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- 03-26-2017, 02:12 PM #201

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## Re: Modules

I have completely re-written "The Relativistic Unit Circle" to show its role in the Binomial Theorem and the proof of Fermat's Theorem.. The old document can still be accessed by a link at the beginning of the new document. (The Theory of Relativity's fundamental equation is positive definite, as is the Binomial Expansion. As is the Lorentz transform - since to solve it one has to square the initial expression of Lorentz)

Dirac introduced negative numbers (energy) into this expression as an extension from Pauli (which I showed long ago - at least it seems to me)....

But, Neverfly - continue in your delusion, since you have never solved Lorentz's original equation for yourself... I have, and it is in my pdf's on my website, and corresponds to (is consistent with) Bergmann's derivation in "Introduction to the Theory of Relativity")

(Neverfly still thinks he can understand Relativity by cutting and pasting equations and doing high school algebra with them).

I will be happy to discuss it when and if you can say something intelligent about it.Last edited by BuleriaChk; 03-26-2017 at 02:56 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 03-26-2017, 04:44 PM #202
## Re: Modules

--Inter Arma Enim Silent Leges--

“Science needs the light of free expression to flourish. It depends on the fearless questioning of authority, and the open exchange of ideas.” ― Neil deGrasse Tyson

"When photons interact with electrons, they are interacting with the charge around a "bare" mass, and thus the interaction is electromagnetic, hence light. This light slows the photon down." - BuleriaChk

- 03-27-2017, 07:27 AM #203

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## Re: Proof of Fermat's Theorem

Fermat's Theorem is valid because negative numbers cannot be invoked to "destroy" mulitiplicative products in the positive half of the plane, where for n=2, Fermat's expression is , but is also true for n>2 .

That is, is not included in the set , but rather in the set , so is therefore not in the set of positive integers, and Fermat's Theorem is valid for n=2, as well as for higher dimensions of the Binomial Expansion n>2.

(Pythagorean Triples require the negative number as above, and so are not in the set of positive real numbers , but rather in the set , so that the Pythagorean Triples really can be characterized as a Jedi mind trick - the idea that a and b are positive for all real numbers is an illusion).

In the same sense, , the function does not belong to the set , but rather to the set

This is also true for positive real numbers if subtraction (i.e. negative scaling) is not allowed. The relativistic unit circle validates the plane (x,y) of real numbers and shows why the null vector is necessary to provide commutativity in multiplicative products for propositions that include "all" real numbers.

In fact, it is also true for non-negative exponents and complex numbers : The Binomial Theorem (Wikipedia)

So the issue is not whether Fermat's Theorem applies to integers, but rather the completeness (or incompleteness) of the system w.r.t. the negative -rem(a,b,n) that must be added to the Binomial Expansion to make Fermat's Theorem valid (true also of real numbers)....

Like I said, the idea that Fermat's Theorem hasn't been proved long ago is either a scam or a Jedi mind trick...

I think it is a Jedi mind trick, myself....

Or, (humbly), I am a fricken' genius... Or at least have at last become a JediLast edited by BuleriaChk; 03-27-2017 at 02:50 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 03-27-2017, 07:36 AM #204

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## Re: Modules

"The Relativistic Unit Circle" has been completely re-written with better diagrams, and to focus in a more organized way on the salient points. Links to the original document are included in the new version. I will be updating directly to this document (but will be tracking the updates on my server).

Also updated the addendum to FLT proof.Last edited by BuleriaChk; 03-27-2017 at 02:49 PM.

_______________________________________

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 03-28-2017, 02:33 AM #205

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- 03-28-2017, 09:55 AM #206

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## Re: Modules

03/28/2017 7:40 AM PST

Updated the Relativistic Unit Circle to include addition of relativistic velocities between the two relativistic sets to show how addition of relativistic velocities corresponds to velocity multiplication in the final state of the RUC, and thus to Newton's law (two particles, either colliding or not) for , and how they are related to the Galilean coordinate system.

(This is because a and b characterize complete and independent real number systems (x,y), where their interaction is characterized by corresponding to the interaction term in the Binomial Expansion for n=2.Last edited by BuleriaChk; 03-28-2017 at 10:02 AM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 03-28-2017, 01:10 PM #207

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## Re: Modules

Just added a couple of lines in the above addendum to show why Einstein was motivated by infinitesimal Differential Geometry to characterize the effect of light-on light interaction as gravity, with interpreted as the charge-to-mass ratio for two photons characterized by {a} and {b},and also its relation to Planck's constant as a characterization of a (light-equivalent) photo-electron.

Correction to this latest: I had to replace with in the mass interpretation of relativistic charge-to-mass ratio. Makes the notation awkward, but it is important to get it right w.r.t. the RUC.Last edited by BuleriaChk; 03-28-2017 at 03:17 PM.

"Flamenco Chuck" Keyser

The Relativistic Unit Circle**03/28/2017 07:40 AM PST**

Proof of Fermat's Last Theorem Updates**03/19/2017 8:23 PM PST**

**Ignore List -The Peanut Gallery.**

- 03-29-2017, 11:12 AM #208
## Re: Proof of Fermat's Theorem

Am I supposed to imagine an imaginary number in there?

What is also true for n>2? What are you trying to say?

That is, is not included in the set , but rather in the set , so is therefore not in the set of positive integers, and Fermat's Theorem is valid for n=2, as well as for higher dimensions of the Binomial Expansion n>2.

(Pythagorean Triples require the negative number as above, and so are not in the set of positive real numbers , but rather in the set , so that the Pythagorean Triples really can be characterized as a Jedi mind trick - the idea that a and b are positive for all real numbers is an illusion).

By definition, Fermat's Last Theorem is limited to positive integers.

In the same sense, , the function does not belong to the set , but rather to the set

This is also true for positive real numbers if subtraction (i.e. negative scaling) is not allowed. The relativistic unit circle validates the plane (x,y) of real numbers and shows why the null vector is necessary to provide commutativity in multiplicative products for propositions that include "all" real numbers.

In fact, it is also true for non-negative exponents and complex numbers : The Binomial Theorem (Wikipedia)

So the issue is not whether Fermat's Theorem applies to integers, but rather the completeness (or incompleteness) of the system w.r.t. the negative -rem(a,b,n) that must be added to the Binomial Expansion to make Fermat's Theorem valid (true also of real numbers)....

Like I said, the idea that Fermat's Theorem hasn't been proved long ago is either a scam or a Jedi mind trick...

I think it is a Jedi mind trick, myself....

Or, (humbly), I am a fricken' genius... Or at least have at last become a Jedi

E) Troll

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