AP's 255th book of science // Conservation Law in Mathematics-- Pythagorean Theorem// Theoretical Math by Archimedes Plutonium.

I seem to have come to a special place in my science endeavors. A place where I am doing Philosophy-Math and Philosophy-Physics and Theoretical Math and Theoretical Physics.

Of course in these books I must detail what "philosophy" means and what "theoretical" means. But the title and subject matter of these books immediately tells the reader I am mixing physics with mathematics, and creating something new in both that was never there before.

Who would have thought Physics laws of Conservation rest inside of mathematics also? And who would realize that time in physics is angle in mathematics.

The Pythagorean Theorem conserves squares on the sides of right triangles. Electricity is 90 degrees to magnetism and physics has conservation of angular momentum and of energy. The Electric Field is angular momentum.

AP

Now in this book I need to define a "Conservation Law of Mathematics" for some would think it simply means equality. Any equation in math of equality is a conservation. No. What I need to do is show where a part of Mathematics has what I call Double Equality, a new concept.

Double Equality is found in the Pythagorean Theorem in that you have Geometry and three sides of a right triangle.

But you also have mathematics equality of 3^2 + 4^2 = 5^2. Just pure number theory algebra equality. With no connection to geometry. In fact (3*k)^2 + (4*k)^2 = (5*k)^2.

But, when we include geometry into that algebra, we have to have a second equality of (p degrees) + (q degrees) = 90 degrees. And then place the Pythagorean Theorem as (3*k)^2 + (4*k)^2 = (5*k)^2 == (p degrees) + (q degrees) = 90 degrees, where the == means double-equality.

There are not many double-equalities in Mathematics and what few there are, for I only know of the Pythagorean Theorem. What few there are, are Conservation Laws of Mathematics.

There maybe another in the Parallelogram Rule of Vector Physics.

AP, King of Science, especially Physics & Logic

On Sunday, June 11, 2023 at 5:28:07 PM UTC-5, Archimedes Plutonium wrote:
> Now in this book I need to define a "Conservation Law of Mathematics" for some would think it simply means equality. Any equation in math of equality is a conservation. No. What I need to do is show where a part of Mathematics has what I call Double Equality, a new concept.
>
> Double Equality is found in the Pythagorean Theorem in that you have Geometry and three sides of a right triangle.
>
> But you also have mathematics equality of 3^2 + 4^2 = 5^2. Just pure number theory algebra equality. With no connection to geometry. In fact (3*k)^2 + (4*k)^2 = (5*k)^2.
>
> But, when we include geometry into that algebra, we have to have a second equality of (p degrees) + (q degrees) = 90 degrees. And then place the Pythagorean Theorem as (3*k)^2 + (4*k)^2 = (5*k)^2 == (p degrees) + (q degrees) = 90 degrees, where the == means double-equality.
>
> There are not many double-equalities in Mathematics and what few there are, for I only know of the Pythagorean Theorem. What few there are, are Conservation Laws of Mathematics.
>
> There maybe another in the Parallelogram Rule of Vector Physics.

My memory was bad on this issue, thinking Linear Momentum was not conserved but Kinetic Energy was conserved-- which the exact opposite is true.

I suspect there are basically just 2 conservation laws in mathematics.

In some sense physics has just 2 conservation laws-- total energy and total momentum.

Recently I did a book on cycloid wave and the rolling of one figure over its copy and I found that the smooth curves of circle, ellipse converse their identities. And cycloid waves are Light Waves so the speed of light as a constant is a conservation law of physics. Do we classify Light Speed as momentum conservation or as energy/mass conservation?

So I think I found the two conservation laws of mathematics-- one is the Pythagorean Theorem and the other is cycloid geometry in motion.

I find myself in a lovely position in science research, where prior work is lifting me up in insight into future work.

My 240th published book.

New True Geometry starting with cycloid correction and Geometry-of-Motion // math research

by Archimedes Plutonium

Preface: Motion Geometry such as producing the Cycloid curve in Old Math was in error. Looking at the Limacon we see this error in Motion Geometry at its worst. And the fix of the error has to come from physics of Electromagnetic theory where magnetic field is always perpendicular to electric field. The mistake made in Old Math Geometry is that they had two motions in a cycloid and limacon construction. They had the motion of a circle, but had arbitrary motion for the Pointer-Marker. This book addresses the Old Math Geometry mistakes and opens up the entire field of new math of Motion Geometry.. In the midst of that correction several major conjectures were discovered and proven in this book which has created a complete overhaul of Old Math's conic sections. For the parabola and hyperbola are not open curves but closed loop circuits of ellipse, oval, circle. The nasty mistake of Old Math to think cones are apex to apex is ridiculous to the nth degree, for true conics are base to base <>, not apex to apex ><. And I finish this book with a stunning proof that 3 arbitrary non-collinear points in the plane not only produces a unique circle, but produces a unique ellipse, yet Old Math claimed it requires 5 points to produce a unique ellipse. I suspect Old Math's 5 point requirement is based on the square or rectangle, whereas my 3 point requirement is a parallelogram that is not square and not a rectangle. If I can find a unique ellipse inside a unique circle produced by 3 arbitrary points non-collinear, then I can say in general all 3 arbitrary non-collinear points produces a unique ellipse.

Cover Picture: My photograph of holding two cones base to base. Two cones base to base forms the foundation of Conic Sections, and not the silly apex to apex.

Product details
• ASIN ‏ : ‎ B0C5VL38ZK
• Publication date ‏ : ‎ May 20, 2023
• Language ‏ : ‎ English
• File size ‏ : ‎ 649 KB
• Text-to-Speech ‏ : ‎ Enabled
• Screen Reader ‏ : ‎ Supported
• Enhanced typesetting ‏ : ‎ Enabled
• X-Ray ‏ : ‎ Not Enabled
• Word Wise ‏ : ‎ Not Enabled
• Sticky notes ‏ : ‎ On Kindle Scribe
• Print length ‏ : ‎ 109 pages

Alright, I am going to start all of mathematics, both Numbers and Geometry from right triangles.

The Right Triangles give me the discreteness of Numbers I want, and gives me the Decimal Grid System of Numbers that I want.

All I need is 1,1,sqrt2 and the 3,4,5 Right Triangles. For I get 1,2,3,4,5 out of them to make the 5 factorial = 120 for the infinity borderline 1*10^604 and its algebraic completeness 1^10^1208.

For not only are Right Triangles in Pythagorean Theorem discrete in Primitive Pythagorean Triples, but also discrete in fractions.

To obtain the 2 in 5 factorial I divide the 3,4,5 Right Triangle by the factor of 1/2 and get 3/2, 2, 5/2. Here note that 1.5 is in 10 Grid as well as 2.5. So I have all the numbers of 5 factorial, 1,2,3,4,5.

In New Math, we need only Primitive Pythagorean Triples to use the generator mechanism of obtaining Primitive P-triples, but we make no distinction between Primitive and Compound P-triples. For we every number in 10 Grid to cover, including fractions such as 0.1, 0.2, 0.3,.., 9.8, 9.9

To obtain all those fractions we take a Primitive P-triple and multiply by a factor.

In this manner all the numbers of Mathematics comes from P-triples and all geometry comes from Pythagorean theorem because every triangle is a addition of 2 right triangles.

Every closed figure is a composition of right triangle, even curved figures for curved figures are straightline segments as we have a infinity borderline.

AP

I need to review Feynman's "Character of Physical Law", to spot if I can the feasibility that all of Physics has just 2 Laws of Conservation-- energy and momentum.

Of course, then I will need to translate those physics laws into mathematical laws.

AP

Archimedes Plutonium wrote:

> I need to review Feynman's "Character of Physical Law", to spot if I can
> the feasibility that all of Physics has just 2 Laws of Conservation--
> energy and momentum.
>
> Of course, then I will need to translate those physics laws into
> mathematical laws.

not true. *_The_IC_componnents_* chips from the destroyed american and
*_german_tanks_*, Abrams and Panther2, are reused by Russians
*_in_their_washing_machines_*.

https://mf.b37mrtl.ru/files/2023.06/l/64859c5f20302706c64056bc.jpg