Pythagoras -- the first mathematician?

While this philosopher was certainly not the first person in the world to work with numbers, many people think of him as the first mathematician. He founded a school in southern Italy in the sixth century BC to study musical harmony and geometry. One of his most important observations concerned the length of the sides of a right triangle.

The Pythagorean theorem tell us that the sum of the squares of the lengths of the sides of a right triangle is equal to the square of the length of the hypotenuse. In a simple triangle, the relationship looks like this:

This triangle is often called the 3, 4, 5 triangle because it shows what Pythagoras discovered in simple terms. It just happens that five squared (25) is exactly equal to three squared (9) plus four squared (16). This relationship is true for any right triangle that contains a right angle, or an angle of 90 degrees.

The Pythagorean theorem works with any triangle that contains a right angle, even if the numbers don't come out even and neat like the 3, 4, 5 triangle shown here.