"Fermat's Last Theorem" Disproved?
in [Math]
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From: Frederick Williams on 15 Jul 2010 10:15 Thomas Nordhaus wrote: > > Frederick Williams schrieb: > > > The case n = 3 of FLT was (almost) dealt with by Euler in the sixteenth > > century > > Make that the eighteenths century. Oops! Sorry. -- I can't go on, I'll go on.
From: tonysin on 15 Jul 2010 10:50 On Jul 14, 2:18 pm, cjcountess <cjcount...(a)yahoo.com> wrote: > "Has anyone taken two cubes, created from two equal and right angular lines of triangle, and one made from cube of hypotenuse, and measured their volumes, to see if the c cube equals the a cube + the b cube?" Well, let's do it now and make sure. In your isosceles right triangle, the lengths of the three sides are x, x, and x*sqrt(2). The areas of their squares are x^2, x^2, and 2x^2, satisfying the Pythagorean Theorem. The volumes of their cubes are x^3, x^3, and 2x^2*x*sqrt(2). The sum of the cubes of the short sides is 2x^3, which does not equal the cube of the third side, which is 2x^3*sqrt(2). So even though you violated the conditions of Fermat's Theorem by using non-integral lengths, the numbers still don't add up. What about that is not clear?
From: cjcountess on 15 Jul 2010 11:17 Yesterday I made an assertion that I could disprove Fermats Last Theorem, which states that the Pythagorean Theorem, which states that a^2 + b^2 =c^2, only works for numbers of which the exponent is 2, and no other. I asserted that just as we square a 1 dimensional line by extending it in 2D at right angle to the first at equal length as the original line, we can again repeat the same process to cube the square by lying it on its side and square it from there in same manner, and furthermore that if Pythagorean theorem continues to hold, the square of the square a + the square of the square b, should = the square of the square c. This would in fact mean that a^3 + b^3 = c^3 and thus Fermat's Last Theorem is broken down and Pythagoras theorem is extended into the 3D Well to my dismay it did not hold which means that I was totally wrong provided the wrong experiment for reason I will explain and /or am right by extension since the Pythagorean Theorem did not hold for squaring the square. But if there is no such thing as squaring the square, as one reader suggested, than I am wrong on that point, but if there is, than I am correct on count of both Pythagorean Theorem and Fermats Last Theorem break down when extended into 3D, because while Pythagoras says its true that a^2 + b^2 = c^2 , Fermat backs it but adds that it is only true for squares. I must admit that the original idea came to me while contemplating "E=mc^2". It occurred to me that as this equation states the energy content of matter of 3D form, it must extend into 3D space, And as I traced the measurement of energy from E=hf/c^2 to E=mc^2, one can see that the energy moves from a relatively straight line at its lowest form, to waves that contract, gaining energy exponentially. This means that each time frequency doubles, wavelength halfs, and energy increase 4 times. This is also called an energy increase to the square of the frequency. I further investigated this and found it analogical, logically, mathematically, geometrically, and statistically probable that, analogous to a line of 1 inch in linear direction x 1 inch in 90 degree angular direction to create a square inch, when energy reaches c^2 to form matter, this is c in the linear direction x c in the 90 degree angular direction, which creates circular and or spherical motion, through a balance of centrifugal /centripetal forces. Thus circular motion is also sometimes referred to as v^2, and the same equation that measures objects falling to earth, or moving period, can also apply to circular motion, which are (F=mv^2, F=mv/r^2 and F=mv^/ r). It is precisely because all these are related that the same equations apply. I believe that the formation of a spherical particle from energy at c^2 indicates that the squaring of energy extends into the third dimension, by continual squaring. And that just as physical objects are not compose of square shaped energy, but circular and spherical are more likely the shape of elementary particles, and a cube is the squaring of a square and the Pythagorean and Fermat theorems break down there. see: Conrad J Countess
From: smallfrey on 15 Jul 2010 07:27 In 1897, Hilbert proved that Fermat's equation for "regular" prime exponents has only the trivial solution in the cyclotomic field Q(zeta). So, even saying there are real solutions is dicey.
From: Virgil on 15 Jul 2010 16:01
In article <1898eadf-7a46-485e-aa6c-53572bfb8921(a)w12g2000yqj.googlegroups.com>, cjcountess <cjcountess(a)yahoo.com> wrote: > Yesterday I made an assertion that I could disprove �Fermat�s Last > Theorem�, which states that the �Pythagorean Theorem�, which states > that �a^2 + b^2 =c^2�, only works for numbers of which the exponent is > 2, and no other. That is not �Fermat�s Last Theorem� that many of us know and love, but an incomplete misstatement of it. The correct statement also requires that a, b and c be integers, i.e., whole numbers only. And that added restriction makes your claimed proof into mere irrelevant nonsense. |