9, 2022 at 7:45:18 PM UTC-4, Chris M. Thomasson wrote:
>>>> On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
>>>>> On 7/7/2022 8:56 AM, Dan joyce wrote:
>>>>>> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
>>>>>>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
>>>>>>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
>>>>>>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
>>>>>>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
>>>>>>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
>>>>>>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
>>>>>>>>>>>>> Thomasson wrote:
>>>>>>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> sqrt(-1) =
>>>>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
>>>>>>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
>>>>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
>>>>>>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
>>>>>>>>>>>>>>> coordinate system
>>>>>>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
>>>>>>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
>>>>>>>>>>>>>>> of the parabola
>>>>>>>>>>>>>>> going in the positive and the mirror image going into the
>>>>>>>>>>>>>>> negative.
>>>>>>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
>>>>>>>>>>>>>>> number.
>>>>>>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
>>>>>>>>>>>>>>> same results.
>>>>>>>>>>>>>>>
>>>>>>>>>>>>>>> Just having some fun. ;-)!!!
>>>>>>>>>>>>>> Check this out:
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> https://youtu.be/d0vY0CKYhPY
>>>>>>>>>>>>>>
>>>>>>>>>>>>>> ;^)
>>>>>>>>>>>>> Interesting.
>>>>>>>>>>>>> The many different crazy places pi will appear.
>>>>>>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
>>>>>>>>>>>>> equation.
>>>>>>>>>>>>>
>>>>>>>>>>>>> I did this plot in the third quadrant where each new frame was
>>>>>>>>>>>>> a continuation of
>>>>>>>>>>>>> the last frame. So the parabolic curve keeps slightly
>>>>>>>>>>>>> increasing the distance from the
>>>>>>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
>>>>>>>>>>>>> exact duplicate of its'
>>>>>>>>>>>>> reverse mirror image of the side of the parabola in the first
>>>>>>>>>>>>> quadrant starting @ x=1
>>>>>>>>>>>>> and y=0. Where x+y=x^2
>>>>>>>>>>>>> A whole different calculation is required in the third quadrant
>>>>>>>>>>>>> for x + y=x^2 to duplicate
>>>>>>>>>>>>> x + y=x^2 from the first quadrant.
>>>>>>>>>>>>> That is where the third quadrant value of the sqrt -1 =
>>>>>>>>>>>>> ((sqrt6)-2)/2
>>>>>>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
>>>>>>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
>>>>>>>>>>>>> = 2 in the first quadrant.
>>>>>>>>>>>>> but only equal too -1 in the third quadrant.
>>>>>>>>>>>>> Negative integer points of -x\-y in the parabola in the third
>>>>>>>>>>>>> quadrant --
>>>>>>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
>>>>>>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
>>>>>>>>>>>> Explaining this plot in the third quadrant---
>>>>>>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
>>>>>>>>>>>> the minus quadrant
>>>>>>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
>>>>>>>>>>>>
>>>>>>>>>>>> These points on the parabola in the third quadrant of the
>>>>>>>>>>>> Cartesian coordinate
>>>>>>>>>>>> system start @ y=-0.5 and x=0
>>>>>>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
>>>>>>>>>>>> part of the
>>>>>>>>>>>> parabola that falls only in the third quadrant.
>>>>>>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
>>>>>>>>>>>> the first quadrant
>>>>>>>>>>>> and in it's mirror image flipped state reflex's only that part
>>>>>>>>>>>> of the parabola
>>>>>>>>>>>> falling in the 3rd quadrant .
>>>>>>>>>>>>
>>>>>>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
>>>>>>>>>>>> -y=-0.7752551287... -x here represents
>>>>>>>>>>>> the square root of -1 where -x+-y= -1
>>>>>>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
>>>>>>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
>>>>>>>>>>>> -1.9243247976...
>>>>>>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
>>>>>>>>>>>> -2.1291713067...
>>>>>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>>>>>>> -2.2332969077...
>>>>>>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
>>>>>>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
>>>>>>>>>>>> -2.8786796565...
>>>>>>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
>>>>>>>>>>>> -3.6547921201...
>>>>>>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
>>>>>>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
>>>>>>>>>>>> -5.2613872124...
>>>>>>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
>>>>>>>>>>>> -6.0845240525... .
>>>>>>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
>>>>>>>>>>>> ...
>>>>>>>>>>>>
>>>>>>>>>>>> A certain way to do the squaring and square root function in the
>>>>>>>>>>>> third negative
>>>>>>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
>>>>>>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
>>>>>>>>>>>> Where n can be any number that will represent the two plotted
>>>>>>>>>>>> points
>>>>>>>>>>>> on the reversed mirror image of the parabola -x+-y.
>>>>>>>>>>>>
>>>>>>>>>>>> Just a novel way to express negative values.
>>>>>>>>>>> What is interesting is that----
>>>>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
>>>>>>>>>>> -2.2332969077... summed =pi
>>>>>>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
>>>>>>>>>>> pi but the ratio applied to
>>>>>>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
>>>>>>>>>>> 2.458777240...+1= 3.4587772407...
>>>>>>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
>>>>>>>>>>> same ratio between -x/-y and x/y.
>>>>>>>>>>> This is probably true for all numbers.
>>>>>>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
>>>>>>>>>> 3.4587772407... and this ratio
>>>>>>>>>> becomes the new x value in the first quadrant. Giving the same
>>>>>>>>>> ratio of -x/-y from the third quadrant that
>>>>>>>>>> when summed -x+-y = -pi .
>>>>>>>>>>
>>>>>>>>>> The same with e and any other number.
>>>>>>>>> There is a direct correlation between the first quadrant x\y where
>>>>>>>>> x^2 = x + y = x^2 and the third quadrant
>>>>>>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
>>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
>>>>>>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
>>>>>>>>> the ratio =4.4494897427... and this becomes the new x in the first
>>>>>>>>> quadrant where x+y=x^2 and the ratio y/x =
>>>>>>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
>>>>>>>>> subtract 2 from x in the first quadrant
>>>>>>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
>>>>>>>>> quadrant.
>>>>>>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
>>>>>>>>>
>>>>>>>>> Dan
>>>>>>>> (r)=ratio and (n) = any number.
>>>>>>>>
>>>>>>>> Then for all negative -n in the third quadrant --- -x=((((
>>>>>>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
>>>>>>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
>>>>>>>> the same valued (r) as in the negative third
>>>>>>>> quadrant but with a different value for (n) in the first quadrant as
>>>>>>>> x + y=((r+1) ^2) or x + y =x^2 =n
>>>>>>>>
>>>>>>>> Neat huh?
>>>>>>>>
>>>>>>>> Dan
>>>>>>> I finally have the proof.
>>>>>>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
>>>>>>> with the first positive (x\y) quadrant.
>>>>>>>
>>>>>>> Enter below into Wolfram alpha---
>>>>>>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
>>>>>>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
>>>>>>> The left side of the equation represents the 3rd quadrant (up too and
>>>>>>> including the third (,) above.
>>>>>>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
>>>>>>> It took awhile but I finally presented it the right way for Wolfram.
>>>>>>>
>>>>>>> Pick any value for n and you will see why n=0--->oo.
>>>>>>
>>>>>> When -x = -pi in the third quadrant then, to find the the negative
>>>>>> square of
>>>>>> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
>>>>>> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
>>>>>> third
>>>>>> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
>>>>>>
>>>>>> The ratio of -y/-x = 4.3007475966...
>>>>>> Apply that to the first quadrant giving x = 4.3007475966... +1 =
>>>>>> 5.3007475966...
>>>>>> x^2 = 28.0979250837...
>>>>>> y = x^2 - x= 5.3007475966... = 22.797177487...
>>>>>> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
>>>>>> quadrant.
>>>>>>
>>>>>> The same procedure (added values to a number) will work with any
>>>>>> number in
>>>>>> the negative -x\-y third quadrant. Then cross checking with the first
>>>>>> quadrant
>>>>>> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
>>>>>> y/x after
>>>>>> adding 1 to the ratio and then x=r applied to the first quadrant.
>>>>>>
>>>>>> This is not imaginary but using real numbers in just 2 dimensions
>>>>>> depicting
>>>>>> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
>>>>>> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
>>>>>> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
>>>>>> third
>>>>>> quadrant the parabola is flipped from the up to the down position and
>>>>>> then
>>>>>> flipped over to the left.
>>>>>> Is this the only way to give a square root of a negative number
>>>>>> without using
>>>>>> imaginary (i)?
>>>>>>
>>>>>> The math works but the negative squares and square roots are probably
>>>>>> not the
>>>>>> correct meaning of all this?
>>>>>>
>>>>>> Any thoughts?
>>>>>
>>>>> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
>>>>> component, then convert back to rectangular form, and we have 0-1i.
>>>>> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
>>>>>
>>>>> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
>>>>> purely real because the imaginary part is zero. ;^)
>>>>>
>>>>> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
>>>>>
>>>>> This creates the borders of the four quadrants of a unit circle.
>>>>>
>>>>> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
>>>>> the point 0-1i.
>>>>>
>>>>> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
>>>>>
>>>>> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
>>>>> Keep in mind that the radius of the imaginary unit is one.
>>>>>
>>>>> With polar form in mind:
>>>>>
>>>>> 1+0i + PI = -1+0i
>>>>>
>>>>> Also:
>>>>>
>>>>> 1+0i + PI/2 = 0+1i = the imaginary unit.
>>>> Argh!
>>>>
>>>> That has to be a mistake of mine! 0+1i plus PI = -1+0i. So, adding PI +
>>>> PI / 2 to 0+1i has to be 0-1i... Right?
>>> The only thing I came up with is --- 1+0i + pi^ei = 0+1i
>> I would guess it is logical when e^pi(i)= -1 and then reversing the two -- pi^ei = 1
>> I am probably wrong because Iam' not into the imaginary (i) but an interesting question.
>
> What is also interesting ---
> n= (e^(e^((pi^e)*-1))). Where n = 1.0000000001762429... or 1 more zero below after the decimal point.
> n= (e^(e^((e^pi)*-1))). Where n = 1.00000000008915072558...
>
> Is this where they get e^pi(i) =-1?
> Probably not but still interesting with that many zeros after the decimal point.
> Can the math be that close in the polar coordinates to assume e^pi(i) = -1?

On Sunday, July 10, 2022 at 5:05:46 PM UTC-4, Chris M. Thomasson wrote:
> On 7/10/2022 10:53 AM, djoyce099 wrote:
> > On Sunday, July 10, 2022 at 1:17:53 PM UTC-4, djoyce099 wrote:
> >> On Sunday, July 10, 2022 at 12:53:24 PM UTC-4, djoyce099 wrote:
> >>> On Saturday, July 9, 2022 at 7:45:18 PM UTC-4, Chris M. Thomasson wrote:
> >>>> On 7/7/2022 2:42 PM, Chris M. Thomasson wrote:
> >>>>> On 7/7/2022 8:56 AM, Dan joyce wrote:
> >>>>>> On Monday, July 4, 2022 at 12:32:49 AM UTC-4, Dan joyce wrote:
> >>>>>>> On Sunday, July 3, 2022 at 1:36:31 PM UTC-4, Dan joyce wrote:
> >>>>>>>> On Friday, July 1, 2022 at 10:08:33 AM UTC-4, Dan joyce wrote:
> >>>>>>>>> On Thursday, June 30, 2022 at 11:59:58 AM UTC-4, Dan joyce wrote:
> >>>>>>>>>> On Thursday, June 30, 2022 at 8:26:43 AM UTC-4, Dan joyce wrote:
> >>>>>>>>>>> On Wednesday, June 29, 2022 at 6:03:36 PM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>> On Sunday, June 26, 2022 at 12:05:25 PM UTC-4, Dan joyce wrote:
> >>>>>>>>>>>>> On Sunday, June 26, 2022 at 12:50:12 AM UTC-4, Chris M.
> >>>>>>>>>>>>> Thomasson wrote:
> >>>>>>>>>>>>>> On 6/25/2022 1:34 PM, Dan joyce wrote:
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> sqrt(-1) =
> >>>>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Pi * ((sqrt6)+2)*(((sqrt6)-2)/2)*-1 = -pi
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Where the sqrt of -1 is the second half of the equation above --
> >>>>>>>>>>>>>>> (((sqrt6)-2)/2)*-1 =
> >>>>>>>>>>>>>>> -0.22474487139158904909864203735294569598297374032833...
> >>>>>>>>>>>>>>> Where -x+-y = -1 in the third quadrant of the Cartesian
> >>>>>>>>>>>>>>> coordinate system
> >>>>>>>>>>>>>>> Where -y =-.05 and x=0 starts the plot into the third quadrant.
> >>>>>>>>>>>>>>> A mirror image of the x + y= x^2 plot starting at y=-.25 part
> >>>>>>>>>>>>>>> of the parabola
> >>>>>>>>>>>>>>> going in the positive and the mirror image going into the
> >>>>>>>>>>>>>>> negative.
> >>>>>>>>>>>>>>> Just enter the above equation into Wolfram Alpha using any
> >>>>>>>>>>>>>>> number.
> >>>>>>>>>>>>>>> pi(in this case),e , golden ratio, the primes etc. giving the
> >>>>>>>>>>>>>>> same results.
> >>>>>>>>>>>>>>>
> >>>>>>>>>>>>>>> Just having some fun. ;-)!!!
> >>>>>>>>>>>>>> Check this out:
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> https://youtu.be/d0vY0CKYhPY
> >>>>>>>>>>>>>>
> >>>>>>>>>>>>>> ;^)
> >>>>>>>>>>>>> Interesting.
> >>>>>>>>>>>>> The many different crazy places pi will appear.
> >>>>>>>>>>>>> I just used pi as one of the ---> oo numbers that work in this
> >>>>>>>>>>>>> equation.
> >>>>>>>>>>>>>
> >>>>>>>>>>>>> I did this plot in the third quadrant where each new frame was
> >>>>>>>>>>>>> a continuation of
> >>>>>>>>>>>>> the last frame. So the parabolic curve keeps slightly
> >>>>>>>>>>>>> increasing the distance from the
> >>>>>>>>>>>>> -y axis. This part of the curve starts @ x=0 and -y= -0.5. An
> >>>>>>>>>>>>> exact duplicate of its'
> >>>>>>>>>>>>> reverse mirror image of the side of the parabola in the first
> >>>>>>>>>>>>> quadrant starting @ x=1
> >>>>>>>>>>>>> and y=0. Where x+y=x^2
> >>>>>>>>>>>>> A whole different calculation is required in the third quadrant
> >>>>>>>>>>>>> for x + y=x^2 to duplicate
> >>>>>>>>>>>>> x + y=x^2 from the first quadrant.
> >>>>>>>>>>>>> That is where the third quadrant value of the sqrt -1 =
> >>>>>>>>>>>>> ((sqrt6)-2)/2
> >>>>>>>>>>>>> Duplicating the same part of the parabola in the first quadrant --
> >>>>>>>>>>>>> x= (((sqrt6)-2)/2)+1 and y = 1- (((sqrt6)-2)/2) then x+y = x^2
> >>>>>>>>>>>>> = 2 in the first quadrant.
> >>>>>>>>>>>>> but only equal too -1 in the third quadrant.
> >>>>>>>>>>>>> Negative integer points of -x\-y in the parabola in the third
> >>>>>>>>>>>>> quadrant --
> >>>>>>>>>>>>> -x = -1 \-y = -2.5 , -x = -2 \-y = -6.5 , -x = -3\-y = -12.5 ,
> >>>>>>>>>>>>> -x = -4\-y = -20.5 , -x = -5\-y = -30.5
> >>>>>>>>>>>> Explaining this plot in the third quadrant---
> >>>>>>>>>>>> The third quadrant of the Cartesian coordinate system = -x\-y is
> >>>>>>>>>>>> the minus quadrant
> >>>>>>>>>>>> opposed to the first quadrant where x\y is the plus quadrant.
> >>>>>>>>>>>>
> >>>>>>>>>>>> These points on the parabola in the third quadrant of the
> >>>>>>>>>>>> Cartesian coordinate
> >>>>>>>>>>>> system start @ y=-0.5 and x=0
> >>>>>>>>>>>> So the first y=-0.5 is not in the -y calculations below but that
> >>>>>>>>>>>> part of the
> >>>>>>>>>>>> parabola that falls only in the third quadrant.
> >>>>>>>>>>>> Seeing this as a flip mirror image of the standard x+y= x^2 in
> >>>>>>>>>>>> the first quadrant
> >>>>>>>>>>>> and in it's mirror image flipped state reflex's only that part
> >>>>>>>>>>>> of the parabola
> >>>>>>>>>>>> falling in the 3rd quadrant .
> >>>>>>>>>>>>
> >>>>>>>>>>>> (((sqrt(1*4+2))-2)/2) *-1 =-x=-0.2247448713...then
> >>>>>>>>>>>> -y=-0.7752551287... -x here represents
> >>>>>>>>>>>> the square root of -1 where -x+-y= -1
> >>>>>>>>>>>> (((sqrt(2*4+2))-2)/2)*-1 = -x=-0.58113883...then -y= -1.41886117...
> >>>>>>>>>>>> (((sqrt(e*4+2))-2)/2) *-1 = -x=-0.7939570308...then -y=
> >>>>>>>>>>>> -1.9243247976...
> >>>>>>>>>>>> (((sqrt(3*4+2))-2)/2)*-1 = -x=-0.8708286933...then -y=
> >>>>>>>>>>>> -2.1291713067...
> >>>>>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> >>>>>>>>>>>> -2.2332969077...
> >>>>>>>>>>>> (((sqrt(3.5*4+2))-2)/2)*-1 = -x=-1 then -y= -2.5
> >>>>>>>>>>>> (((sqrt(4*4+2))-2)/2)*-1 = -x= -1.1213203435... then -y=
> >>>>>>>>>>>> -2.8786796565...
> >>>>>>>>>>>> (((sqrt(5*4+2))-2)/2)*-1 = -x= -1.3452078799... then -y=
> >>>>>>>>>>>> -3.6547921201...
> >>>>>>>>>>>> (((sqrt(6*4+2))-2)/2)*-1 = -x= -1.5495097567 then -y= -4.4504902433
> >>>>>>>>>>>> (((sqrt(7*4+2))-2)/2)*-1 = -x= -1.7386127875...then -y=
> >>>>>>>>>>>> -5.2613872124...
> >>>>>>>>>>>> (((sqrt(8*4+2))-2)/2)*-1 = -x= -1.9154759474...then -y=
> >>>>>>>>>>>> -6.0845240525... .
> >>>>>>>>>>>> (((sqrt(8.5*4+2))-2)/2)*-1= -x=-2 then -y=6.5 | .
> >>>>>>>>>>>> ...
> >>>>>>>>>>>>
> >>>>>>>>>>>> A certain way to do the squaring and square root function in the
> >>>>>>>>>>>> third negative
> >>>>>>>>>>>> quadrant where -x+-y= (-x^2) only by a special formula
> >>>>>>>>>>>> ((((sqrt(n*4+2))-2)/2)*-1 .
> >>>>>>>>>>>> Where n can be any number that will represent the two plotted
> >>>>>>>>>>>> points
> >>>>>>>>>>>> on the reversed mirror image of the parabola -x+-y.
> >>>>>>>>>>>>
> >>>>>>>>>>>> Just a novel way to express negative values.
> >>>>>>>>>>> What is interesting is that----
> >>>>>>>>>>> (((sqrt(pi*4+2))-2)/2)*-1 = -x=-0.9082957458...then -y=
> >>>>>>>>>>> -2.2332969077... summed =pi
> >>>>>>>>>>> The ratio of -y/-x = 2.4587772407... above is where both summed =
> >>>>>>>>>>> pi but the ratio applied to
> >>>>>>>>>>> the first quadrant where x+y =x^2 then add 1 to the above ratio
> >>>>>>>>>>> 2.458777240...+1= 3.4587772407...
> >>>>>>>>>>> and you have x= 3.4587772407... and y= 7.2209119859 giving the
> >>>>>>>>>>> same ratio between -x/-y and x/y.
> >>>>>>>>>>> This is probably true for all numbers.
> >>>>>>>>>> I should have stated, add 1 to the above ratio 2.458777240...+1=
> >>>>>>>>>> 3.4587772407... and this ratio
> >>>>>>>>>> becomes the new x value in the first quadrant. Giving the same
> >>>>>>>>>> ratio of -x/-y from the third quadrant that
> >>>>>>>>>> when summed -x+-y = -pi .
> >>>>>>>>>>
> >>>>>>>>>> The same with e and any other number.
> >>>>>>>>> There is a direct correlation between the first quadrant x\y where
> >>>>>>>>> x^2 = x + y = x^2 and the third quadrant
> >>>>>>>>> where -x\-y where -x+-y = -1 then -1+ x= -y . -x=
> >>>>>>>>> (((sqrt6)-2)/2)*-1 = -0.2247448713...-( -1) = 0.7752551286*-1 =
> >>>>>>>>> -0.7752551286... The ratio of -y/-x = 3.4494897427... Now add 1 to
> >>>>>>>>> the ratio =4.4494897427... and this becomes the new x in the first
> >>>>>>>>> quadrant where x+y=x^2 and the ratio y/x =
> >>>>>>>>> 3.4494897427... the same ratio from the third quadrant -x/-y. Also
> >>>>>>>>> subtract 2 from x in the first quadrant
> >>>>>>>>> 4.4494897427 -2 = (sqrt6). That is how -x is produced in the third
> >>>>>>>>> quadrant.
> >>>>>>>>> So not too far fetched to say--- (sqrt-1) = -0.2247448713... ;-)
> >>>>>>>>>
> >>>>>>>>> Dan
> >>>>>>>> (r)=ratio and (n) = any number.
> >>>>>>>>
> >>>>>>>> Then for all negative -n in the third quadrant --- -x=((((
> >>>>>>>> sqrt(n*4+2))-2)/2) *-1). -y= (n +-x)*-1. r=-y/-x.
> >>>>>>>> Then for all r+1 = x in the first quadrant. ((x + y =x^2)-y.)/x = r
> >>>>>>>> the same valued (r) as in the negative third
> >>>>>>>> quadrant but with a different value for (n) in the first quadrant as
> >>>>>>>> x + y=((r+1) ^2) or x + y =x^2 =n
> >>>>>>>>
> >>>>>>>> Neat huh?
> >>>>>>>>
> >>>>>>>> Dan
> >>>>>>> I finally have the proof.
> >>>>>>> Joining the full negative Cartesian coordinate third quadrant (-x\-y)
> >>>>>>> with the first positive (x\y) quadrant.
> >>>>>>>
> >>>>>>> Enter below into Wolfram alpha---
> >>>>>>> -x=(((( sqrt(n*4+2))-2)/2) *-1),-y= ((n +-x)*-1), r=-y/-x,
> >>>>>>> x=r+1,x+y=x^2,y/x=r, n=0--->oo
> >>>>>>> The left side of the equation represents the 3rd quadrant (up too and
> >>>>>>> including the third (,) above.
> >>>>>>> From x=r + 1,x+y=x^2,y/x=r, n =--->oo represents the first quadrant.
> >>>>>>> It took awhile but I finally presented it the right way for Wolfram.
> >>>>>>>
> >>>>>>> Pick any value for n and you will see why n=0--->oo.
> >>>>>>
> >>>>>> When -x = -pi in the third quadrant then, to find the the negative
> >>>>>> square of
> >>>>>> -pi --- -pi^2 =((((pi+.05)^2)+0.25)+ pi)*-1 = -16.6527897082...
> >>>>>> To check -pi^2 from above by finding the negative sqrt of -pi^2 in the
> >>>>>> third
> >>>>>> quadrant --- -pi^2*-1 = (((sqrt(((pi^2)*4)+2))-2)/2)*-1 = -pi.
> >>>>>>
> >>>>>> The ratio of -y/-x = 4.3007475966...
> >>>>>> Apply that to the first quadrant giving x = 4.3007475966... +1 =
> >>>>>> 5.3007475966...
> >>>>>> x^2 = 28.0979250837...
> >>>>>> y = x^2 - x= 5.3007475966... = 22.797177487...
> >>>>>> Ratio y/x = 4.3007475966... the original ratio of -y/-x in the third
> >>>>>> quadrant.
> >>>>>>
> >>>>>> The same procedure (added values to a number) will work with any
> >>>>>> number in
> >>>>>> the negative -x\-y third quadrant. Then cross checking with the first
> >>>>>> quadrant
> >>>>>> x\y of the Cartesian coordinate system matching the ratio of -y/-x and
> >>>>>> y/x after
> >>>>>> adding 1 to the ratio and then x=r applied to the first quadrant.
> >>>>>>
> >>>>>> This is not imaginary but using real numbers in just 2 dimensions
> >>>>>> depicting
> >>>>>> the same part of the parabola of x+y = x^2 and -x+-y = -x^2
> >>>>>> (-x^2 and sqrt(-y) by a special procedure). The part of the parabola
> >>>>>> starts @ x=1 and y=0 in the first quadrant and x=0 and y=-0.5 in the
> >>>>>> third
> >>>>>> quadrant the parabola is flipped from the up to the down position and
> >>>>>> then
> >>>>>> flipped over to the left.
> >>>>>> Is this the only way to give a square root of a negative number
> >>>>>> without using
> >>>>>> imaginary (i)?
> >>>>>>
> >>>>>> The math works but the negative squares and square roots are probably
> >>>>>> not the
> >>>>>> correct meaning of all this?
> >>>>>>
> >>>>>> Any thoughts?
> >>>>>
> >>>>> Take the polar form of the imaginary unit 0+1i. Add PI to its angle
> >>>>> component, then convert back to rectangular form, and we have 0-1i.
> >>>>> Adding PI to the polar form of 0-1i brings us right back to 0+1i.
> >>>>>
> >>>>> So, adding PI / 2 to the polar form of 0+1i, we have -1+0i. Oh, that is
> >>>>> purely real because the imaginary part is zero. ;^)
> >>>>>
> >>>>> Adding PI + PI / 2 to 0+1i we have 1+0i, again purely real.
> >>>>>
> >>>>> This creates the borders of the four quadrants of a unit circle.
> >>>>>
> >>>>> Say 0+1i is 90 degrees, because it is. 90 + 180 = 270, where we can plot
> >>>>> the point 0-1i.
> >>>>>
> >>>>> 0+1i is 90 degrees. 90 + 90 = 180, where we can plot -1+0i.
> >>>>>
> >>>>> For instance, add in 90 more degrees to 0-1i, 270 + 90 = 360, is 1+0i.
> >>>>> Keep in mind that the radius of the imaginary unit is one.
> >>>>>
> >>>>> With polar form in mind:
> >>>>>
> >>>>> 1+0i + PI = -1+0i
> >>>>>
> >>>>> Also:
> >>>>>
> >>>>> 1+0i + PI/2 = 0+1i = the imaginary unit.
> >>>> Argh!
> >>>>
> >>>> That has to be a mistake of mine! 0+1i plus PI = -1+0i. So, adding PI +
> >>>> PI / 2 to 0+1i has to be 0-1i... Right?
> >>> The only thing I came up with is --- 1+0i + pi^ei = 0+1i
> >> I would guess it is logical when e^pi(i)= -1 and then reversing the two -- pi^ei = 1
> >> I am probably wrong because Iam' not into the imaginary (i) but an interesting question.
> >
> > What is also interesting ---
> > n= (e^(e^((pi^e)*-1))). Where n = 1.0000000001762429... or 1 more zero below after the decimal point.
> > n= (e^(e^((e^pi)*-1))). Where n = 1.00000000008915072558...
> >
> > Is this where they get e^pi(i) =-1?
> > Probably not but still interesting with that many zeros after the decimal point.
> > Can the math be that close in the polar coordinates to assume e^pi(i) = -1?
> e^(i*x) = cos(x) + i*sin(x)

On 7/10/2022 1:05 PM, mitchr...@gmail.com wrote:
> On Thursday, July 7, 2022 at 2:42:37 PM UTC-7, Chris M. Thomasson wrote:
[...]
>>
>> 1+0i + PI/2 = 0+1i = the imaginary unit.
>
> That unit is just imaginary.

Are you real? ;^)

mitchr...@gmail.com wrote:

>> 1+0i + PI/2 = 0+1i = the imaginary unit.
>
> That unit is just imaginary.

nonsense. Nothing tells that pi/2 is imaginary. You have to take it in
context with something else. Plus that the idiot forgot 1 real, so in
context of s/z-plane would become 1+i, which gives a damping frequency.
You guys are uneducated, having no apparatus and instruments. I see no
instruments. Show him your apparatus.

On Monday, July 11, 2022 at 7:15:48 AM UTC-4, Chase Nomura wrote:
> mitchr...@gmail.com wrote:
>
> >> 1+0i + PI/2 = 0+1i = the imaginary unit.
> >
> > That unit is just imaginary.
> nonsense. Nothing tells that pi/2 is imaginary. You have to take it in
> context with something else. Plus that the idiot forgot 1 real, so in
> context of s/z-plane would become 1+i, which gives a damping frequency.
> You guys are uneducated, having no apparatus and instruments. I see no
> instruments. Show him your apparatus.

It seems no one wants to answer this. ---
What about --- 1+0i + pi^ei = 0+1i

Chris M. Thomasson wrote:

>>> 1+0i + PI/2 = 0+1i = the imaginary unit.
>>
>> That unit is just imaginary.
>
> Are you real? ;^)

How to destroy a country

make art ugly
make porn free
make God a joke
make food poison
make dads optional
make politician rich
make money worthless
make buildings oppressive
make men and women compete
make children hate their ancestors
arm heavily the fictitious "u_kraine" (no_land) to bomb people in Donesk
People's Republic and Luhansk People's Republic, in their apartments.
US-supplied HIMARS kill three civilians in Donbass
https://www.rt.com/russia/558770-us-rockets-kill-donbass/
(change your DNS provider if problems accessing the link)

On Sunday, July 10, 2022 at 8:15:18 PM UTC-4, Chris M. Thomasson wrote:
> On 7/10/2022 1:05 PM, mitchr...@gmail.com wrote:
> > On Thursday, July 7, 2022 at 2:42:37 PM UTC-7, Chris M. Thomasson wrote:
> [...]
> >>
> >> 1+0i + PI/2 = 0+1i = the imaginary unit.
> >
> > That unit is just imaginary.
> Are you real? ;^)

But Chris these negative values are real and nothing to do with the imaginary (i)
Explaining it further below using the x^2 = x+y parabola and -x^2=-x+-y same part
of the curve of the parabola between the third negative quadrant and the first positive
quadrant of the Cartesian coordinate system. This is just in 2d where (i) is derived
from 3d.
Explaining it more on my sqrt of any negative number.
The parabola of x+y= x^2 applied to the first x\y and third quadrant -y\-x.
The part of the parabola in the third quadrant starts @ x=0 and -y=.05.
Traveling down for -y and to the left from x too -x. Cross referencing to the
first quadrant of x+y=x^2 the same part of the parabola starts at x=1 and y=0.

The relationship is just -.5 difference between the third and the first quadrant.
Third quadrant -x\-y where the sqrt(-1) (in real values) in the third quadrant =
=(((sqrt((1*4)+2))-2)/2*-1 = -0.22474487139158904909...

Then put in first quadrant.
-0.22474487139158904909...*-1 = 0.22474487139158904909...
0.22474487139158904909... add (1) 1.22474487139158904909...
1.22474487139158904909...^2 = 1.5 = 0.5 >1

sqrt(-pi) in the 3rd quadrant = (((sqrt((pi*4)+2))-2)/2)*-1 = -0.90829574583967283927...
Then put in the first quadrant.
*-1 = 0.90829574583967283927... and add 1 = 1.90829574583967283927...
1.90829574583967283927... ^2 = 3.64159265358979323846... = 0.5 >pi.

Use any number. I just used 1 and pi as examples.

Probably a wacky idea but definitely thinking outside the box!
Dan

On Monday, July 11, 2022 at 12:51:22 PM UTC-4, Dan joyce wrote:
> On Sunday, July 10, 2022 at 8:15:18 PM UTC-4, Chris M. Thomasson wrote:
> > On 7/10/2022 1:05 PM, mitchr...@gmail.com wrote:
> > > On Thursday, July 7, 2022 at 2:42:37 PM UTC-7, Chris M. Thomasson wrote:
> > [...]
> > >>
> > >> 1+0i + PI/2 = 0+1i = the imaginary unit.
> > >
> > > That unit is just imaginary.
> > Are you real? ;^)
> But Chris these negative values are real and nothing to do with the imaginary (i)
> Explaining it further below using the x^2 = x+y parabola and -x^2=-x+-y same part
> of the curve of the parabola between the third negative quadrant and the first positive
> quadrant of the Cartesian coordinate system. This is just in 2d where (i) is derived
> from 3d.
> Explaining it more on my sqrt of any negative number.
> The parabola of x+y= x^2 applied to the first x\y and third quadrant -y\-x.
> The part of the parabola in the third quadrant starts @ x=0 and -y=.05.
> Traveling down for -y and to the left from x too -x. Cross referencing to the
> first quadrant of x+y=x^2 the same part of the parabola starts at x=1 and y=0.
>
> The relationship is just -.5 difference between the third and the first quadrant.
> Third quadrant -x\-y where the sqrt(-1) (in real values) in the third quadrant =
> =(((sqrt((1*4)+2))-2)/2*-1 = -0.22474487139158904909...
>
> Then put in first quadrant.
> -0.22474487139158904909...*-1 = 0.22474487139158904909...
> 0.22474487139158904909... add (1) 1.22474487139158904909...
> 1.22474487139158904909...^2 = 1.5 = 0.5 >1
>
> sqrt(-pi) in the 3rd quadrant = (((sqrt((pi*4)+2))-2)/2)*-1 = -0.90829574583967283927...
> Then put in the first quadrant.
> *-1 = 0.90829574583967283927... and add 1 = 1.90829574583967283927...
> 1.90829574583967283927... ^2 = 3.64159265358979323846... = 0.5 >pi.
>
> Use any number. I just used 1 and pi as examples.
>
> Probably a wacky idea but definitely thinking outside the box!
> Dan

I did a plot on my old Commodore 64, years ago, where the upper right side of
the whole screen started the plot @ y=-0.5 an x=0. When the curve reached
the bottom of the screen I just continued the plot at the same location (-x)
where it left on the bottom of the screen and continued on with the curve at
the top also with the -y value. Each curve would close in tighter and tighter
as -x and -y grew more negative until the entire screen was filled with curves
from right to left.
Then cleared that screen and started another with many more curves to complete
that screen. The screen pixel count in those days was small compared to the
resolution of todays computers.
So this is an easy plot of the third quadrant.

On 7/11/2022 11:56 AM, Joel Kanada wrote:

> arm heavily the fictitious "u_kraine" (no_land)

Nymshifter, why do you Russian troll apologists always lie?

"у" means "in", "on", "at", "with" etc. in both Ukrainian and Russian.
It doesn't mean "no". "у країна" literally means "in the country" but
the origin was apparently "the borderland" or similar.

> to bomb people in Donesk

Is that more of a war crime than invading and bombing Ukraine,
especially places like Mariupol (90% Russian speakers!), which Russia
flattened? And several other cities in the Donbass? And why does Russia
attack apartment buildings, hospitals, schools while Ukraine targets
military targets? Is 卐Ru⚡︎⚡︎ia卐 simply uncivilized?

Question: What's worse than being a Russian speaker in Ukraine?

Answer: Being "liberated" by the 卐Ru⚡︎⚡︎ians卐!
(Answer 2: Being a Russian tank driver in Ukraine!)

> US-supplied HIMARS kill three civilians in Donbass

And 卐Ru⚡︎⚡︎ia卐 just killed 26 Ukrainians by bombing their apartment
building!

You may now go get your 50 ml of borsht for making your post.

卐Путин卐 хуйло!

Michael Moroney wrote:

> On 7/11/2022 11:56 AM, Joel Kanada wrote:
>
>> arm heavily the fictitious "u_kraine" (no_land)
>
> Nymshifter, why do you Russian troll apologists always lie?
>
> "у" means "in", "on", "at", "with" etc. in both Ukrainian and Russian.
> It doesn't mean "no". "у країна" literally means "in the country" but
> the origin was apparently "the borderland" or similar.

a *u* is the negation of the term i many european languages, you fucking
idiot. Kindergarten knowledge.

>> US-supplied HIMARS kill three civilians in Donbass
>And 卐Ru⚡︎⚡︎ia卐 just killed 26 Ukrainians by bombing their apartment

you lying bitch, all the crap weapon from the west only can kill people in
the independent countries of DPR and LPR. There are no other
possibilities. And your unicodes sucks. Unicode that makes sense are these

🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴
🔴🔴🔴🔴🔴🌕🌕🔴🌕🌕🔴🔴🔴🔴🔴
🔴🔴🔴🔴🌕🌕🌕🔴🔴🌕🌕🔴🔴🔴🔴
🔴🔴🔴🌕🌕🌕🌕🔴🔴🔴🌕🌕🔴🔴🔴
🔴🔴🌕🌕🌕🌕🔴🔴🔴🔴🌕🌕🌕🔴🔴
🔴🌕🌕🌕🌕🌕🌕🔴🔴🔴🔴🌕🌕🔴🔴
🔴🔴🌕🌕🔴🌕🌕🌕🔴🔴🔴🌕🌕🌕🔴
🔴🔴🔴🔴🔴🔴🌕🌕🌕🔴🔴🔴🌕🌕🔴
🔴🔴🔴🔴🔴🔴🔴🌕🌕🌕🔴🌕🌕🌕🔴
🔴🔴🔴🔴🌕🔴🔴🔴🌕🌕🌕🌕🌕🔴🔴
🔴🔴🔴🌕🌕🌕🔴🔴🔴🌕🌕🌕🔴🔴🔴
🔴🌕🌕🌕🔴🌕🌕🌕🌕🌕🌕🌕🌕🔴🔴
🔴🌕🌕🔴🔴🔴🌕🌕🌕🔴🔴🌕🌕🔴🔴
🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴

On Monday, July 11, 2022 at 2:25:20 PM UTC-4, Elvi Ikina wrote:
> Michael Moroney wrote:
>
> > On 7/11/2022 11:56 AM, Joel Kanada wrote:
> >
> >> arm heavily the fictitious "u_kraine" (no_land)
> >
> > Nymshifter, why do you Russian troll apologists always lie?
> >
> > "у" means "in", "on", "at", "with" etc. in both Ukrainian and Russian.
> > It doesn't mean "no". "у країна" literally means "in the country" but
> > the origin was apparently "the borderland" or similar.
> a *u* is the negation of the term i many european languages, you fucking
> idiot. Kindergarten knowledge.
> >> US-supplied HIMARS kill three civilians in Donbass
> >And 卐Ru⚡︎⚡︎ia卐 just killed 26 Ukrainians by bombing their apartment
> you lying bitch, all the crap weapon from the west only can kill people in
> the independent countries of DPR and LPR. There are no other
> possibilities. And your unicodes sucks. Unicode that makes sense are these
>
> 🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴
> 🔴🔴🔴🔴🔴🌕🌕🔴🌕🌕🔴🔴🔴🔴🔴
> 🔴🔴🔴🔴🌕🌕🌕🔴🔴🌕🌕🔴🔴🔴🔴
> 🔴🔴🔴🌕🌕🌕🌕🔴🔴🔴🌕🌕🔴🔴🔴
> 🔴🔴🌕🌕🌕🌕🔴🔴🔴🔴🌕🌕🌕🔴🔴
> 🔴🌕🌕🌕🌕🌕🌕🔴🔴🔴🔴🌕🌕🔴🔴
> 🔴🔴🌕🌕🔴🌕🌕🌕🔴🔴🔴🌕🌕🌕🔴
> 🔴🔴🔴🔴🔴🔴🌕🌕🌕🔴🔴🔴🌕🌕🔴
> 🔴🔴🔴🔴🔴🔴🔴🌕🌕🌕🔴🌕🌕🌕🔴
> 🔴🔴🔴🔴🌕🔴🔴🔴🌕🌕🌕🌕🌕🔴🔴
> 🔴🔴🔴🌕🌕🌕🔴🔴🔴🌕🌕🌕🔴🔴🔴
> 🔴🌕🌕🌕🔴🌕🌕🌕🌕🌕🌕🌕🌕🔴🔴
> 🔴🌕🌕🔴🔴🔴🌕🌕🌕🔴🔴🌕🌕🔴🔴
> 🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴🔴
PLEASE!
Off Topic!
There are plenty of political cites you can air your differences.