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 **R**^{n} 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 **R**^{n}!

See ya,

Emerick

___________________________________________

Dr. Emerick Gallego Arteche Ph.D

Cerro Coso College

Dept. of Mathematics

3000 S. College Heights Blvd

Ridgecrest, CA 93555

61247341 |