A Pythagorean Triple consists of three positive integers a, b, and c that satisfy the equation a^2 + b^2 = c^2. This relationship is derived from the Pythagorean Theorem, which is used in geometry to determine the lengths of the sides of a right triangle. In a right triangle, c represents the length of the hypotenuse, while a and b are the lengths of the other two sides. Common examples of Pythagorean triples include (3, 4, 5) and (5, 12, 13). These sets of numbers can be used to create right triangles with integer side lengths. Pythagorean triples are important in various fields, including mathematics, physics, and engineering, as they provide simple solutions to problems involving right triangles.