[Relativity FAQ] - [Copyright]

Original by Philip Gibbs 8-August-1997

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.