Pi has so many uses in the mathematics of Physics. At the moment I am dealing with a lot of Quantum Mechanics and so come across h-bar a lot. That is Planck's constant divided by 2pi. I have found out that this should really be called the reduced Planck constant and that it was introduced by Bohr whilst he was trying to come up with the quantum for the angular momentum of an electron
https://en.wikipedia.org/wiki/Planck_constant I had assumed that it came from the conversion from frequency f to angular frequency w where w=2(pi)f.
