Pythagorean Theorem

One of the most famous theorems of geometry, often attributed to Pythagoras of Samos (Greece) in the sixth century B.C., states the sides a, b, and c of a right triangle satisfy the relation c² = a² + b² where c is the length of the hypotenuse of the triangle and a and b are the lengths of the other two sides.

This theorem was likely to have been known earlier to be the Babylonians, Pythagoras is said to have traveled to Babylon as a young man, where he could have learned the famous theorem. Nevertheless, Pythagoras (or some member of his school) is credited with the first proof of the theorem.

The converse of the Pythagorean theorem is also true. That is if a triangle with sides a, b, and c has a² = b² + c², we know that the triangle is a right triangle.

A special form of the theorem was used by the Egyptians for making square corners when they re-surveyed the land adjacent to the Nile river after the annual flood. They used a rope loop with 12 knots tied at equal intervals along the rope. Three of the knots were used as the vertices of a triangle. Since 3² + 4² = 5² we know, by the converse of the Pythagorean theorem, that we have a right triangle.