True, but it certainly is a dimensionless number that you can't get rid of (and that actually shows up in physical formulae, such as http://en.wikipedia.org/wiki/Coulomb%27s_law). Come to think of it, so is 2.
I guess if you tried to measure π by constructing circles, you'd actually be measuring the curvature tensor of space (which is an experimental observation), not π (which is just π).
π being, simply, the measurement of the curvature tensor of an ideal Euclidean plane. If we lived in a universe that was non-Euclidean at macro-scale, π would be just another irrational number, and some other quantity would be exalted as "fundamental."
I wouldn't have said Pi was a physical constant - it's not like we actually measure circles to derive it empirically.
True, but it certainly is a dimensionless number that you can't get rid of (and that actually shows up in physical formulae, such as http://en.wikipedia.org/wiki/Coulomb%27s_law). Come to think of it, so is 2.
I guess if you tried to measure π by constructing circles, you'd actually be measuring the curvature tensor of space (which is an experimental observation), not π (which is just π).
π being, simply, the measurement of the curvature tensor of an ideal Euclidean plane. If we lived in a universe that was non-Euclidean at macro-scale, π would be just another irrational number, and some other quantity would be exalted as "fundamental."
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