Involute - or evolvent - curves are used as the shape of teeth of gears. For an introduction to more advanced math, see https://en.wikipedia.org/wiki/Involute.
Inhoud
What is an involute curve?
The quick and dirty example in the picture says more than words.
So if
The main reason for using gears with involute shapes is that there is no friction between teeth - against common believe. The teeth roll on each other when rotating.
It is the gear application that makes a polar calculation based on radii more useful than a Cartesian calculation based on (x,y) - we are only interested in the first small part that starts from the base circle.