Is any mathematical universe who could support π (Pi) = 1 ?

Question

In the Euclidean universe 2d or 3d, π=3.1415...
But as issued from [ i² = -1 ] there is a universe for the Euler's identity : [ e^(i*π)+1=0 ] ...

An imaginary "squared" universe may possibly verify the circle's quadrature π=4 ..... (yes or no ?)

Then will it be any possible mathematical universe who could support π=1 ?

Answer 1

An universe of negative curvature would do it. In Euclidean geometry, a circle of diameter 1 would have a circumference of 3.14159..., but if we lived in a universe of negative curvature (as a matter of fact, we are, in the presense of gravitation), this circumference is slightly less than 3.14159. In an universe of extreme negative curvature (black hole, maybe?), pi could become 1.

Answer 2

well... anything to the zero power is one...

I can't really think of anything else it could be off the top of my head.