In AP's 188th book of Science, he derives the Infinity borderline of mathematics from the Physics constants of speed of light and Planck's constant.

As I write in my 188th book of science:

So, I am trying to obtain the infinity borderline from that of speed of light constant. The infinity borderline is 1*10^604 from Huygen's tractrix and from AP's regular polyhedra existence coming from 120 = 5! of all possible angles at infinity border represented in the 6 regular polyhedra.

So I notice that 604/23 and 604/26 are connected.

I note that speed of light is 3.16*10^8 meters/second
I note that Planck's constant in eV*Hz^-1 and in eV*seconds is 4.135*10^-15 and 6.582*10^-16 eV*second respectively.

So I divide both by 3.16*10^8 and obtain in the first 1*10^-23 and 2*10^-24 in seconds.

Logical Reasoning: The square root of 604 is 24.57. If we view infinity borderline as a Psi^2 of physics probability. Then we can argue that Planck's constant squared is 604 from 24.57... from that of 1*10^-23 and 2*10^-24 in seconds.

On Friday, May 20, 2022 at 2:57:10 PM UTC-5, Archimedes Plutonium wrote:
> In AP's 188th book of Science, he derives the Infinity borderline of mathematics from the Physics constants of speed of light and Planck's constant.
>
> As I write in my 188th book of science:
>
> So, I am trying to obtain the infinity borderline from that of speed of light constant. The infinity borderline is 1*10^604 from Huygen's tractrix and from AP's regular polyhedra existence coming from 120 = 5! of all possible angles at infinity border represented in the 6 regular polyhedra.
>
> So I notice that 604/23 and 604/26 are connected.

So, earlier this year I noticed a remarkable feature of the number 604, perhaps a unique feature that no other number in mathematics has (not sure of that claim as yet)?

The feature of 604/23 = 26.260....

while 604/26 = 23.230....

Let me call this very special math feature of a Psi^2 of mathematics. A physics feature upon mathematics. For I do not know if that feature is Unique to mathematics. It is a upper and lower bound on 604.

So, we ask the mathematicians worth their weight in salt, can you come up with another Psi^2 number in mathematics, or is 604 the only Psi^2 number in all of mathematics.

AP, King of Science, especially physics-chemistry

On Friday, May 20, 2022 at 3:42:50 PM UTC-5, Archimedes Plutonium wrote:

>
> The feature of 604/23 = 26.260....
>
> while 604/26 = 23.230....
>
> Let me call this very special math feature of a Psi^2 of mathematics. A physics feature upon mathematics. For I do not know if that feature is Unique to mathematics. It is a upper and lower bound on 604.
>
> So, we ask the mathematicians worth their weight in salt, can you come up with another Psi^2 number in mathematics, or is 604 the only Psi^2 number in all of mathematics.
>

So, here is a fascinating question of both physics and mathematics. Is the pure number of 604 with square root being 24.57641.... the only number in all of mathematics that is boxed in by an upper and lower bound of 26.260 and 23.230?

Is there any other number in pure math that has those upper and lower bound features. Or is 604 unique with those features.

I tried making a algebra formula to guide to see if any other number is like that. To no avail.

AP

On Friday, May 20, 2022 at 7:43:42 PM UTC-5, Archimedes Plutonium wrote:
> On Friday, May 20, 2022 at 3:42:50 PM UTC-5, Archimedes Plutonium wrote:
>
> >
> > The feature of 604/23 = 26.260....
> >
> > while 604/26 = 23.230....
> >
> > Let me call this very special math feature of a Psi^2 of mathematics. A physics feature upon mathematics. For I do not know if that feature is Unique to mathematics. It is a upper and lower bound on 604.
> >
> > So, we ask the mathematicians worth their weight in salt, can you come up with another Psi^2 number in mathematics, or is 604 the only Psi^2 number in all of mathematics.
> >
> So, here is a fascinating question of both physics and mathematics. Is the pure number of 604 with square root being 24.57641.... the only number in all of mathematics that is boxed in by an upper and lower bound of 26.260 and 23.230?
>
> Is there any other number in pure math that has those upper and lower bound features. Or is 604 unique with those features.
>
> I tried making a algebra formula to guide to see if any other number is like that. To no avail.
>

Now we can see that 23.23 x 26 = 603.98

while 26.26 x 23 = 603.98

And I was using that as a algebra to see if I can spot any other integer like 604 with that amazing symmetry.

Of course algebra cannot fetch out some symmetries.

And of course there are 2 Planck constants, and this 2 constants makes 604 be a special and unique integer.

AP

So far, found no counterexample to the claim, that the whole number 604 has a unique division of 604/23 = 26.260... and 604/26 = 23.230... Let me call it a Symmetry Number. And this is needed for physics of speed of light versus two Planck constants.

Math needs something very special with a infinity border number which is exactly 1*10^604. And unless I can find a counterexample, that 604 is unique in this feature.

I keep looking, tonight tried 1208 and 60400. No luck.

So I think 604 has a uniqueness not possessed by any other number, unless we want to call 1 as Symmetry, perfect symmetry number.

AP

On Sunday, May 22, 2022 at 1:47:10 AM UTC-5, Archimedes Plutonium wrote:
> So far, found no counterexample to the claim, that the whole number 604 has a unique division of 604/23 = 26.260... and 604/26 = 23.230... Let me call it a Symmetry Number. And this is needed for physics of speed of light versus two Planck constants.
>
> Math needs something very special with a infinity border number which is exactly 1*10^604. And unless I can find a counterexample, that 604 is unique in this feature.
>
> I keep looking, tonight tried 1208 and 60400. No luck.
>
> So I think 604 has a uniqueness not possessed by any other number, unless we want to call 1 as Symmetry, perfect symmetry number.

This book of mine, 188th is about translating language into math or science format. So let me translate that remarkable feature of the number 604, perhaps a unique feature in all of mathematics. And we expect something special of a number which involves the Infinity borderline of math and physics 1*10^604 and 1*10^-604.

That algebra translation is this.

x= 604
y= 23
z= 26

x/y = z + (z/1000)
x/z = y + (y/1000)

So the question burning on my mind, is the number 604 the only solution number?

AP

On Sunday, May 22, 2022 at 4:02:19 PM UTC-5, Archimedes Plutonium wrote:
> On Sunday, May 22, 2022 at 1:47:10 AM UTC-5, Archimedes Plutonium wrote:
> > So far, found no counterexample to the claim, that the whole number 604 has a unique division of 604/23 = 26.260... and 604/26 = 23.230... Let me call it a Symmetry Number. And this is needed for physics of speed of light versus two Planck constants.
> >
> > Math needs something very special with a infinity border number which is exactly 1*10^604. And unless I can find a counterexample, that 604 is unique in this feature.
> >
> > I keep looking, tonight tried 1208 and 60400. No luck.
> >
> > So I think 604 has a uniqueness not possessed by any other number, unless we want to call 1 as Symmetry, perfect symmetry number.
> This book of mine, 188th is about translating language into math or science format. So let me translate that remarkable feature of the number 604, perhaps a unique feature in all of mathematics. And we expect something special of a number which involves the Infinity borderline of math and physics 1*10^604 and 1*10^-604.
>
> That algebra translation is this.
>
> x= 604
> y= 23
> z= 26
>
> x/y = z + (z/1000)
> x/z = y + (y/1000)
>
> So the question burning on my mind, is the number 604 the only solution number?
>
So, can I go anywhere with these two simultaneous equations? Can I find another solution, other than 604, between 1 and 1000? I doubt it. And so here is a case in point where those two equations need to be plugged into a computer search program to see if 604 is the only such number between 1 and 1000 that solves those two equations.

AP

On Sunday, May 22, 2022 at 4:02:19 PM UTC-5, Archimedes Plutonium wrote:
> On Sunday, May 22, 2022 at 1:47:10 AM UTC-5, Archimedes Plutonium wrote:
> > So far, found no counterexample to the claim, that the whole number 604 has a unique division of 604/23 = 26.260... and 604/26 = 23.230... Let me call it a Symmetry Number. And this is needed for physics of speed of light versus two Planck constants.
> >
> > Math needs something very special with a infinity border number which is exactly 1*10^604. And unless I can find a counterexample, that 604 is unique in this feature.
> >
> > I keep looking, tonight tried 1208 and 60400. No luck.
> >
> > So I think 604 has a uniqueness not possessed by any other number, unless we want to call 1 as Symmetry, perfect symmetry number.
> This book of mine, 188th is about translating language into math or science format. So let me translate that remarkable feature of the number 604, perhaps a unique feature in all of mathematics. And we expect something special of a number which involves the Infinity borderline of math and physics 1*10^604 and 1*10^-604.
>
> That algebra translation is this.
>
> x= 604
> y= 23
> z= 26

My mistake:
x/y = z + (z/100) + (0/1000)
x/z = y + (y/100) + (0/1000)

So the question burning on my mind, is the number 604 the only solution number?

On Monday, May 23, 2022 at 9:33:09 AM UTC-5, Archimedes Plutonium wrote:
> > That algebra translation is this.
> >
> > x= 604
> > y= 23
> > z= 26
> My mistake:
> x/y = z + (z/100) + (0/1000)
> x/z = y + (y/100) + (0/1000)
> So the question burning on my mind, is the number 604 the only solution number?

AP has been in science far too long to know that a problem of math never has just one angle of interpretation. That all science and math has 2 angles of attack.

What I am thinking is the above two simultaneous equations

x/y = z + (z/100) + (0/1000)
x/z = y + (y/100) + (0/1000)

and multiplying by yz gives

xz = yz^2 + yz^2/100 + 0/1000
xy = zy^2 + zy^2/100 + 0/1000

Multiply by 1000

1000xz = 1000yz^2 + 10yz^2
1000xy = 1000zy^2 + 10 zy^2

And I ask the question, are those parabolas? If so, a parabola has a unique focal point, or a unque apex point.

AP

On Monday, May 23, 2022 at 2:53:05 PM UTC-5, Archimedes Plutonium wrote:
> On Monday, May 23, 2022 at 9:33:09 AM UTC-5, Archimedes Plutonium wrote:
> > > That algebra translation is this.
> > >
> > > x= 604
> > > y= 23
> > > z= 26
> > My mistake:
> > x/y = z + (z/100) + (0/1000)
> > x/z = y + (y/100) + (0/1000)
> > So the question burning on my mind, is the number 604 the only solution number?
> AP has been in science far too long to know that a problem of math never has just one angle of interpretation. That all science and math has 2 angles of attack.
>
> What I am thinking is the above two simultaneous equations
> x/y = z + (z/100) + (0/1000)
> x/z = y + (y/100) + (0/1000)
> and multiplying by yz gives
>
> xz = yz^2 + yz^2/100 + 0/1000
> xy = zy^2 + zy^2/100 + 0/1000
>
> Multiply by 1000
>
> 1000xz = 1000yz^2 + 10yz^2
> 1000xy = 1000zy^2 + 10 zy^2
>
> And I ask the question, are those parabolas? If so, a parabola has a unique focal point, or a unque apex point.

Dividing the first equation by z and the second by y, gives.

1000x = 1000yz + 10yz
1000x = 1000zy + 10 zy

Adding up both gives.

2000x = 2000yz + 20yz

Dividing by 20 gives.

100x = 100yz + yz

100x = 101yz

I am not sure I can recognize 604 and 23, and 26 in that equation.

Let me try:

100 x 604 = 60400

101x 23 x 26 = 60398 close enough, but I must have missed something in the algebra.

If it is a parabola, I certainly have the uniqueness I have been searching for. For a parabola has a unique focal point but it also has a unique point of inflection along its straightline curve which I call the apex tip of the parabola.

AP

I changed my mind. It is probably not a parabola but a pencil ellipse I so often have been talking about, for all light waves are pencil ellipses.

But not to worry for a ellipse has unique points just as well as the parabola, and even more so.

Because in this exercise I have been dealing with 2 Planck constants and the speed of light.

And the idea that infinity borderline has a microinfinity also. Where we have 2 infinities-- 1*10^-604 and 1*10^604. A parabola cannot deal with 2 infinity borderlines but a ellipse, especially a pencil ellipse can deal with 2 borderlines.

Yes, yes indeed, I am dealing with a pencil ellipse.

And everyone should expect the true infinity borderline to have some SPECIAL FEATURE OF ALGEBRA-- a uniqueness of roots of the exponent 604. The number 604 has to be as special as the number "pi" has 3 zero digits in a row in 604 place value.

AP

Now the traditional parabola formula is Y = kxx.

And Old Math calls it a vertex, but I prefer Apex because a vertex to me is a sharp corner.

And what I get is 100x = 101yz.

On Monday, May 23, 2022 at 11:57:54 PM UTC-5, Archimedes Plutonium wrote:
> Now the traditional parabola formula is Y = kxx.
>
> And Old Math calls it a vertex, but I prefer Apex because a vertex to me is a sharp corner.
>
> And what I get is 100x = 101yz.

I am edging ever more closer to a final solution of uniqueness. If we study the parabola we see a factor of 1/4 for focal point and apex.

As I solved prior to the above formula 100x = 101yz that turns out to be 60398 rather than 60400, and missing by 2 for precision.

But instead of the parabola with factor 1/4, what I need is a factor of 1/6, for the 6 involved, so that if we have 101 x 6 = 606 which misses the precision mark of 604 by 2 extra.

Looking at geometry figures for x = yz in 3rd dimension I end up with ellipsoids or with rectangular boxes enclosing ellipsoids. This is where I get a factor of 1/6 or what I need the factor 6, for 6 faces. Same can be said of a reduction to cube with sphere inside is a factor of 6 faces.

So I cannot escape notice that my formula of 100x = 101yz is unique in number 604 as a factor of 6, where we eliminate the 2 short of 60400, by having 2 extra in 606.

So, well, that is a proof of Uniqueness of the number 604 as the only number in all of mathematics (except the trivial solution 1) that 604 is the unique number in all of mathematics that obeys Symmetry of exponent. This is required in a Infinity Borderline Number 1*10^604 and its inverse microinfinity.

Now, I dare any computer program operator, any computer expert, I dare and challenge him or her to come up with a counterexample. For I am stating emphatically that the only number in all of mathematics (besides the trivial solution 1) to have this property is 604.

The Property stated again is that 604, 604/23 = 26.260.. while 604/26 = 23.230..

A counterexample would have this Mirror Reflected Symmetry.

And this is so important for physics for physics constantly has to shift back and forth between h and h-bar in Planck's constant and this shifting back and forth is because infinity shifts back and forth between 23.230 and 26..260.

So I encourage and challenge any computer expert to see if they can defeat my mini proof above that 604 is unique with this property. Give it a go, for I am confident I win.

AP, King of Science, especially physics-chemistry, and math is but a brunch snack for the King