Pythagoras’ theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle.
The theorem is named for the Greek philosopher Pythagoras, born around 570 BC. The theorem has been proven numerous times by many different methods – possibly the most for any mathematical theorem.
The squared distance between two points equals the sum of squares of the difference in each coordinate between the points.
The Pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power. Popular references in literature, plays, musicals, songs, stamps, and cartoons abound.
Pythagoras of Samos was an ancient Ionian Greek philosopher and founder of Pythagoreanism. His political and religious teachings were well known in Magna Graecia and influenced the philosophies of Plato, Aristotle, and, through them, the West in general.
The teaching most securely identified with Pythagoras is metempsychosis, or the “transmigration of souls”. He may have also devised the doctrine of musica universalis, which holds that the planets move according to mathematical equations.
In antiquity, Pythagoras was credited with many mathematical and scientific discoveries. He was the first man to call himself a philosopher, and was first to divide the globe into five climatic zones. Many of the discoveries credited to him likely originated earlier or were made by his colleagues or successors.
Pythagoras influenced Plato’s dialogues, especially his Timaeus, exhibit Pythagorean teachings. His ideas on mathematical perfection also impacted ancient Greek art. His teachings underwent a major revival in the first century BC among Middle Platonists.