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.
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