noun A set of three positive integers a, b, and c, such that a^2 + b^2 = c^2, representing the sides of a right triangle
adjective Describing a set of three integers that satisfy the Pythagorean theorem
In mathematics, a Pythagorean triple is a set of three positive integers a, b, and c, such that a^2 + b^2 = c^2. These triples are commonly used in geometry and number theory.
In geometry, Pythagorean triples are used to represent the sides of right-angled triangles, where the lengths of the sides satisfy the Pythagorean theorem.
In number theory, Pythagorean triples are studied for their properties related to integer solutions of the Pythagorean equation a^2 + b^2 = c^2.
Pythagorean triples are used in mathematics by mathematicians to study relationships between the sides of right-angled triangles.
Physicists use Pythagorean triples in various calculations, such as determining distances in 3D space or analyzing forces in mechanical systems.
Engineers often use Pythagorean triples in structural design, such as calculating diagonal bracing in buildings or determining the length of cables in suspension bridges.