A couple of years ago when I was teaching the Pythagorean Theorem to my Advanced 7th grade class, I gave the students a “formula” for creating Pythagorean Triplets (a,b, c values that form right triangles). They went mad with it. I had students creating lists of triplets into the the hundreds, just for fun!

Here’s how you do it:

If **a** ≥ 3 and a is odd, then **b** = (**a**²-1)/2, and **c** = **b** + 1

**a**=3 ** b**= (3²-1)/2=4 **c**=4+1=5

**a**=5 **b**=(5²-1)/2=12 **c**=12+1=13

If **a** ≥ 6 and **a** is even, then **b**=(**a**/2)² – 1 and **c** = **b** + 2

**a**=6 **b**= (6/2)² -1=8 **c** = 8 + 2 = 10

**a**=8 ** b**=(8/2)² – 1=15 **c** = 15 + 2 = 17

There are other variations on these formulas to finding the triplets, but I like how these work. Also note, that if a Pythagorean triplet has an odd number in it, there has to be two odd numbers. The triplets always have either all even numbers, or 2 odd numbers and an even number.

I LOVE Pythagorean triples! It appeals to my sense of order!

I give my students several examples then have THEM come up with a formula and give me a few more. It’s a great task for pattern recognition.