Mathematical equations have shaped our understanding of the universe, and these nine have played a key role in changing the world.

One idea he came up with was a mathematical equation that's used all the time ... of the squares of two sides equals the square of the hypotenuse (the longest side).

The hypotenuse is the longest side and is ... Image caption, These three equations are true for all right-angled triangles. They are known as the three trigonometric ratios because they show ...