Inspired by Indiana, consider a hyperbolic plane where pi equals 4; that is, the angle around a point is not 360 degrees or 6.28... radians but 8 radians, or 5 squares can share a corner, with 0.09 radians left over.
Is there anything interesting about this space? Is the perimeter of a circle 8r? Do a circle inscribed in a square both have the same perimeter? (Probably not.)
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