Pythagorean Triples

Date: 05/31/99 at 00:48:24
From: lea
Subject: Pythagorean triples

Hi -

I've learned about the Pythagorean theorem in school. I just read 
something on Pythagorean triples, e.g. 3^2 + 4^2 = 5^2

Is there a formula for Pythagorean triples?
Thanks for your time.

Date: 05/31/99 at 17:36:34
From: Doctor White
Subject: Re: Pythagorean triples

Lea:

You can find some neat articles on Pythagorean Triplets by searching 
the Dr. Math archives.

One way I use to teach my students to find triplets is as follows:

Pick any two numbers greater than 2. We will call them M and N.

The triplet is formed by:  M^2 + N^2
                           M^2 - N^2  (absolute value)
                           2MN

Example: choose M = 4 and N = 7.

  M^2 + N^2 = 4^2 + 7^2 = 16 + 49 = 65
  
  M^2 - N^2 = 4^2 - 7^2 = 16 - 49 = -33 (absolute value = 33)

        2MN = 2 x 4 x 7 = 56.

  So, the triplet is 33, 56 and 65

 You can test it by: 33^2 + 56^2 = 65^2
                     1089 + 3136 = 4225

Hope this helps you with your problem. Let me know if you need further 
info. Come back to see us soon.

- Doctor White, The Math Forum
  http://mathforum.org/dr.math/