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Topic: ----- ----- Pythagorous Theorem
Replies: 9   Last Post: Jul 17, 2013 4:18 PM

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Peter Percival

Posts: 2,623
Registered: 10/25/10
Re: ----- ----- Pythagorous Theorem
Posted: Jul 15, 2013 8:29 AM
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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 cross-product v only
makes sense, iirc, in real spaces of dimensions 1, 3 and 7. And v
dot-product 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

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