|The Pythagorean theorem:
a2 + b2 = c2
The Pythagorean theorem or Pythagoras' theorem is a relation in Euclidean geometry among the three sides of a right triangle. The theorem is named after the Greek mathematician Pythagoras, who is traditionally credited with its discovery, although knowledge of the theorem almost certainly predates him.
The theorem is as follows:
In any right triangle, the area of the square whose side is the hypotenuse (the side of a right triangle opposite the right angle) is equal to the sum of areas of the squares whose sides are the two legs (i.e. the two sides other than the hypotenuse).
This provides a simple relation among the three sides of a right triangle so that if the lengths of any two sides are known, the length of the third side can be found. This theorem may have more known proofs than any other. The Pythagorean Proposition, a book published in 1940, contains 370 proofs of Pythagoras' theorem, including one by American President James Garfield.