Phi

For my Science Research Independent Study this year I am studying the ratio phi in relation to sound. For those of you who don't know, phi is an irrational ratio (like pi), and is equal to about 1.618. Phi was first discovered by Euclid when he explored the "extreme and mean" ratio. This ratio says that if you take a line segment AC and divide at a point B such that AC:AB=AB:BC then the ratio that both expressions share must be equal to phi, 1.618. It also appears in geometry in an Equilateral Pentagon. If the diagonals are drawn such that a pentagram is inscribed withing the equilateral pentagon, then the ratio of the diagnols to the sides is 1.618. The ratio also appears constantly in nature. The ratio of successively larger shells of the Chambered Nautilus is equal to phi. Phi also governs the growth of rose petals. Even in the human body if you were to take the distance from the floor to the top of your head and divide it by the distance from the floor to your belly button, you should get approximately phi.