What's pi got to do with it?

Last week at Meet the Mathematicians I saw a talk by Jon Keating , "Some thoughts on the unreasonable effectiveness of mathematics" (an essay by Wigner). One element that I have taken away from this was when Jon was talking about the unexpected connections between mathematical concepts, illustrated using the normal distribution (an example from the original essay). The bell shaped curve depends on the mean and the variance, which is perfectly reasonable. The curve depends as well on pi. So Jon posed the question: If you take a large group of people, measure their heights (or other body parts, or lots of other types of data) and arrange them on a histogram, what has that to do with the ratio between the circumference and diameter of a circle?

There was also a session in which audience questions were put to a panel of mathematicians. I walked in during the question "What is your favourite equation?" and during this the answer of one panellist was Euler's identity. This is again peculiar and wonderful: this arranges (only) the multiplicative and additive identities, the base of the natural logarithm, the ratio of any circle's circumference to it's diameter and the square root of negative one into one a single, simple equation.

Anyway, this reminds me of this cartoon from xkcd.com, which I think sums this all up succinctly (if crudely):