Comment by rjmunro

Pi is the "the ratio of circumference to diameter of a circle in Euclidian space". Everyone agrees that. What people are arguing is that when you have a circle in non-Euclidian space, so that the ratio of it's circumference to diameter is different, do we still call this new ratio Pi.

Most people would argue that we don't. They say "the ratio is not Pi" rather than "Pi is a different value".