My tongue in cheek suggestion for an addition to the Yellow "Maths for Idiots" Book list.

A definition of Pi not making use (perhaps) of plain geometry

From Wikipedia https://en.wikipedia.org/wiki/Pi on Pi:

...A variation on the same idea, making use of sophisticated mathematical concepts of topology and algebra, is the following theorem: there is a unique (up to automorphism) continuous isomorphism from the group R/Z of real numbers under addition modulo integers (the circle group), onto the multiplicative group of complex numbers of absolute value one. The number π is then defined as half the magnitude of the derivative of this homomorphism.

I won't pretend, I have not the faintest idea what that means!!!