Does Pi Change in Curved Space Geometry?

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SUMMARY

The discussion focuses on the value of pi in curved space geometry, specifically addressing the misconception that pi can change based on the size of a circle drawn on a spherical object, such as a volleyball. Participants clarify that pi remains constant and is not defined as a ratio in spherical geometry. Instead, the formulas governing geometric relationships, such as the angles of triangles, are altered in curved spaces. This distinction is crucial for understanding geometry in non-Euclidean contexts.

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  • Basic mathematical skills for ratio and circumference calculations
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If i have a volleyball and draw a circle around the centre, then draw a line between the top of the ball and the centre and measure the two line I find that the ratio circumference of the circle to diameter of the circles is 4, thus implying that in this case pi is 4, however if I drew a circle of a different size I would get a different ratio.

Could anyone tell me if the value of pi changes in curved space, or if it is the equations that need to be updated?

Thanks in advance for your help.
 
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pi does not change. it is not defined as a ratio of anything in spherical geometry (a priori, at least). the formulae of things in spherical geometry all change: the angles of triangles no longer add to pi either.
 
Thanks for your help Matt, that clears up some confusion
 

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