Here's a Python implementation of the algorithm we developed:

  1. Consider a regular \(n\)-gon inscribed in a circle of radius 1: Show that its perimeter is given by \(2n \sin\left(\frac{360^\circ}{2n}\right).\)
  2. Recall that \(\Twopi\) is defined to be the circumference of a unit circle, and \(\pi\) is defined to be half this quantity. Compute approximate values of \(\Twopi\) and \(\pi\) (to 4 decimal points, say).