Re: Cute math puzzle

James Dow Allen wrote:
Robert Israel wrote:
Let g(x) = 1/(1-x). This fractional linear transformation has
period 3, i.e. g(g(g(x))) = x.

Obpuzzle: Find a "fractional linear transformation"
with period 5.

(Professional mathematicians please wait a few days before spoiling
this.)


Taking a hint from Robert Israel's enlightening posts, I'd consider a composition of the following: A mapping from the real line to a circle in the complex plane, a rotation of the circle by 2 pi / 5, and an inverse mapping from the circle back to the real line. I think these are all conformal mappings so the composition should be too.
.

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