Spirals Are Seen in Nature - in the Swirl of a Pine

Short Answer

Spirals are seen in nature - in the swirl of a pine cone; they are also used in machinery to convert motions. An Archimedes Spiral has the general equation r = a θ. A more general form for the quation of a spiral is r = aθ^1/n where n is a constant that determines how tightly the spiral is wrapped. Compare the Archimedes Sprial r = θ with the spiral

by graphing both on the same polar graph.