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Comment by SAI_Peregrinus | Hacker News Reader

Which means it depends on the geometry of spacetime. If spacetime is quantized such that the Euclidean norm doesn't apply, then the value of pi will be different. See the "Extremal values of pi" paper[1].

[1]https://e.math.cornell.edu/people/Nikhil_Sahoo/files/pi_pape...

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Pi falls out of infinite sums, exponentials and differential equations all over the place. It's a universal constant, first discovered via geometry, but it's independent of geometry.

For example,

pi = the square root of the sum of 6/x^2 over x = (1, 2, 3...).

pi = the smallest positive value of ln(-1)/i.

pi = half the period of non-zero solutions to the differential equation f = -f''.

You can define Pi without universal geometry. And it's still a constant, nothing arbitrary, unlike

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