Question

Is there any way to solve the recurrence relation:
x[n] = Sqrt( 2 - 2*Sqrt(1 - (x[n-1]/2)² ) such that you get an iterative formula?

Answer 1

For clarity:
\[x_{n}=\sqrt{2-2 \sqrt{1-(x_{n-1}/2)²}}\]

Answer 2

It might be possible to denest the radical but u will still be left with one somewhere.

Answer 3

I am looking for a more accurate rewritten formula (than above) for computing the sides of polygon with 3*2^n sides (approximating a circle). Any tip where to focus, what kind of computations I need to do? I would be thankful for any suggestion.