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Date: Sun, 3 Nov 1996 01:19:24 -0800
From: "Émerick Arteche Gallego"
HI,
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 |
PS
(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!
See ya,
Emerick
___________________________________________
Dr. Emerick Gallego Arteche Ph.D
Cerro Coso College
Dept. of Mathematics
3000 S. College Heights Blvd
Ridgecrest, CA 93555
emerick@ridgecrest.ca.us
emerick@gauss.math.ucdavis.edu
http://www.ridgecrest.ca.us/~emerick/HTML1.html
Copyright © 1996-2008 Alexander Bogomolny
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