Pythagorean triple

Also known as Pythagorean triples

three positive integers, the squares of two of which sum to the square of the third

AI overview

A Pythagorean triple is a set of three positive whole numbers where the squares of two of them add up to equal the square of the third. These number combinations are useful in geometry and construction because they create perfect right triangles without needing decimals or approximations.

AI-generated from the Wikipedia summary — may contain errors.

~40 min read

Encyclopedic overview

Animation demonstrating the smallest Pythagorean triple, 3 + 4 = 5 A Pythagorean triple consists of three positive integers a, b, and c, such that a + b = c. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and called a Pythagorean triangle.

A primitive Pythagorean triple is one in which a, b and c are coprime (that is, they have no common divisor larger than 1). For example, (3, 4, 5) is a primitive Pythagorean triple whereas (6, 8, 10) is not. Every Pythagorean triple can be scaled to a unique primitive Pythagorean triple by dividing (a, b, c) by their greatest common divisor. Conversely, every Pythagorean triple can be obtained by multiplying the elements of a primitive Pythagorean triple by a positive integer (the same for the three elements).

Excerpted from Wikipedia’s “Pythagorean triple” article, available under the CC BY-SA 4.0 licence.