Learn Java with Math: Using Fun Projects and Games

© Ron Dai 2019

R. DaiLearn Java with Mathhttps://doi.org/10.1007/978-1-4842-5209-3_16

16. Pythagorean Triples

Ron Dai¹ 

(1)

Seattle, WA, USA

 

The Pythagorean Theorem is well known among elementary to middle school students, given its elegantly looking equation that applies to all right triangles.

Math: Pythagorean Triples

Inside a right triangle, a and b are the two legs, and c is the hypotenuse.

• a² + b² = c²

When a, b, and c are positive integers satisfying the Pythagorean Theorem, (a, b, c) are called “Pythagorean Triples.”. Obviously (3, 4, 5) is the first Pythagorean triple, followed by (5, 12, 13), (6, 8, 10), and so forth. The number of Pythagorean triples is infinite.

Example

So, how do we find all the Pythagorean triples below 100?

Answer

We can multiply ...