# Generating Pythagorean Triples

Generating Pythagorean Triples

A Pythagorean Triple consists of three positive integers a, b and c such that a^2 + b^2 = c^2.

Such a triple is commonly written as (a, b, c) and a well-known example is (3,4,5). Other Pythagorean Triples can be generated by the following process:

Step One : Choose any two positive integers , s and t such that s > t.

Step Two : Let a = s^2 – t^2

b = 2st

c = s^2 + t^2

Exanple One : Let s = 3 amd t = 2

a = 3^2 - 2^2

9 -4 = 5

b = 2(3)(2) = 12

c = 3^2 + 2^2

= 9 + 4 = 13

The Pythagorean Triple generated is 5, 12, 13

Check if they satisfy Pythagorean Theorem :

5^2 + 12^2 = 13^2

25 + 144 = 169

169 = 169

Example Two : Let s = 4 and t = 3

a = 4^2 - 3^2

16 - 9 = 7

b = 2 (4)(3) = 24

c = 4^2 + 3^2

= 16 + 9 = 25

The Pythagorean Triple generated is 7, 24, 25

Check : 7^2 + 24^2 = 25^2

49 + 576 = 625

625 = 625

SOURCE : XP GEOMETRY By

Dr. Jose A. Marasigan.

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## Comments 6 comments

The title grabbed my attention. I just had to see what it was about. I'm glad you have other interests that you write about. This one will be for the pythagorean's. They need something interesting to peruse also.

Wow, very interesting -- I am not a math wiz but I can see how many will be challenged by your presentation.

That is wonderful. I voted up for sure.

6