Pi - why?

[Fangs4themammaries]

I think Pi Day (14 March) passed unnoticed on here. Can someone please tell me why Pi is so important in maths (or life?). I get that it is impossible to convert the exact area of a circle into an equivalent square ('squaring the circle') To me, that is just mildly puzzling - but not world-shattering. I get that perhaps it was important in ancient times (maybe still today, who knows?) in exactly parcelling out land. But beyond that, I can't see why mathematicians cannot be content with the couple of decimal places it is possible to find the value of Pi to. Apparently the Romans could not be bothered with it beyond that, and it didn't hold them back.

If you are not a scientist, mathematician, engineer or philosophical dreamer you can certainly live quite happily without giving pi a second thought, but it is, nevertheless, an interesting number that is knitted into the fabric of maths and the reality it can describe.

The significance of pi for me is that it is a mathematical constant that transcends this particular universe – if that doesn’t sound too cosmic! What I mean is that I can conceive of another universe in which, say, the charge on the electron is different or another fundamental particle takes the place of the electron, but pi would have the same value in all possible universes. So pi has a fundamental and eternal character – like Euler’s number e, and the two are nicely interrelated through:

e^i(pi) = - 1

The existence of pi and the way in which it crops up again and again in so many branches of maths and science is intriguing but the calculation of pi to a humongous number of decimal places is not a pursuit that particularly interests me!