Fermat at infinite power

Aug 2015
58
3
Chiddingfold, Surrey
The following can't be a solution to Fermat's last theorem because it is too simple, but it is very interesting:.
Power 2 Pythagoras can be represented by a right-angled triangle with the hypotenuse as the base , and a power 1 can be represented by a straight line of length a = b+c with 180 degrees between b an c
Now applying the same to powers higher than 2, and calculating the angle between b and c where a^n = b^n + c^n shows that the only rational angle with a rational cosine is 60 degrees and this is not possible unless the power is infinite. This is represented by an equilateral triangle with one side as the base and the other two as 0.5 +.866 i and 0.5 - 0.866 i
 

skipjack

Forum Staff
Dec 2006
21,481
2,470
By definition, the sides would have to be equal for the triangle to be equilateral.