Of course pi is a social construct. For fuck's sake, circles are a social construct. Thank somebody older than Christ society can be arsed to construct.
Re: social construction, geometry
@pigworker and we can construct them with a compass – no straightedge needed, phew!
@pigworker Depends what you mean by "social construct", no?
We could have been interested in things other than euclidean circles. But, having decided to be interested in euclidean circles, their circumference/diameter couldn't have been anything other than pi.
(Of course pi isn't just about circles. E.g., pi/4 = 1 - 1/3 + 1/5 - 1/7 + ...; are odd numbers and arithmetic social constructs? Maybe, kinda, but again there isn't any _different_ answer we could get having asked the question.)
@gjm Well, of course it does! When you clamp a pencil in a compass and do a flingaround, the point slips and as you draw the circle, the compass dilates. The graphite nib degenerates slightly as you sweep, and the trace it leaves is far from infinitely thin. Fronds of the paper are flecked by the nib if they happen to be in range and narrowly missed if not. All of these things are well worth ignoring and doing so is a (very tasteful) choice.