My Math Forum FLT (n=2, n=3) the correct end of the story:

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March 25th, 2016, 09:19 AM   #51
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Quote:
 Originally Posted by complicatemodulus ... that has higher and higher "medium roof" due to the littlest terms that becomes littlest and littlest once you rise K..o
Sorry the "roof" of our gnomons bars, becomes lower and lower rising K,

So it means we are able to cover a littlest and littlest area rising K...

While in the reality (so with FLT equation false) is true the vice-versa,

We are sure of that because we can prove that for $\displaystyle K\to\infty$ we fullfit the area bellow the derivate from B to C, (also) with C irrationals....

Is for that reason I show the rational integration and the integration process via limit of the reational integration ... just to remember the good way.

Than I use another result coming from FLT (supposed true) as reductio as absurdum...

It hope it wll work...

 March 29th, 2016, 04:46 AM #52 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 ...again in a round circle.... my fault !
 April 6th, 2016, 10:08 PM #53 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 I hope all this helps you to think about what we are doing "squaring" the derivate with the finite sum of gnomons. FLT conditions imply a "geometric" condition on the derivate I hope will give us the solution: If $C-B$ is an integer, (on the example n=3) it means that the medium height of the derivate y'=3x^2 between B and C is an integer too since the area bellow the derivate is (must be) A^3 I remember we keep as integer. If this height it's an integer, due to the fact that each gnomon's roof already "cut" the curve exactly in a way that it (the gnomon's roof) is the medium eight.... That means (since B-C is and Odd number) that the missing area of the sum of the gnomons on the left of our "central" reference gnomon, must be equal to the right area in excess given by the area of the sum of the gnomons on the right side of our "central" gnomon. But this can clearly happen JUST if the curve is a line... while if it is a curve the right area in excess is always bigger than the left one... I hope it will work in math to... Thanks Ciao Stefano Last edited by complicatemodulus; April 6th, 2016 at 10:26 PM.
 April 6th, 2016, 10:51 PM #54 Banned Camp   Joined: Dec 2012 Posts: 1,028 Thanks: 24 Remembering to draw all on the X-Y plane, In a n=3 example, to understand where on X a "generic" Gnomon's roof is equal to the height of the derivate y'=3x^2, (I call this point $X_{CG}$) solve where it's true: $\displaystyle \int_{P-1}^{X_{CG}} (3x^2) dx = \int_{X_{CG}}^{P} (3x^2) dx$ with: $\displaystyle 3P^2-3P+1 = \int_{P-1}^{P} (3x^2) dx$ Since on the known derivate of y=x^n with n>2 curves, $X_CG$ it's a....

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