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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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    • cristina327 profile image
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      Maria Cristina Aquino Santander 5 years ago from Manila

      Thank you IntegrityYes. God bless you. Best regards.

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      IntegrityYes 5 years ago

      That is wonderful. I voted up for sure.

    • cristina327 profile image
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      Maria Cristina Aquino Santander 5 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.

    • teaches12345 profile image

      Dianna Mendez 5 years ago

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

    • cristina327 profile image
      Author

      Maria Cristina Aquino Santander 5 years ago from Manila

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

    • EBlank90 profile image

      EBlank90 5 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.