Monday, February 21, 2011

Bit of a maths puzzle.

Ugh! This comes out nicely on my blog but looks like crap in Google reader, presumably because the javascript can't run.
Define a function:
$f(x) = \frac{2x}{1 - x^2}$ In case that maths layout thing isn't working, that's f(x) = 2x/(1-x^2)
Now, $f(0) = 0$ so that repeats. Also $f(\sqrt 3) = -\sqrt 3$ and $f(\sqrt -3) = \sqrt 3$ so that repeats too.
The question is, what values repeat if you keep applying f to the result? I thought I knew the answer but now I think maybe it's more tricky.