There are many alternate derivations of pi number 3.14159.... but this is the first time a geometry 3rd dimension derivation of pi comes.

--- quoting my 205th book of science ---
Faraday Law is inverse projective-geometry of Coulomb-gravity Law//Physics-Math

by Archimedes Plutonium

Preface: This book discusses the symmetry of the 4 differential laws of Electromagnetic theory, the Faraday law, Ampere-Maxwell law, Coulomb-gravity law and the Transformer law. This book also dives into the numbers of importance of physics and math, the
1/137, the pi, the pi subtract 2.71... and much more.

Cover Picture: Is my iphone photograph of 840 windings of slinky toy to form a torus that is the proton torus of physics of its 840MeV with a muon stuck inside at 105MeV doing the Faraday law.


Now I play with those numbers and see what becomes of them for the Conjectures I placed so far. The most important being the idea that 840 windings is the physical geometry of the Fine Structure Constant as a torus the produces Maximum Electricity in the
Faraday law.

Alright, well it is easy to see that 210/65 is 3.230... So I went back to the lab and m

Currently I am doing my 257th book of science 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

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