# 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** c^{2 }= a^{2 }+ b^{2} 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 a^{2} = b^{2 }+ c^{2}, 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 3^{2 }+ 4^{2 }= 5^{2} we know, by the converse of the Pythagorean theorem, that we have a right triangle.

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