I try to solve the following recursion for $n \in \mathbb{N}$.
$r_i = r_{i-1} - \frac{1}{2} \cdot \sqrt{1 - \frac{4\pi^2\cdot r_{i-1}^2}{n^2} \cdot \cos^2 \left(\frac{\pi}{n}\right)}$
$r_0 = \frac{n}{2\pi}$
I translated it into the following code for Mathematica:
RSolve[{g[x]==g[x-1]- 1/2 Sqrt[1 - 4 Pi^2 g[x-1]^2/n^2 (Cos[Pi/n])^2], g[0]==n/(2 Pi)}, g[x], x]
However, Mathematica cannot interpret this and I get the input as result. Is there any mistake from my side or is Mathematica not able to solve this?
