# Generating Pythagorean Triples

Updated on September 21, 2012

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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• AUTHOR

Maria Cristina Aquino Santander

6 years ago from Manila

Thank you IntegrityYes. God bless you. Best regards.

• IntegrityYes

6 years ago

That is wonderful. I voted up for sure.

• AUTHOR

Maria Cristina Aquino Santander

6 years ago from Manila

Hi teaches12345 Thank you for visiting this hub. I am glad you find this interesting and challenging. Your visit and comments are much appreciated. Blessings to you always and your family.

• Dianna Mendez

6 years ago

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

• AUTHOR

Maria Cristina Aquino Santander

6 years ago from Manila

Hi Eblamk90 thank you for appreciating this hub. Remain blessed always. Best regards.

• EBlank90

6 years ago from MIchigan

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.

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