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.