n. the theorem in Euclidean geometry that, in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides; the figure below represents this result geometrically. The lengths of the sides of a right-angled triangle, in integer multiples of an appropriate unit, thus form a Pythagorean triple of integers. (Named after the Greek philosopher, mathematician and mystic, Pythagoras of Samos (c. 580 - 500 BC), who founded a school of thought that influenced Plato. He and his followers believed that `All is number', recognizing the mathematical nature of music, and extending this through the `music of the spheres' to a mystical numerical harmony of the universe.)
Pythagoras' theorem. The sum of the areas of the dark squares equals that of the light square.