The Pythagorean Theorem is a main concept in mathematics, and more specifically in Euclidean geometry, developed by the ancient philosopher and mathematician Pythagor, who lived around 500 years B.C. (570 B.C. - 495 B.C.). It is widely used in many areas of math, and it is used as a fundamental for many other theorems. The Pythagoras theorem simply states:

In a right triangle, the area of the square whose side is the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares whose sides are the two legs.

This is simply expressed with the formula: a² + b² = c² , where a and b, are the lengths of the legs of a right triangle and c is the length of its hypotenuse.

To be more clear, take a look at the following image:

The theorem can be proofed in many different ways: using similar triangles, algebraic proof, complex numbers proof and some others.