On 7/11/2022 4:15 AM, 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.

The Mandelbrot set is a nice and _fun_ way to show off complex numbers.

1+0i is 100% real because it's imaginary component is zero. Wrt polar
form adding PI/2 to it makes it rotate around counter clockwise to the
imaginary unit at 0+1i. Its real part is zero.

The complex numbers are very similar to normal vectors, except when
multiplying, dividing, ect...

Adding complex numbers is just like normal vectors. The absolute value
of a complex number is the same as taking the length of a vector.

Dan joyce wrote:

>> >> 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.

impossible, the difference is aimed to be addressed here. Reread the context.

Chris M. Thomasson wrote:

> 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> form adding PI/2 to it makes it rotate around counter clockwise to the
> imaginary unit at 0+1i. Its real part is zero.

err, there is no "polar form" in pi/2. Go read what a pi stands for.

On Monday, July 11, 2022 at 2:47:18 PM UTC-4, Chris M. Thomasson wrote:
> On 7/11/2022 4:15 AM, 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.
> The Mandelbrot set is a nice and _fun_ way to show off complex numbers.
>
> 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> form adding PI/2 to it makes it rotate around counter clockwise to the
> imaginary unit at 0+1i. Its real part is zero.
>
> The complex numbers are very similar to normal vectors, except when
> multiplying, dividing, ect...

As is in this case. It requires a different process for multiplying and the sqrt. function only.
in the negative quadrant (-x\-y) opposed to the first quadrant where x+y =x^2.
Which means -x+-y = -x^2 that requires that different process shown in my posts.
It uses the same part of the parabola beginning x=0 and -y=-0.5 in the third quadrant
heading left( _x) and down(-y) and x=1 and y=0 in the first quadrant heading right(x) and up(y).
The same curve --->oo of the parabola only heading in opposite directions, +x\+y -x\-y.

> Adding complex numbers is just like normal vectors. The absolute value
> of a complex number is the same as taking the length of a vector.

On 7/11/2022 2:25 PM, 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.

But not in Ukrainian, Russian nor English. Maybe it is in Basque, I
don't know. But I do know it's not relevant, and in both Ukrainian and
Russian, "у" means "in", "on", "at", "with" etc.
>
>>> US-supplied HIMARS kill three civilians in Donbass
>> And 卐Ru⚡︎⚡︎ia卐 just killed 26 Ukrainians by bombing their apartment building!
>
> you lying bitch, all the crap weapon from the west only can kill people in
> the independent countries of DPR and LPR.

They seem to do a great job killing the 卐Ru⚡︎⚡︎ian卐 invaders! What is
it now, 37,000 dead 卐Ru⚡︎⚡︎ian卐 soldiers? Certainly more by now.
That's 37,000 mothers who will never see their sons again. And most of
them won't even have a body or grave to mourn at, because the 卐
Ru⚡︎⚡︎ian卐 invaders either abandon or destroy most of the bodies. Looks
like next year will be a bumper crop of sunflowers for the Ukrainian
farmers! (and for Ukrainian scrap metal dealers as well)

And my Unicode is accurate, you must admit! Can you read the next line,
nymshifter?

卐Путин卐 хуйло!

Michael Moroney wrote:

>> a *u* is the negation of the term i many european languages, you
>> fucking idiot. Kindergarten knowledge.
>
> But not in Ukrainian, Russian nor English. Maybe it is in Basque, I
> don't know. But I do know it's not relevant, and in both Ukrainian and
> Russian, "у" means "in", "on", "at", "with" etc.

I hear you guys in america are menstruating.

On Monday, July 11, 2022 at 4:19:28 PM UTC-4, Dan joyce wrote:
> On Monday, July 11, 2022 at 2:47:18 PM UTC-4, Chris M. Thomasson wrote:
> > On 7/11/2022 4:15 AM, 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.
> > The Mandelbrot set is a nice and _fun_ way to show off complex numbers.
> >
> > 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> > form adding PI/2 to it makes it rotate around counter clockwise to the
> > imaginary unit at 0+1i. Its real part is zero.
> >
> > The complex numbers are very similar to normal vectors, except when
> > multiplying, dividing, ect...
> As is in this case. It requires a different process for multiplying and the sqrt. function only.
> in the negative quadrant (-x\-y) opposed to the first quadrant where x+y =x^2.
> Which means -x+-y = -x^2 that requires that different process shown in my posts.
> It uses the same part of the parabola beginning x=0 and -y=-0.5 in the third quadrant
> heading left( _x) and down(-y) and x=1 and y=0 in the first quadrant heading right(x) and up(y).
> The same curve --->oo of the parabola only heading in opposite directions, +x\+y -x\-y.
> > Adding complex numbers is just like normal vectors. The absolute value
> > of a complex number is the same as taking the length of a vector.

An easy way to find the negative square root of any number---
In the first quadrant, say you want to find the negative square root of 36.
Add (36+0.5) = 36.5, ((sqrt(36.5) -1)*-1) = - -5.0415229867...

Cross check with the third quadrant --- (((((5.0415229867... *2) +2)^2)-2)/4)*-1 = -36
-36 -y= (36 - 5.0415229867---)*-1 = -y= -30.9584770132... where -x+-y = -36.
All this is doing is duplicating the parabolic curve beginning at certain points in the
1st and 3rd quadrants. 1st quadrant x= 1,y= 0. 3rd quadrant x= 0 ,-y= -0.5.
The two curves going off in the opposite direction of one another.
Leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=1 and y=0 into the first quadrant.
and leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=0 and y= - 0.5 into the third quadrant.
Creating an exact copy of the parabolic curve going in opposite directions. One curve in the positive
x\y and one duplicate curve in the negative -x\-y where each point of x --> -x and y --> -y have the
maximum separation dictated by the parabolic curve. What is this rate of separation for each point of
x and -x , y and -y ?

Dan

On 7/11/2022 11:53 AM, Nat Enoki wrote:
> Chris M. Thomasson wrote:
>
>> 1+0i is 100% real because it's imaginary component is zero. Wrt polar
>> form adding PI/2 to it makes it rotate around counter clockwise to the
>> imaginary unit at 0+1i. Its real part is zero.
>
> err, there is no "polar form" in pi/2. Go read what a pi stands for.

Ummm. What do you mean? You know what polar form is right?

Chris M. Thomasson wrote:

> On 7/11/2022 11:53 AM, Nat Enoki wrote:
>> Chris M. Thomasson wrote:
>>> 1+0i is 100% real because it's imaginary component is zero. Wrt polar
>>> form adding PI/2 to it makes it rotate around counter clockwise to the
>>> imaginary unit at 0+1i. Its real part is zero.
>>
>> err, there is no "polar form" in pi/2. Go read what a pi stands for.
>
> Ummm. What do you mean? You know what polar form is right?

pi is a real number, idiot. It has nothing to do with "polar". Watch this
*_black_satanist_* proclaiming wanting to kill you, with no other
explanation.

CDC Director ((Rochelle Walensky)) - 'Many Americans are 'under
vaccinated' https://www.bitchute.com/video/G9IAhc0SqDho/

why on earth is this ugly bitch not yet arrested??

On 7/12/2022 1:19 PM, Hever Sonoda wrote:
> Chris M. Thomasson wrote:
>
>> On 7/11/2022 11:53 AM, Nat Enoki wrote:
>>> Chris M. Thomasson wrote:
>>>> 1+0i is 100% real because it's imaginary component is zero. Wrt polar
>>>> form adding PI/2 to it makes it rotate around counter clockwise to the
>>>> imaginary unit at 0+1i. Its real part is zero.
>>>
>>> err, there is no "polar form" in pi/2. Go read what a pi stands for.
>>

Ummm. What do you mean? You know what polar form is right?

Perhaps you don't know what an angle is and how it directly relates to pi?

>
> pi is a real number, idiot. It has nothing to do with "polar". Watch this
> *_black_satanist_* proclaiming wanting to kill you, with no other
> explanation.
>
> CDC Director ((Rochelle Walensky)) - 'Many Americans are 'under
> vaccinated' https://www.bitchute.com/video/G9IAhc0SqDho/
>
> why on earth is this ugly bitch not yet arrested??

Chris M. Thomasson wrote:

> Ummm. What do you mean? You know what polar form is right?
> Perhaps you don't know what an angle is and how it directly relates to
> pi?

that's a real number, you fucking idiot. What is pi/2 then? Angles are
about *radians*, not pi. Idiot.

>> pi is a real number, idiot. It has nothing to do with "polar". Watch
>> this *_black_satanist_* proclaiming wanting to kill you, with no other
>> explanation.
>>
>> CDC Director ((Rochelle Walensky)) - 'Many Americans are 'under
>> vaccinated' https://www.bitchute.com/video/G9IAhc0SqDho/
>>
>> why on earth is this ugly bitch not yet arrested??

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.
^^^^^^^^^^^^^^^^^^

Chris M. Thomasson wrote:

> Humm... This is wrong above:
> Starting at point 0+1i, adding pi gets us to -1+0i. Therefore adding
> PI/2 to this -1+0i, gets us to 0-1i. PI + PI / 2 is 75% of the circle.
> Counter clockwise. (PI + PI / 2) + 0+1i = 0-1i.

pi is a real number, fucking stupid. You add it wrong places, what an
idiot. This guy don't know how to add a real number to a complex.

here's some capitalism, for you to have.

ANTIVAXXERS STORM CHILDREN'S VAX CENTRE IN NEW YORK ONLY TO FIND ITS
ENTIRELY RUN BY CHINESE! https://www.bitchute.com/video/TbiN12EB60cf/

Chris M. Thomasson was thinking very hard :
> 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.
> ^^^^^^^^^^^^^^^^^^
>
> [....]
>
> Humm... This is wrong above:
>
> Starting at point 0+1i, adding pi gets us to -1+0i

On 7/14/2022 4:38 PM, FromTheRafters wrote:
> Chris M. Thomasson was thinking very hard :
>> 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.
>> ^^^^^^^^^^^^^^^^^^
>>
>> [....]
>>
>> Humm... This is wrong above:
>>
>> Starting at point 0+1i, adding pi gets us to -1+0i
>
> Adding pi what? Shouldn't you just get the complex conjugate here --
> another purely imaginary number?

On 7/14/2022 4:58 PM, Chris M. Thomasson wrote:
> On 7/14/2022 4:38 PM, FromTheRafters wrote:
>> Chris M. Thomasson was thinking very hard :
>>> 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.
>>> ^^^^^^^^^^^^^^^^^^
>>>
>>> [....]
>>>
>>> Humm... This is wrong above:
>>>
>>> Starting at point 0+1i, adding pi gets us to -1+0i
>>
>> Adding pi what? Shouldn't you just get the complex conjugate here --
>> another purely imaginary number?
>
> That works as well in 2-ary. 0+1i = 0-1i conj... ;^)

On 7/14/2022 5:06 PM, Chris M. Thomasson wrote:
> On 7/14/2022 4:58 PM, Chris M. Thomasson wrote:
>> On 7/14/2022 4:38 PM, FromTheRafters wrote:
>>> Chris M. Thomasson was thinking very hard :
>>>> 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.
>>>> ^^^^^^^^^^^^^^^^^^
>>>>
>>>> [....]
>>>>
>>>> Humm... This is wrong above:
>>>>
>>>> Starting at point 0+1i, adding pi gets us to -1+0i
>>>
>>> Adding pi what? Shouldn't you just get the complex conjugate here --
>>> another purely imaginary number?
>>
>> That works as well in 2-ary. 0+1i = 0-1i conj... ;^)
>
> The negated complex number from a 2-ary setup wrt taking the negated
> number from the sqrt of a complex number works as well. One can create a
> 2-ary IFS from this alone.

Chris M. Thomasson brought next idea :
> On 7/14/2022 5:06 PM, Chris M. Thomasson wrote:
>> On 7/14/2022 4:58 PM, Chris M. Thomasson wrote:
>>> On 7/14/2022 4:38 PM, FromTheRafters wrote:
>>>> Chris M. Thomasson was thinking very hard :
>>>>> 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.
>>>>> ^^^^^^^^^^^^^^^^^^
>>>>>
>>>>> [....]
>>>>>
>>>>> Humm... This is wrong above:
>>>>>
>>>>> Starting at point 0+1i, adding pi gets us to -1+0i
>>>>
>>>> Adding pi what? Shouldn't you just get the complex conjugate here --
>>>> another purely imaginary number?
>>>
>>> That works as well in 2-ary. 0+1i = 0-1i conj... ;^)
>>
>> The negated complex number from a 2-ary setup wrt taking the negated number
>> from the sqrt of a complex number works as well. One can create a 2-ary IFS
>> from this alone.
>
> Read all of:
>
> http://paulbourke.net/fractals/multijulia/

On 7/14/2022 5:26 PM, FromTheRafters wrote:
> Chris M. Thomasson brought next idea :
>> On 7/14/2022 5:06 PM, Chris M. Thomasson wrote:
>>> On 7/14/2022 4:58 PM, Chris M. Thomasson wrote:
>>>> On 7/14/2022 4:38 PM, FromTheRafters wrote:
>>>>> Chris M. Thomasson was thinking very hard :
>>>>>> 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.
>>>>>> ^^^^^^^^^^^^^^^^^^
>>>>>>
>>>>>> [....]
>>>>>>
>>>>>> Humm... This is wrong above:
>>>>>>
>>>>>> Starting at point 0+1i, adding pi gets us to -1+0i
>>>>>
>>>>> Adding pi what? Shouldn't you just get the complex conjugate here
>>>>> -- another purely imaginary number?
>>>>
>>>> That works as well in 2-ary. 0+1i = 0-1i conj... ;^)
>>>
>>> The negated complex number from a 2-ary setup wrt taking the negated
>>> number from the sqrt of a complex number works as well. One can
>>> create a 2-ary IFS from this alone.
>>
>> Read all of:
>>
>> http://paulbourke.net/fractals/multijulia/
>
> Will that make the statement "Starting at point 0+1i, adding pi gets us
> to -1+0i" make more sense? Adding pi (radians) gets you halfway around
> the circle. Pure reals remain purely reals and pure imaginaries remain
> purely imaginary on the complex plane. Your statement goes from an
> imaginary to a real, not to the purely imaginary complex conjugate.

On 7/14/2022 5:44 PM, Chris M. Thomasson wrote:
> On 7/14/2022 5:26 PM, FromTheRafters wrote:
>> Chris M. Thomasson brought next idea :
>>> On 7/14/2022 5:06 PM, Chris M. Thomasson wrote:
>>>> On 7/14/2022 4:58 PM, Chris M. Thomasson wrote:
>>>>> On 7/14/2022 4:38 PM, FromTheRafters wrote:
>>>>>> Chris M. Thomasson was thinking very hard :
>>>>>>> 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.
>>>>>>> ^^^^^^^^^^^^^^^^^^
>>>>>>>
>>>>>>> [....]
>>>>>>>
>>>>>>> Humm... This is wrong above:
>>>>>>>
>>>>>>> Starting at point 0+1i, adding pi gets us to -1+0i
>>>>>>
>>>>>> Adding pi what? Shouldn't you just get the complex conjugate here
>>>>>> -- another purely imaginary number?
>>>>>
>>>>> That works as well in 2-ary. 0+1i = 0-1i conj... ;^)
>>>>
>>>> The negated complex number from a 2-ary setup wrt taking the negated
>>>> number from the sqrt of a complex number works as well. One can
>>>> create a 2-ary IFS from this alone.
>>>
>>> Read all of:
>>>
>>> http://paulbourke.net/fractals/multijulia/
>>
>> Will that make the statement "Starting at point 0+1i, adding pi gets
>> us to -1+0i" make more sense? Adding pi (radians) gets you halfway
>> around the circle. Pure reals remain purely reals and pure imaginaries
>> remain purely imaginary on the complex plane. Your statement goes from
>> an imaginary to a real, not to the purely imaginary complex conjugate.
>
> 0+1i plus PI radians gets us to -1+0i. So, two ary, MultiJulia!

Chris M. Thomasson wrote:

>> 0+1i plus PI radians gets us to -1+0i. So, two ary, MultiJulia!
>
> What are the 2-ary roots of 0+1i, where the result of each root squared
> is 0+1i? This is multijulia... We create an iterated function system out
> of the roots and points. Paul wrote out my formula. Remember since I

idiots. You are stealing from the nazi uKraine starting before 2014, when
you *killed* the elected government, with your nazis. You liar gave them
weapons and *trainees*, to kill the russian population, resident in that
region for millennia. Provable with pictures, documents and videos.

moreover, capitalist polakia, will be so fucked. The capitalist
bulgaria, likewise. Let's see capitalism without *stolen_energy* on
*fake_funny_money* from other countries, here from Russia.

the communism went down *planed*, starting *10_years_before_1989*, having
the corrupted central committees, selling energy, food and quality
products, on *fake_money* to the *capitalist_west*.

Proxy War - Poland hands over 232 T-72M1 tanks to Ukraine
https://www.bitchute.com/video/R3STgBsEbJsR/

Chris M. Thomasson wrote:

>> purely imaginary on the complex plane. Your statement goes from an
>> imaginary to a real, not to the purely imaginary complex conjugate.
>
> 0+1i plus PI radians gets us to -1+0i. So, two ary, MultiJulia!

what happens with the nazis, sincerely wanting the russian people
*_"reduced_to_50_millions"_* (the disgusting uneducated capitalist wanker,
polaker lech walensa), or erased from the face of the earth.

Ukrainian saboteurs tried to enter Kherson but got absolutely BLASTED in
the end https://www.bitchute.com/video/vOrLzkti9K8X/

On Tuesday, July 12, 2022 at 10:59:51 AM UTC-4, Dan joyce wrote:
> On Monday, July 11, 2022 at 4:19:28 PM UTC-4, Dan joyce wrote:
> > On Monday, July 11, 2022 at 2:47:18 PM UTC-4, Chris M. Thomasson wrote:
> > > On 7/11/2022 4:15 AM, 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.
> > > The Mandelbrot set is a nice and _fun_ way to show off complex numbers.
> > >
> > > 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> > > form adding PI/2 to it makes it rotate around counter clockwise to the
> > > imaginary unit at 0+1i. Its real part is zero.
> > >
> > > The complex numbers are very similar to normal vectors, except when
> > > multiplying, dividing, ect...
> > As is in this case. It requires a different process for multiplying and the sqrt. function only.
> > in the negative quadrant (-x\-y) opposed to the first quadrant where x+y =x^2.
> > Which means -x+-y = -x^2 that requires that different process shown in my posts.
> > It uses the same part of the parabola beginning x=0 and -y=-0.5 in the third quadrant
> > heading left( _x) and down(-y) and x=1 and y=0 in the first quadrant heading right(x) and up(y).
> > The same curve --->oo of the parabola only heading in opposite directions, +x\+y -x\-y.
> > > Adding complex numbers is just like normal vectors. The absolute value
> > > of a complex number is the same as taking the length of a vector.
> An easy way to find the negative square root of any number---
> In the first quadrant, say you want to find the negative square root of 36.
> Add (36+0.5) = 36.5, ((sqrt(36.5) -1)*-1) = - -5.0415229867...
>
> Cross check with the third quadrant --- (((((5.0415229867... *2) +2)^2)-2)/4)*-1 = -36
> -36 -y= (36 - 5.0415229867---)*-1 = -y= -30.9584770132... where -x+-y = -36.
> All this is doing is duplicating the parabolic curve beginning at certain points in the
> 1st and 3rd quadrants. 1st quadrant x= 1,y= 0. 3rd quadrant x= 0 ,-y= -0.5.
> The two curves going off in the opposite direction of one another.
> Leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=1 and y=0 into the first quadrant.
> and leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=0 and y= - 0.5 into the third quadrant.
> Creating an exact copy of the parabolic curve going in opposite directions. One curve in the positive
> x\y and one duplicate curve in the negative -x\-y where each point of x --> -x and y --> -y have the
> maximum separation dictated by the parabolic curve. What is this rate of separation for each point of
> x and -x , y and -y ?
>
>
> Dan

There is a exponential separation between y and -y after each integer processed in both quadrants..
In finding the right triangle the hypotenuse grows exponentially longer.
The x\-x axis has only 0.5 as side (a) and the only change in the hypotenuse (c) between integers is
the the new length side (b) where side (a) remains the same y= (0.5) length.
So the rate of separation between x\-x of each hypotenuse length grows at a much slower rate then the 2 points (y\-y) for each integer processed.

On Saturday, July 16, 2022 at 8:38:09 AM UTC-4, Dan joyce wrote:
> On Tuesday, July 12, 2022 at 10:59:51 AM UTC-4, Dan joyce wrote:
> > On Monday, July 11, 2022 at 4:19:28 PM UTC-4, Dan joyce wrote:
> > > On Monday, July 11, 2022 at 2:47:18 PM UTC-4, Chris M. Thomasson wrote:
> > > > On 7/11/2022 4:15 AM, 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.
> > > > The Mandelbrot set is a nice and _fun_ way to show off complex numbers.
> > > >
> > > > 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> > > > form adding PI/2 to it makes it rotate around counter clockwise to the
> > > > imaginary unit at 0+1i. Its real part is zero.
> > > >
> > > > The complex numbers are very similar to normal vectors, except when
> > > > multiplying, dividing, ect...
> > > As is in this case. It requires a different process for multiplying and the sqrt. function only.
> > > in the negative quadrant (-x\-y) opposed to the first quadrant where x+y =x^2.
> > > Which means -x+-y = -x^2 that requires that different process shown in my posts.
> > > It uses the same part of the parabola beginning x=0 and -y=-0.5 in the third quadrant
> > > heading left( _x) and down(-y) and x=1 and y=0 in the first quadrant heading right(x) and up(y).
> > > The same curve --->oo of the parabola only heading in opposite directions, +x\+y -x\-y.
> > > > Adding complex numbers is just like normal vectors. The absolute value
> > > > of a complex number is the same as taking the length of a vector.
> > An easy way to find the negative square root of any number---
> > In the first quadrant, say you want to find the negative square root of 36.
> > Add (36+0.5) = 36.5, ((sqrt(36.5) -1)*-1) = - -5.0415229867...
> >
> > Cross check with the third quadrant --- (((((5.0415229867... *2) +2)^2)-2)/4)*-1 = -36
> > -36 -y= (36 - 5.0415229867---)*-1 = -y= -30.9584770132... where -x+-y = -36.
> > All this is doing is duplicating the parabolic curve beginning at certain points in the
> > 1st and 3rd quadrants. 1st quadrant x= 1,y= 0. 3rd quadrant x= 0 ,-y= -0.5.
> > The two curves going off in the opposite direction of one another.
> > Leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=1 and y=0 into the first quadrant.
> > and leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=0 and y= - 0.5 into the third quadrant.
> > Creating an exact copy of the parabolic curve going in opposite directions. One curve in the positive
> > x\y and one duplicate curve in the negative -x\-y where each point of x --> -x and y --> -y have the
> > maximum separation dictated by the parabolic curve. What is this rate of separation for each point of
> > x and -x , y and -y ?
> >
> >
> > Dan
> There is a exponential separation between y and -y after each integer processed in both quadrants..
> In finding the right triangle the hypotenuse grows exponentially longer.
> The x\-x axis has only 0.5 as side (a) and the only change in the hypotenuse (c) between integers is
> the the new length side (b) where side (a) remains the same y= (0.5) length.
> So the rate of separation between x\-x of each hypotenuse length grows at a much slower rate then the 2 points (y\-y) for each integer processed.

Doing some triangulation from the third quadrant to the first quadrant
-y to y is the hypotenuse length = sqrt (a^2 + b^2) taken from side a,b below.
c =
2.1225226906132756389169748389479083440865903914552031882237560831428179284692158...
Side (a) is from third quadrant -x\-y to x\-y in the fourth quadrant =
side (a) length =
1.4494897427831780981972840747058913919659474806566701284326925672509603774573150...
Side (b) from x\-y in the fourth quadrant to x\y in the first quadrant =
b length =
1.5505102572168219018027159252941086080340525193433298715673074327490396225426849...
Multiply a*b =
10 * .22474487139158904909864203735294569598297374032833506421634628362548018872865751...
=
2.2474487139158904909864203735294569598297374032833506421634628362548018872865751...
The same as the negative sqrt(-1) *10.
and also a+b = 3
A classic example of 2 irrationals summed = an integer.

So
a right triangle within the first parameter of -x+-y = -x^2 =-1 through a
simple process has interesting math properties when triangulating a right triangle
within the 3 quadrants.

Triangulating the next -- -x+-y = -x^2 = -2. Again, produced through a
different process (-x+-y = -x^2)
sqrt (2.5) =
1.5811388300841896659994467722163592668597775696626084134287524263962972193196191...

+.5811388300841896659994467722163592668597775696626084134287524263962972193196191...
= a =
2.1622776601683793319988935444327185337195551393252168268575048527925944386392382...
b =
2.8377223398316206680011064555672814662804448606747831731424951472074055613607617...
Derived from -2 -
-.5811388300841896659994467722163592668597775696626084134287524263962972193196191
=-1.4188611699158103340005532277836407331402224303373915865712475736037027806803809...
+-.5 =
=-1.9188611699158103340005532277836407331402224303373915865712475736037027806803809
(+2.5) - (1.581138830084189665999446772216359266859777569662608413428752426396297219319619)*-1
= -0.918861169915810334000553227783640733140222430337391586571247573603702780680380889
= b
= -2.837722339831620668001106455567281466280444860674783173142495147207405561360761789
a*b has no relevance here.
a+b =5

Hypotenuse length from sqrt(a^2+b^2) =
3.5676480708784448925821073137180751226569847576953249535451884899220250936231137...

Next -x+-y = -x^2= -3
1.870828693386970692791874366158274650878009903889363473151872733660017578153469...
+0.870828693386970692791874366158274650878009903889363473151872733660017578153469...
=
(a) = 2.7416573867739413855837487323165493017560198077787269463037454673200351563069390...
(b) = 4.2583426132260586144162512676834506982439801922212730536962545326799648436930609...
a+b= 7
Hypotenuse length from sqrt(a^2+b^2) =
5.0645993956155165046488007814887632760480000444348255473186179861833484680981602

Next -x+-y = -x^2= -4
(a) = 3.2426406871192851464050661726290942357090156261308442195300392139721974353863211...
(b) = 5.7573593128807148535949338273709057642909843738691557804699607860278025646136788...
Again a+b = 9
(c) = sqrt(a^2+b^2)
= 6.6077155570874664261884248225403561849152682828511919850384332878401620445355386...
At this point (c) has no math implications after -x^2 = -1
Where the hypotenuse is 10* - .22474487.. where -.22474487..= -x for -x+-y =-x^2

So the next -- -x^2 = -5
Then a+b of the right triangle will = 11

On Sunday, July 17, 2022 at 3:32:35 PM UTC-4, djoyce099 wrote:
> On Saturday, July 16, 2022 at 8:38:09 AM UTC-4, Dan joyce wrote:
> > On Tuesday, July 12, 2022 at 10:59:51 AM UTC-4, Dan joyce wrote:
> > > On Monday, July 11, 2022 at 4:19:28 PM UTC-4, Dan joyce wrote:
> > > > On Monday, July 11, 2022 at 2:47:18 PM UTC-4, Chris M. Thomasson wrote:
> > > > > On 7/11/2022 4:15 AM, 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.
> > > > > The Mandelbrot set is a nice and _fun_ way to show off complex numbers.
> > > > >
> > > > > 1+0i is 100% real because it's imaginary component is zero. Wrt polar
> > > > > form adding PI/2 to it makes it rotate around counter clockwise to the
> > > > > imaginary unit at 0+1i. Its real part is zero.
> > > > >
> > > > > The complex numbers are very similar to normal vectors, except when
> > > > > multiplying, dividing, ect...
> > > > As is in this case. It requires a different process for multiplying and the sqrt. function only.
> > > > in the negative quadrant (-x\-y) opposed to the first quadrant where x+y =x^2.
> > > > Which means -x+-y = -x^2 that requires that different process shown in my posts.
> > > > It uses the same part of the parabola beginning x=0 and -y=-0.5 in the third quadrant
> > > > heading left( _x) and down(-y) and x=1 and y=0 in the first quadrant heading right(x) and up(y).
> > > > The same curve --->oo of the parabola only heading in opposite directions, +x\+y -x\-y.
> > > > > Adding complex numbers is just like normal vectors. The absolute value
> > > > > of a complex number is the same as taking the length of a vector.
> > > An easy way to find the negative square root of any number---
> > > In the first quadrant, say you want to find the negative square root of 36.
> > > Add (36+0.5) = 36.5, ((sqrt(36.5) -1)*-1) = - -5.0415229867...
> > >
> > > Cross check with the third quadrant --- (((((5.0415229867... *2) +2)^2)-2)/4)*-1 = -36
> > > -36 -y= (36 - 5.0415229867---)*-1 = -y= -30.9584770132... where -x+-y = -36.
> > > All this is doing is duplicating the parabolic curve beginning at certain points in the
> > > 1st and 3rd quadrants. 1st quadrant x= 1,y= 0. 3rd quadrant x= 0 ,-y= -0.5.
> > > The two curves going off in the opposite direction of one another.
> > > Leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=1 and y=0 into the first quadrant.
> > > and leaving out the vertex and curve from x=.5 and y= -0.25 ---> x=0 and y= - 0.5 into the third quadrant.
> > > Creating an exact copy of the parabolic curve going in opposite directions. One curve in the positive
> > > x\y and one duplicate curve in the negative -x\-y where each point of x --> -x and y --> -y have the
> > > maximum separation dictated by the parabolic curve. What is this rate of separation for each point of
> > > x and -x , y and -y ?
> > >
> > >
> > > Dan
> > There is a exponential separation between y and -y after each integer processed in both quadrants..
> > In finding the right triangle the hypotenuse grows exponentially longer.
> > The x\-x axis has only 0.5 as side (a) and the only change in the hypotenuse (c) between integers is
> > the the new length side (b) where side (a) remains the same y= (0.5) length.
> > So the rate of separation between x\-x of each hypotenuse length grows at a much slower rate then the 2 points (y\-y) for each integer processed.
> Doing some triangulation from the third quadrant to the first quadrant
> -y to y is the hypotenuse length = sqrt (a^2 + b^2) taken from side a,b below.
> c =
> 2.1225226906132756389169748389479083440865903914552031882237560831428179284692158...
> Side (a) is from third quadrant -x\-y to x\-y in the fourth quadrant =
> side (a) length =
> 1.4494897427831780981972840747058913919659474806566701284326925672509603774573150...
> Side (b) from x\-y in the fourth quadrant to x\y in the first quadrant =
> b length =
> 1.5505102572168219018027159252941086080340525193433298715673074327490396225426849...
> Multiply a*b =
> 10 * .22474487139158904909864203735294569598297374032833506421634628362548018872865751...
> =
> 2.2474487139158904909864203735294569598297374032833506421634628362548018872865751...
> The same as the negative sqrt(-1) *10.
> and also a+b = 3
> A classic example of 2 irrationals summed = an integer.
>
> So
> a right triangle within the first parameter of -x+-y = -x^2 =-1 through a
> simple process has interesting math properties when triangulating a right triangle
> within the 3 quadrants.
>
> Triangulating the next -- -x+-y = -x^2 = -2. Again, produced through a
> different process (-x+-y = -x^2)
> sqrt (2.5) =
> 1.5811388300841896659994467722163592668597775696626084134287524263962972193196191...
>
> +.5811388300841896659994467722163592668597775696626084134287524263962972193196191...
> = a =
> 2.1622776601683793319988935444327185337195551393252168268575048527925944386392382...
> b =
> 2.8377223398316206680011064555672814662804448606747831731424951472074055613607617...
> Derived from -2 -
> -.5811388300841896659994467722163592668597775696626084134287524263962972193196191
> =-1.4188611699158103340005532277836407331402224303373915865712475736037027806803809...
> +-.5 =
> =-1.9188611699158103340005532277836407331402224303373915865712475736037027806803809
> (+2.5) - (1.581138830084189665999446772216359266859777569662608413428752426396297219319619)*-1
> = -0.918861169915810334000553227783640733140222430337391586571247573603702780680380889
> = b
> = -2.837722339831620668001106455567281466280444860674783173142495147207405561360761789
> a*b has no relevance here.
> a+b =5
>
> Hypotenuse length from sqrt(a^2+b^2) =
> 3.5676480708784448925821073137180751226569847576953249535451884899220250936231137...
>
> Next -x+-y = -x^2= -3
> 1.870828693386970692791874366158274650878009903889363473151872733660017578153469...
> +0.870828693386970692791874366158274650878009903889363473151872733660017578153469...
> =
> (a) = 2.7416573867739413855837487323165493017560198077787269463037454673200351563069390...
> (b) = 4.2583426132260586144162512676834506982439801922212730536962545326799648436930609...
> a+b= 7
> Hypotenuse length from sqrt(a^2+b^2) =
> 5.0645993956155165046488007814887632760480000444348255473186179861833484680981602
>
> Next -x+-y = -x^2= -4
> (a) = 3.2426406871192851464050661726290942357090156261308442195300392139721974353863211...
> (b) = 5.7573593128807148535949338273709057642909843738691557804699607860278025646136788...
> Again a+b = 9
> (c) = sqrt(a^2+b^2)
> = 6.6077155570874664261884248225403561849152682828511919850384332878401620445355386...
> At this point (c) has no math implications after -x^2 = -1
> Where the hypotenuse is 10* - .22474487.. where -.22474487..= -x for -x+-y =-x^2
>
> So the next -- -x^2 = -5
> Then a+b of the right triangle will = 11

What is confusing in all this is that negative values are not the same as
there positive counterparts when the sqrt(-n) and the sqrt(n) is performed
for the same (n) due to the different process of sqrt(-n) .
Also in the same vein, -n^2 and n^2 an entirely different process for -n^2
compared to the conventional process for n^2.
Where it gets interesting is when like knowing the sqrt(-1) = -.224744871...,
just add -1 = (-1.224744871...) ^2 in the conventional manner = 1.5.
So instead of the tedius process of (((sqrt(n*4+2))-2)/2)*-1 = -.224744871...
where (n=1)*-1 =-1 or the squaring of -.224744871...
(((((.224744871...*2)+2)^2)-2)/4)*-1 =-1
So instead of going through all that use the first quadrant of x+y = x^2
To find the square root of negative (-1) add .5 =1.5
sqrt(1.5) = 1.224744871... Now subtract 1 = (.224744871...)*-1 = sqrt(-1)
sqrt(2.5) = 1.58113883... subtract 1 = (.58113883...)*-1 = sqrt(-2)
sqrt(3.5) = 1.87082869... subtract 1 = (.87082869...)*-1 = sqrt(-3)
and so on
sqrt(pi+.5) = 1.90829574... subtract 1 =(.90829574...)*-1 = sqrt(-pi)
Square the sqrt(-pi) using the tedius method above for squaring negative
values -- (((((.90829574...*2)+2)^2)-2)/4)*-1 = -pi to confirm -.90829574...
is the sqrt(-pi).

Also the x axis is shiffted from (oo<---(-x),y=0,x--->oo)
to, starts at (-x=0,-y=-0.5,oo<---(-x)).