Let's say you start out with the side of a hexagon. Then you bisect it to get two sides of a dodecagon. Then you bisect those sides to get four sides of a 24-gon. Then you bisect those to get eight sides of a 48-gon, etc. etc.
Is there a neat function that describes the progression of the values of these sides? Let's say, for example, when you plug in 1 for this function, f(x), it gives you the side of the hexagon. Plug in 2, you get the value of one of the sides of the dodecagons, and plug in 3, you get the value of one of the sides of the 24-gon, etc. etc.
Didn't Gauss find anything like this?
Any info is appreciated!
