Fermat logic
From: ben ito (benito20044_at_yahoo-dot-com.no-spam.invalid)
Date: 10/17/04
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Date: 17 Oct 2004 16:24:17 -0500
Fermat's Last Theorem
Ben T. Ito
10-17-04
I will solve Fermat's last theorem using the law of cosine and logic.
1. Introduction
Fermat implied that there was a simple proof that for X^n + Y^n = Z^n
, n>2, does not form integer solutions of X, Y and Z.
2. Wile's Proof
Wiles proof of Fermat's last theorem is described. Wile implies that
n=2 represent an area (X^2), and n=3 represents a volume (X^3);
however, in physics, the fourth dimension (n=4) is the distance of
propagation (d = vt) where v is the velocity and t is the time.
Multiplying the lengths of a cube (X^3) with the distance of
propagation(d) violates logic.
n=4 -------> (X^3) x d = X^4. (EQU 1)
Therefore, Wiles proof of Fermat's theorem is invalid.
3. Proof
I will describe the proof the Fermat's last theorem. I will use X, Y
and Z to represent the sides of a single triangle. When n>2, the
following equation describes the length of Z,
Z = (X^n + Y^n)^(1/n). (EQU 2)
Consequently, when n=3 : X = 1, Y=4 , Z=4.02 using the lengths of X,
Y and Z a triangle is formed. I will prove that integer values of X
and Y never form an integer of Z using the law of cosine.
Z^2 = X^2 + Y^2 - 2 XYcos(A). (EQU 3)
When n>2 the triangle formed is never a right triangle; therefore,
angle A is never 90 degrees. Using equation 1, the minimum angle of
the triangle is greater than 60 degrees.
60 degrees < A < 90 degrees
(EQU 4)
Using the angle range in the Cos(A) , of equation 4, the resulting
value always a string of digits to the right of the decimal since
cosine is base on Pi; I will release equation 3 by stating that the
using any value (integer and none integer) of X and Y that satisfies
equation 4; therefore, the new cosine is a right triangle that
includes the all the angles of the cosine of equation 3.
***************************************************************
(I must prove that a right triangle with the angles 60<B<90, the
cos(B) always forms a string of digits to the right of the decimal.)
*****************************************************************
therefore, 2XYcos(A) of equation 3 cannot form an integer.
Consequently, Z^2 and Z of, equation 3,can never form integer values
when X and Y are integers which solve Fermat's Last theorem.
3. Conclusion
I have proven that, when X and Y are integers, Z never forms an
integer length when n>2 using the law of cosine and logic.
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