What is π?

The number, π, is one of the most ubiquitous constants in all of the world. Despite the fact that it has a very specific definition (taught in any beginning Geometry course, that π is the ratio of the circumference to the diameter of any circle) it has a way of showing up in a wide variety of applications having no apparent connection to the circle.

The animation above illustrates the definition of π. If you were to take a circle with a diameter of one unit with a red tape wrapped around the circumference of the circle and roll it along a number line, then the red tape would cover a length of about 3.14159 diameters along the number line. We call this number of diameters it takes to wrap around the circle, π, because π is the first letter of the Greek word perimeter. Put another way, the circumference of any circle is exactly π times the length of the diameter.