Subject: Proof of Pythagorean Theorem #??????
Date: Sun, 3 Nov 1996 01:19:24 -0800
From: "Émerick Arteche Gallego"
You might like to take a look at this proof of the Pythagorean Theorem:
Let u and v be vectors in Rn orthogonal to each other. By the properties of norm, and the fact that (u, v) = 0 you get:
|||u+v||2 = (u+v, u+v)|
|= (u, u) + 2(u, v) + (v, v)|
|= ||u||2 + ||v||2|
(a, b) is the scalar (dot) product
||u+v||2 = hypotenuse squared
Is this proof worthy of getting recognition on your homepage? It better! It covers Rn!
Dr. Emerick Gallego Arteche Ph.D
Cerro Coso College
Dept. of Mathematics
3000 S. College Heights Blvd
Ridgecrest, CA 93555