Other methods for generating Pythagorean Triples

 

It turns out that these are Pythagorean triples as well. They are not mulitples of 3, 4, and 5

5, 12, 13

7, 24, 25

9, 40, 41

An interesting relationship can be seen.

This can be shown as a formula for generating some Pythagorean Triples.

x ,   (x ² - 1) ÷ 2 ,   (x ² + 1) ÷ 2

These formulas works well for odd initial number.

For instance, choose 11 .

  • 11 ² =121.
  • Subtract 1 and get 120.
  • One-half of 120 is 60.
  • One more than 60 is 61. Therefore,
    • 11, 60, 61 is a Pythagorean Triple

Now you try it. What Pythagorean Triple begins with 15?


 

 

But what if the initial triple is an even number?         Return to Recognizing Special Numbers