Pythagorean Triples

Pythagorean Triples

What is Pythagorean triple? A Pythagorean Triple is a set of positive integers, a, b and c that fits the rule: a2 + b2 = c2. (Pierce) So if there is one true formula that would provide an infinite amount of Pythagorean triples there should be no problem coming up with five more Pythagorean triples. So in this paper I am going to build five more Pythagorean triples and verify them with the Pythagorean Theorem equation.

Five Pythagorean Triples:

(9, 12, 15) 9^2 +12^2 = 15^2 81 + 144 = 225

(12, 16, 20) 12^2 + 16^2 = 20^2 144 + 256 = 400

(15, 20, 25) 15^2 + 20^2 = 25^2 225 +400 = 625

(18, 24, 30) 18^2 + 24^2 = 30^2 324 + 576 = 900

(21, 28, 35) 21^2 + 28^2 = 35^2 441 + 784 =1225

So by using the formula a^2 + b^2 = c^2 and using the first set of Pythagorean triples (3, 4, and 5) you can come up with and endless amount Pythagorean triples. I will use the smallest set of Pythagorean triples to show you how.

First you let n be an integer greater than 1. So you will have:

3n, 4n, and 5n

This will be true because (3n)^2 + (4n)^2 = (5n)^2 (Pierce)

So say that n=2 you will have 6, 8, and 10 as the next set of Pythagorean triples. So to find my five sets of Pythagorean triples I plugged into the equations the following: n=3. N=4, n=5, n=6, and n=7.

To be honest when I first read the word "Pythagorean" I was a little nervous. I had never recalled hearing that before. But once I read up on it and researched it online it was a lot simpler than I had imagined. Knowing that a Pythagorean triple would always have either all even or two odd and an even number were very helpful. Finding that you could just plug a number in that was greater than one into a simple equation made all the difference. By do that I could list and infinite number of Pythagorean triples, just as the text book had suggested.