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

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 Peter Percival Posts: 1,792 Registered: 10/25/10
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 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

Date Subject Author
7/15/13 Deep Deb
7/15/13 Peter Percival
7/15/13 HOPEINCHRIST
7/15/13 Ken.Pledger@vuw.ac.nz
7/15/13 Bart Goddard
7/15/13 Virgil
7/15/13 Ken.Pledger@vuw.ac.nz
7/16/13 david
7/16/13 Brian Q. Hutchings
7/17/13 Brian Q. Hutchings