Pythagorean Triplets

15 Sep

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 = (a²-1)/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.


One Response to “Pythagorean Triplets”

  1. Justin (@JustinAion) October 13, 2013 at 4:04 pm #

    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.

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