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Revision as of 02:54, 3 March 2007

A Pythagorean Triple is a triple of positive integers, $(a, b, c)$ such that $a^2 + b^2 = c^2$. Pythagorean Triples arise in geometry, as the side-lengths of right triangles.

Common Pythagorean Triples

These are some common Pythagorean Triples:

(3, 4, 5)

(20, 21, 29)

(11, 60, 61)

(13, 84, 85)

(5, 12, 13)

(12, 35, 37)

(16, 63, 65)

(36, 77, 85)

(8, 15, 17)

(9, 40, 41)

(33, 56, 65)

(39, 80, 89)

(7, 24, 25)

(28, 45, 53)

(48, 55, 73)

(65, 72, 97)

Primitive Pythagorean Triples

A Pythagorean Triple is primitive if it has no common factors, so that they are relatively prime. All of the above are primitive. Multiples of the above triples will also satisfy $a^2 + b^2 = c^2$; for example, any three numbers in the form of $(3x, 4x, 5x)$, like $(6, 8, 10)$, will also satisfy it.

See also