[Relativity FAQ] - [Copyright]

Original by Philip Gibbs 8-August-1997

Is pi constant in relativity?

Yes. Pi is a mathematical constant usually defined as the ratio of the circumference of a circle to its diameter in Euclidean geometry. It can also be defined in other ways, for example, it can be defined using an infinite series:

   pi/4 = 1 - 1/3 + 1/5 - 1/7 + 1/9 - ... 

In general relativity space and space-time are non-Euclidean geomertries. The ratio of the circumference to diameter of a circle in non-Euclidean geometry can be more or less than pi. For the types of non-Euclidean geometry used in physics the ratio is very nearly pi over small distances so we do not notice the difference in ordinary measurements. This does not mean that pi changes because our definition of pi specified Euclidean geometry, not physical geometry. No new theory or experiment in physics can change the value of mathematically defined constants.