Pythagorean+Triple

**What is it?**

A Pythagorean Triple is a set of three positive integers that fit into the formula a 2 + b 2 = c 2.

The smallest example is a 3, 4, 5 triangle: And you can prove it algebraically like this: a 2 + b 2 = c 2 3 2 + 4 2 = 5 2 9 + 16 = 25 25=25

Here's a few more examples of Pythagorean Triples:

5, 12, 13 6, 8, 10 7, 24, 25 8, 15, 17 9, 40, 41 10, 24, 26 11, 60, 61 <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">12, 35, 37 <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">13, 84, 85

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">and there's infinitely many more!!

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">HINT: If you want to create your own Pythagorean Triple, use one you already know, preferably a small one, and increase each integer in the set by the same scale factor.

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">For example, take a 6, 8, 10 triangle and scale it up by 2 to make a 12, 16, 20 triangle. <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Now test it! <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">a 2 + b 2 = c 2 <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">12 2 + 16 2 = 20 2 <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">144 + 256 = 400 <span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">400 = 400

<span style="color: #137272; font-family: Georgia,serif; font-size: 120%;">Want to go back to home?