Lo and behold, the 256 in 0.256 is itself a perfect square of 16^2 as is 25 = 5^2. Notice also that the square root of 0.256 is 0.505... and perhaps is the prefix number for the Dirac magnetic monopole 0.5MeV that JJ Thomson discovered in 1897.

So all I need is to show that where Meissel-Mertens obtained a constant from primes, reciprocal prime summation of 0.261, AP needs to find a Constant from Perfect Squares of value of 0.256.

I am beginning to see a Rate Constant in Chemistry of 0.256. Have to check more into that.

AP

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On Sunday, September 24, 2023 at 3:07:24 PM UTC-5, Archimedes Plutonium wrote:

Lo and behold, the 256 in 0.256 is itself a perfect square of 16^2 as is 25 = 5^2. Notice also that the square root of 0.256 is 0.505... and perhaps is the prefix number for the Dirac magnetic monopole 0.5MeV that JJ Thomson discovered in 1897.

So all I need is to show that where Meissel-Mertens obtained a constant from primes, reciprocal prime summation of 0.261, AP needs to find a Constant from Perfect Squares of value of 0.256.

I am beginning to see a Rate Constant in Chemistry of 0.256. Have to check more into that.

Chemistry has an Equilibrium Constant that is sometimes the value of 0.256. Can we begin to see that gravity is a form of equilibrium between electricity shot from one mass particle into a second mass particle and whose pathes are following the magnetic
field of lines of force of 1st mass particle (Sun to Earth)??? I suspect so.

Can we find something special in Chemistry that the 0.256 is extraordinary over all other Chemical Equilibrium constants?

Now I must begin to make clear what the EM force is beyond gravity. In gravity Sun to Earth, the Sun sets Lines of Magnetic Force in Space, and planet Earth follows in that magnetic lines of force, but the Sun also pushes and pulls on Earth in that
magnetic field lines of force path. Pushing Earth by hitting it aft with electric current and pulling Earth fore by electric current what is called emf potential.

Can I describe the Coulomb force in the same manner??? A magnetic field path of lines of force, then a push and pull by magnetic monopoles of electricity pushing and pulling the particle as it moves in the path.

As for the Strong Nuclear force, no need since Atoms have no nucleus, but are elaborate structures of toruses. In fact the donut hole of a torus is empty space of a nucleus except for neutron parallel plate capacitors in that donut hole.

The Weak Nuclear force is more of a imbalance in atoms and the atom is attempting to correct the imbalance by emission.

So, well, this is wrapping up nicely, to where no-one in the future needs to measure experimentally the Constant of Newton Gravity, for it is the PSI -squared of 1.618*10^-19 magnetic monopole (Millikan oil drop experiment) times the constant 0.256 which
is the minimum for PSI-squared in space.

Looking up the precision of 1.618*10^-19 and how close Millikan arrived at that. Apparently it is exact with the oil drop experiment in concert agreement.

AP, King of Science especially physics and logic

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My last few posts on this topic gave me the idea of Crafting, and Constructing a Constant of Physics.

Notice that the 0.256 constant begins a pattern with Psi^2 of physics. For 25 square root is 5 and 256 square root begets 16. Now what should be the next digit in the constant 0.256 ???? Well, if we allow fractions in the square root then 2560 is the
square root of 50.6 so our next digit in the Constant 0.256 is 0.2560. Then the next digit is going to be another 0 as that of 0.25600 for 160^2.

Thus, I build a Constant of Physics and Chemistry.

Now, is the number 0.256.... special in this regard?? Can another number create craft construct a constant whose digits are square and square root for successive digits. Or does 0.256 stand alone in this feature trait??

AP

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Page 2-10, Feynman Lectures on Physics, 1963, discusses the force of gravity relative strength against the other forces. Feynman puts it at 10^-40 and says it is a dimensionless coupling constant.

I am assuming that Feynman got that number from knowing the Newton Gravitational Constant in terms of eV measure units is 6.70*10^-39 GeV/c^2. Correct me if wrong.

And we can see from this that by 1963, Feynman should have eliminated all measure units except eV. Convert everything possible in Physics to eV.

As AP keeps saying of the Primal Axiom over all physics, overall science is -- All is Atom, and Atoms are nothing but electricity and magnetism.

When we have thousands of different measuring units-- joule, BTU, horsepower, dynes, Newton, Newton *meter, etc etc we end up with scatterbrained physics.

Just like in mathematics with their thousands of different functions for calculus, when calculus has but one Valid function-- the polynomial, and that is why Old Math is kook and scatterbrained.

So , please, in physics, convert every unit-measure to eV, electron volt and thereby we can relate one topic to another.

AP, King of Science

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An example of my forgetfulness is that I meant Asimov, not Gamow. Asimov wrote 280 science books, several novels and many short stories in addition to being editor of many publications. AP should surpass Asimov by 2025. But there is a huge difference in
writing original science ideas books and books written to explain science already known.

AP

--- SoupGate-Win32 v1.05
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On Sunday, September 24, 2023 at 7:21:45 PM UTC-5, Archimedes Plutonium wrote:

Page 2-10, Feynman Lectures on Physics, 1963, discusses the force of gravity relative strength against the other forces. Feynman puts it at 10^-40 and says it is a dimensionless coupling constant.

I am assuming that Feynman got that number from knowing the Newton Gravitational Constant in terms of eV measure units is 6.70*10^-39 GeV/c^2. Correct me if wrong.

And we can see from this that by 1963, Feynman should have eliminated all measure units except eV. Convert everything possible in Physics to eV.

As AP keeps saying of the Primal Axiom over all physics, overall science is -- All is Atom, and Atoms are nothing but electricity and magnetism.

When we have thousands of different measuring units-- joule, BTU, horsepower, dynes, Newton, Newton *meter, etc etc we end up with scatterbrained physics.

Just like in mathematics with their thousands of different functions for calculus, when calculus has but one Valid function-- the polynomial, and that is why Old Math is kook and scatterbrained.

So , please, in physics, convert every unit-measure to eV, electron volt and thereby we can relate one topic to another.

I decided to bump this book up in the cue line to be my 257th published book of science.

Ironic and funny that my previous published book was 256th was the number digits of 0.256 that I make so much fuss over in this book, my 257th.

But considering the huge importance of the subject material, and the fact that this book is near complete while my alternative 257th book is quasi complete, I chose to publish this book first.

And that is good for my ultimate request in life-- AP publishing at least 500 books of science. I am on track for that. I believe I have 20 more good years in health and fitness, publishing one book per month. By the end of 2023, I will be at my 260th
book. Then 12 books per year for 20 years makes 240 books. So 240 + 260 = 500 books. I am already gearing myself and psyching myself for that accomplishment. Pray my health keeps going, although I am painfully beginning to notice forgetfulness.
Forgetfulness can halt my writing if it gets bad enough, but no signs of that with this book of 257th.


And this book is a pleasure as a fast book. I mean, I started this book Sept 23 and here it is Sept 24 almost complete. So in two days time, I can write a important meaningful book of science. That is probably a world record, not even Gamow could do such,
not Feynman.

This is what it means-- to live a life of Science-- Atom.

AP

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Call them the AP PSI-squared numbers. Here I build psi-squared numbers for physics constants.

So let me try another number other than the 0.25600.

Let me see if a different number can serve to build a psi-squared pattern. Let me start with the digit 3 instead of 2 and I have 0.3 and the next digit has to be 6 to make a psi-squared. So far I have 0.36. Now what is the next digit such that it is
square root of 36d ??? Well, that is pretty easy for it is 0.361 since 19^2 is 361. What is the next digit for 0.361d such that it is psi-squared? Well, it is not a whole number but 0.3612 for 60.1. Then 0.36120 and I am stuck. So maybe 0.256 is unique
in psi-squared building.

Let me try another number 0.16d and the first psi is 4 for 16. The next digit is 9 to make 0.169 for 13^2. What is the d in 0.169d? And here it falls apart.

Again is there something special with 0.256 as a psi-squared number??

AP

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On Monday, September 25, 2023 at 3:44:45 PM UTC-5, Archimedes Plutonium wrote:

So I am wavering today, not steady and assured.

So the Golden Mean number 1.618... is truly marvelous for I square it and it seems to produce the identical digits.

1.618 x 1.618 = 2.618 provided we go far enough out on the digits 1.61803398874989 etc etc

But how about 2.618033988 X 0.261803 = 0.685409

We started with Coulomb magnetic monopole force of 1.602176*10^-19 for which I am saying is really 1.618 instead of 1.602. How much sigma error is that? 1.618/1.602 = 0.9% sigma error, quite acceptable.

We started with G gravitational constant in eV units as 6.70*10^-39 GeV/c^2

If I multiply 1.618 by 1.618 then I end up with 2.618 and if I then multiply by 0.256 I end up with what I need of 0.670. Perfectly with what I need. But is there a physics constant of 0.256 that relates to Psi-squared of quantum mechanics?

There is a Meissel-Mertens constant of 0.261 but it talks about using prime numbers. I need to use only squares and square roots for Psi-squared. The sigma error here is 261/256 = 1.9% not acceptable. However, here I need to replace primes with that of

Perfect Squares 1, 4, 9, 16, 25, etc and the constant that emerges from that replacement may very well be 0.256. If that is true, well, case is solved. If not true, then I look at 6.70 for doctoring-up.

Could it be that the Gravity constant 6.70*10^-39 GeV/c^2 needs doctoring up to be that of 6.618 rather than 6.70.

If I doctor-up the Gravity Constant 6.70 to be 6.618, then divide by 2.618, I end up with a constant of 0.252 needed, rather than 0.256. Much further away from the Meissel-Mertens constant of 0.261.

Here I am going to stick with 6.70, for, afterall, we should stick with what we seek to derive and not quibble over whether it is off.

In fact, now, let me try this whole entire exercise with sticking to the numbers provided by researchers and experimentalists.

So I take 1.602 x 1.602, and getting 2.566*10^-38 for magnetic monopole. Now I need a factor to reach 6.70*10^-38. And here we have for pure experimental research we have 6.70 divided by 2.566, we have 2.61 calling for a constant of math or physics of 0.
261. Which, lo and behold is the Meissel-Mertens constant smack dab on.

The only reason I am not accepting that at this moment is I spent decades getting rid of prime numbers.

AP

--- SoupGate-Win32 v1.05
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So I am wavering today, not steady and assured.

So the Golden Mean number 1.618... is truly marvelous for I square it and it seems to produce the identical digits.

1.618 x 1.618 = 2.618 provided we go far enough out on the digits 1.61803398874989 etc etc

But how about 2.618033988 X 0.261803 = 0.685409

We started with Coulomb magnetic monopole force of 1.602176*10^-19 for which I am saying is really 1.618 instead of 1.602. How much sigma error is that? 1.618/1.602 = 0.9% sigma error, quite acceptable.

We started with G gravitational constant in eV units as 6.70*10^-39 GeV/c^2

If I multiply 1.618 by 1.618 then I end up with 2.618 and if I then multiply by 0.256 I end up with what I need of 0.670. Perfectly with what I need. But is there a physics constant of 0.256 that relates to Psi-squared of quantum mechanics?

There is a Meissel-Mertens constant of 0.261 but it talks about using prime numbers. I need to use only squares and square roots for Psi-squared. The sigma error here is 261/256 = 1.9% not acceptable. However, here I need to replace primes with that of
Perfect Squares 1, 4, 9, 16, 25, etc and the constant that emerges from that replacement may very well be 0.256. If that is true, well, case is solved. If not true, then I look at 6.70 for doctoring-up.

Could it be that the Gravity constant 6.70*10^-39 GeV/c^2 needs doctoring up to be that of 6.618 rather than 6.70.

AP

--- SoupGate-Win32 v1.05
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On Monday, September 25, 2023 at 4:09:27 PM UTC-5, Archimedes Plutonium wrote:

On Monday, September 25, 2023 at 3:44:45 PM UTC-5, Archimedes Plutonium wrote:

So I am wavering today, not steady and assured.

So the Golden Mean number 1.618... is truly marvelous for I square it and it seems to produce the identical digits.

1.618 x 1.618 = 2.618 provided we go far enough out on the digits 1.61803398874989 etc etc

But how about 2.618033988 X 0.261803 = 0.685409

We started with Coulomb magnetic monopole force of 1.602176*10^-19 for which I am saying is really 1.618 instead of 1.602. How much sigma error is that? 1.618/1.602 = 0.9% sigma error, quite acceptable.

We started with G gravitational constant in eV units as 6.70*10^-39 GeV/c^2

If I multiply 1.618 by 1.618 then I end up with 2.618 and if I then multiply by 0.256 I end up with what I need of 0.670. Perfectly with what I need. But is there a physics constant of 0.256 that relates to Psi-squared of quantum mechanics?

There is a Meissel-Mertens constant of 0.261 but it talks about using prime numbers. I need to use only squares and square roots for Psi-squared. The sigma error here is 261/256 = 1.9% not acceptable. However, here I need to replace primes with that

of Perfect Squares 1, 4, 9, 16, 25, etc and the constant that emerges from that replacement may very well be 0.256. If that is true, well, case is solved. If not true, then I look at 6.70 for doctoring-up.

Could it be that the Gravity constant 6.70*10^-39 GeV/c^2 needs doctoring up to be that of 6.618 rather than 6.70.

If I doctor-up the Gravity Constant 6.70 to be 6.618, then divide by 2.618, I end up with a constant of 0.252 needed, rather than 0.256. Much further away from the Meissel-Mertens constant of 0.261.

Here I am going to stick with 6.70, for, afterall, we should stick with what we seek to derive and not quibble over whether it is off.

In fact, now, let me try this whole entire exercise with sticking to the numbers provided by researchers and experimentalists.

So I take 1.602 x 1.602, and getting 2.566*10^-38 for magnetic monopole. Now I need a factor to reach 6.70*10^-38. And here we have for pure experimental research we have 6.70 divided by 2.566, we have 2.61 calling for a constant of math or physics of

0.261. Which, lo and behold is the Meissel-Mertens constant smack dab on.

The only reason I am not accepting that at this moment is I spent decades getting rid of prime numbers.

I refuse to believe that prime numbers are a part of physics. Primes never show up in the Chart of Chemical Elements as a physical reality. Primes are nonexistent in chemistry and so nonexistent in physics.

However, in the above, primes in the form of Meissel-Mertens constant appear to show up. However, my hunch is that Coulomb force should be 1.618 and not 1.602*10^-19. That calls for a constant 0.256. Call it the AP constant which has not yet been
discovered by the broader physics and math community. A constant 0.256 that delivers Gravity constant of 6.70*10^-39 GeV/c^2 exactly.

The theory behind AP's derivation of the constant of gravity is based upon Psi-squared of quantum mechanics. Of turning waves into material mass which is then affected by electricity and magnetism.

For gravity I am purely looking for the smallest force possible on two separate objects of mass. The smallest EM force possible. Both Coulomb force and gravity force have identical math formulas-- inverse square with distance, telling us both are the
same, only difference is one is the weakest form of Coulomb.

I cannot see what prime numbers has to do with the weakest form of Coulomb force. I can see how a probability amplitude such as Psi-squared of quantum mechanics would deal with the weakest form of Coulomb.

So I take Coulomb force and square it for a Psi-squared. Now, I look for a Psi-sqaured constant-- look for 0.256 and use that constant to achieve the constant of gravity force, the weakest force of Coulomb.

I reject the Meissel-Mertens, even though it hits smack on to 6.70. Maybe Meissel-Mertens is the framework to build the constant of 0.256.

AP

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On Monday, September 25, 2023 at 9:20:17 PM UTC-5, Archimedes Plutonium wrote:

Currently I am doing my 257th book of science (although I call it the 263rd, but bumped up in cue-line) and the subject title is deriving the Gravitational Constant of physics the 6.70*10^-39 GeV/c^2. With great success, and a very open question in

pure math and physics. A new constant of 0.25600...... Just simply 0.256000 much like the Fine Structure Constant of physics is a pure number 0.007297...

So I am building and constructing a new number of math and physics which I call the Psi-squared number. It has a few rules. It is a fraction and it is a number in which all the digits after the first digit forms a square or square root digit string.

The number is 0.2560000..... and it is my contention that it is the only number to obey these rules. One of the rules is that it can be a squared of a fractional decimal number and need not be all whole numbers. The first two digits are 25 = 5^2, then
256 = 16^2. All good so far. Now the next digit can be built from one of a selection of 0,1,2,3,4,5,6,7,8,9 provided it is a perfect square as a outcome. So with 256d what is the d going to be to form another perfect square? Trying out all those 10
digits, none is able to form a perfect square. So I bound the square in from 2560 to 2569 as that of 50.59^2 to 50.68^2. As per the rule we can use fractions but we cannot use a fraction that is more digits than the whole number itself. Thus we can use
50.6^2 = 2560. Could we use 50.7^2? That becomes 2570, no. How about 50.55^2? That becomes 2555. How about 50.61, for it is within the rules? That becomes 2561, no.

Now the next digit for 0.2560 is another 0 digit because 160^2 is exactly 25600 and is a whole number. So every other new digit will have a solution of a form of 160dddd. But every other in between a whole number solution 160ddd.. needs to have a

fraction solution.

It is my conjecture that 0.2560000... is the only number in all of mathematics that is a Psi-squared number, given those rules I outlined. And by only number, we have to go out to the infinity borderline 1*10^604 to see.

One of the reasons I feel that 0.256000... is this special number is because its range for fractions falls inbetween for 50.59 and 50.68 are in between 50 and 51. For a number such as 0.169 or 0.361 do not work is that they do not fall inbetween their

range of possibilities.

Now the reason I am doing my book 258th following on the heels of my 257th book, is that I remember where deriving 4 of the most important constants in math and physics-- the pi constant, the Fine-Structure constant, the 840 constant of proton is

840MeV, and the constant of full revolution in angles is 360, for 360 degrees.

So this search of Psi-squared constant 0.2560000.... is similar to the 360 degrees as a constant in math geometry with a full circle revolution. What is special about 360 that it must be a full revolution? Is it not arbitrary what number we pick for

degrees of full revolution?? No. Only the number 360 can serve that role.

Take the number 360 for it is a Theory-of-Nines number-- add the digits and they sum to a 9 factor. Now double 360 and it becomes 720 another theory 9 number, double that, and keep doubling and all are theory of 9 numbers.

The number 360 is the smallest number in math to possess the Theory of Nines characteristic.

I contend the number 0.256000... is the smallest number to possess the Psi-squared characteristic. Perhaps the only number to possess Psi-squared attribute.

I am writing my 258th book on that incredible and marvellous discovery I made in my 205th book, that the four important constant numbers of math and physics--- pi, 360, 840, and Fine Structure constant are deeply tied together and produce one another

in the torus geometry. This discovery deserves a whole book in and of itself.


Sorry, the smallest theory of nines number in mathematics and physics is 180 and its degrees are a semicircle. Which is all the better, for in a future book I need to prove, if not already proven by me in a earlier book that the Light Wave is a Cycloid
wave, not a sinusoid. And the theory of nines with 180 degrees the smallest of such angles is further proof that the Light Wave is a cycloid, not a sinusoid.

So, sometimes it is good to make mistakes. Provided we catch them and make use of them.

AP

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Currently I am doing my 257th book of science (although I call it the 263rd, but bumped up in cue-line) and the subject title is deriving the Gravitational Constant of physics the 6.70*10^-39 GeV/c^2. With great success, and a very open question in pure
math and physics. A new constant of 0.25600...... Just simply 0.256000 much like the Fine Structure Constant of physics is a pure number 0.007297...

So I am building and constructing a new number of math and physics which I call the Psi-squared number. It has a few rules. It is a fraction and it is a number in which all the digits after the first digit forms a square or square root digit string. The
number is 0.2560000..... and it is my contention that it is the only number to obey these rules. One of the rules is that it can be a squared of a fractional decimal number and need not be all whole numbers. The first two digits are 25 = 5^2, then 256 =
16^2. All good so far. Now the next digit can be built from one of a selection of 0,1,2,3,4,5,6,7,8,9 provided it is a perfect square as a outcome. So with 256d what is the d going to be to form another perfect square? Trying out all those 10 digits,
none is able to form a perfect square. So I bound the square in from 2560 to 2569 as that of 50.59^2 to 50.68^2. As per the rule we can use fractions but we cannot use a fraction that is more digits than the whole number itself. Thus we can use 50.6^2 =
2560. Could we use 50.7^2? That becomes 2570, no. How about 50.55^2? That becomes 2555. How about 50.61, for it is within the rules? That becomes 2561, no.

Now the next digit for 0.2560 is another 0 digit because 160^2 is exactly 25600 and is a whole number. So every other new digit will have a solution of a form of 160dddd. But every other in between a whole number solution 160ddd.. needs to have a
fraction solution.

It is my conjecture that 0.2560000... is the only number in all of mathematics that is a Psi-squared number, given those rules I outlined. And by only number, we have to go out to the infinity borderline 1*10^604 to see.

One of the reasons I feel that 0.256000... is this special number is because its range for fractions falls inbetween for 50.59 and 50.68 are in between 50 and 51. For a number such as 0.169 or 0.361 do not work is that they do not fall inbetween their
range of possibilities.

Now the reason I am doing my book 258th following on the heels of my 257th book, is that I remember where deriving 4 of the most important constants in math and physics-- the pi constant, the Fine-Structure constant, the 840 constant of proton is 840MeV,
and the constant of full revolution in angles is 360, for 360 degrees.

So this search of Psi-squared constant 0.2560000.... is similar to the 360 degrees as a constant in math geometry with a full circle revolution. What is special about 360 that it must be a full revolution? Is it not arbitrary what number we pick for
degrees of full revolution?? No. Only the number 360 can serve that role.

Take the number 360 for it is a Theory-of-Nines number-- add the digits and they sum to a 9 factor. Now double 360 and it becomes 720 another theory 9 number, double that, and keep doubling and all are theory of 9 numbers.

The number 360 is the smallest number in math to possess the Theory of Nines characteristic.

I contend the number 0.256000... is the smallest number to possess the Psi-squared characteristic. Perhaps the only number to possess Psi-squared attribute.

I am writing my 258th book on that incredible and marvellous discovery I made in my 205th book, that the four important constant numbers of math and physics--- pi, 360, 840, and Fine Structure constant are deeply tied together and produce one another in
the torus geometry. This discovery deserves a whole book in and of itself.

AP

--- SoupGate-Win32 v1.05
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Sorry this is my 257th book of science, and should have it published in the next few days, perhaps even by Wednesday if lucky.

However I do have the hardest part of this book to overcome. Not the mathematics for the math is easy for me. I breeze through the math like a athlete swims freestyle in a swimming pool.

The hard thing is to visualize how gravity is the same as Coulomb force such as two bar magnets before sticking together.

The two bar magnets are Coulombs law, and how can we visualize them coming close to one another then sticking together.

Every day we visualize gravity working as the Earth orbits around the Sun, but the Earth and Sun do not stick together or have the force to make Earth go plunging into the Sun because of Coulomb force which is about 10^38 or 10^39 times stronger than
gravity force.

So the hardest part of this book for me, is explaining how gravity is the weakest and Coulomb the strongest.

But I am half way there, for I explain gravity as Sun creates pathways in Space of its magnetic field, magnetic lines of force for which each of the planets follow in one of those pathway magnetic lines of force ( we all see iron filings lined up in
pathways when a bar magnet is brought close). Then, the Sun shoots electric current along those pathways, a current aft of Earth pushing Earth in that pathway, but also a electric current fore of Earth-- pulling Earth (this is called the electromagnetic
potential) in its magnetic pathway.

So, somehow I need to use that same picture to describe Coulomb force as two bar magnetics get close enough they cause one to stick to the other in the strongest of EM forces.

AP, King of Science

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

On Monday, September 25, 2023 at 9:20:17 PM UTC-5, Archimedes Plutonium wrote:

Currently I am doing my 257th book of science (although I call it the 263rd, but bumped up in cue-line) and the subject title is deriving the Gravitational Constant of physics the 6.70*10^-39 GeV/c^2. With great success, and a very open question in

pure math and physics. A new constant of 0.25600...... Just simply 0.256000 much like the Fine Structure Constant of physics is a pure number 0.007297...

So I am building and constructing a new number of math and physics which I call the Psi-squared number. It has a few rules. It is a fraction and it is a number in which all the digits after the first digit forms a square or square root digit string.

The number is 0.2560000..... and it is my contention that it is the only number to obey these rules. One of the rules is that it can be a squared of a fractional decimal number and need not be all whole numbers. The first two digits are 25 = 5^2, then
256 = 16^2. All good so far. Now the next digit can be built from one of a selection of 0,1,2,3,4,5,6,7,8,9 provided it is a perfect square as a outcome. So with 256d what is the d going to be to form another perfect square? Trying out all those 10
digits, none is able to form a perfect square. So I bound the square in from 2560 to 2569 as that of 50.59^2 to 50.68^2. As per the rule we can use fractions but we cannot use a fraction that is more digits than the whole number itself. Thus we can use
50.6^2 = 2560. Could we use 50.7^2? That becomes 2570, no. How about 50.55^2? That becomes 2555. How about 50.61, for it is within the rules? That becomes 2561, no.

Now the next digit for 0.2560 is another 0 digit because 160^2 is exactly 25600 and is a whole number. So every other new digit will have a solution of a form of 160dddd. But every other in between a whole number solution 160ddd.. needs to have a

fraction solution.

It is my conjecture that 0.2560000... is the only number in all of mathematics that is a Psi-squared number, given those rules I outlined. And by only number, we have to go out to the infinity borderline 1*10^604 to see.

One of the reasons I feel that 0.256000... is this special number is because its range for fractions falls inbetween for 50.59 and 50.68 are in between 50 and 51. For a number such as 0.169 or 0.361 do not work is that they do not fall inbetween their

range of possibilities.

Now the reason I am doing my book 258th following on the heels of my 257th book, is that I remember where deriving 4 of the most important constants in math and physics-- the pi constant, the Fine-Structure constant, the 840 constant of proton is

840MeV, and the constant of full revolution in angles is 360, for 360 degrees.

So this search of Psi-squared constant 0.2560000.... is similar to the 360 degrees as a constant in math geometry with a full circle revolution. What is special about 360 that it must be a full revolution? Is it not arbitrary what number we pick for

degrees of full revolution?? No. Only the number 360 can serve that role.

Take the number 360 for it is a Theory-of-Nines number-- add the digits and they sum to a 9 factor. Now double 360 and it becomes 720 another theory 9 number, double that, and keep doubling and all are theory of 9 numbers.

The number 360 is the smallest number in math to possess the Theory of Nines characteristic.

I contend the number 0.256000... is the smallest number to possess the Psi-squared characteristic. Perhaps the only number to possess Psi-squared attribute.

I am writing my 258th book on that incredible and marvellous discovery I made in my 205th book, that the four important constant numbers of math and physics--- pi, 360, 840, and Fine Structure constant are deeply tied together and produce one another

in the torus geometry. This discovery deserves a whole book in and of itself.


Sorry, the smallest theory of nines number in mathematics and physics is 180 (nay 90 degrees) and its degrees are a semicircle. Which is all the better, for in a future book I need to prove, if not already proven by me in a earlier book that the Light
Wave is a Cycloid wave, not a sinusoid. And the theory of nines with 180 degrees the smallest of such angles is further proof that the Light Wave is a cycloid, not a sinusoid.

So, sometimes it is good to make mistakes. Provided we catch them and make use of them.

AP

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