[Physics FAQ] - [Copyright]

Original by Philip Gibbs 1997.

Is π constant in relativity?

Yes.  π 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:

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

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