Geometry Tutorials: What exactly is Pi?

As I stated in a previous Geometry Tutorial on how to calculate the surface area of circles, Pi describes the relationship between the circumference of a circle, and the circle's diameter. The size of the circle does not matter. It can have a radius of 10mm or 100000 KM, Pi will never the less be applicable.

The symbol that describes is a Greek symbol of the same name, which is actually called Pi:

Pi = Π

It was chosen as the definition of Pi, since the symbol is the first letter for the Greek translation of border area. However, if you are reading this you are probably more interested in what makes Pi so special, rather than its historical background.

Pi is a real number. However, it is not a rational one. It cannot be written as a fraction, as Johann Heinrich Lambert proved, all the way back in 1767. This means that whenever you use Pi for hand calculations you will probably have to resort to a shorter version of the number. For instance:

Π = 3.14159

Thanks to this very real but irrational number we can calculate the following items: circumferences of circles, surface area of circles, volume of spheres, surface areas of spheres and the volume of cylinders and pipes.