
Re:   Pythagorous Theorem
Posted:
Jul 15, 2013 8:29 AM


Deep wrote: > > Consider (1) below: > > x^(2n) + y^(2n) = z^(2n) (1) > > where x, y, z are coprime integers, integer n > 0. > > (1) can be written as (2) > > (x^n)^2 + (y^n)^2 = (z^n)^2 (2) > > By Pythagorous theorem (2) can be represented by the three sides of a right triangle XYZ where > > YZ = x^n, ZX = y^n, XY = z^n > > Observation:each of x^n, y^n, z^n will have now magnitude and direction. > > My question: Can the three variables in x, y, z in (1) be treated as vectors not scalar?
What does it mean to raise a vector to a power? v crossproduct v only makes sense, iirc, in real spaces of dimensions 1, 3 and 7. And v dotproduct v is a scalar (and thus v^{2n} is a scalar also).
> Any helpful comment will be appreciated. >
 I think I am an Elephant, Behind another Elephant Behind /another/ Elephant who isn't really there.... A.A. Milne

