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?

  • 1
    $\begingroup$ Almost certainly the latter. $\endgroup$ Commented Mar 14, 2019 at 14:22

1 Answer 1


Will using RecurrenceTable helps?

RecurrenceTable[{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, 1, 3}]

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.