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

  1. Consider a regular nn-gon inscribed in a circle of radius 1: Show that its perimeter is given by 2nsin(3602n).2n \sin\left(\frac{360^\circ}{2n}\right).
  2. Recall that \(\Twopi\) is defined to be the circumference of a unit circle, and π\pi is defined to be half this quantity. Compute approximate values of \(\Twopi\) and π\pi (to 4 decimal points, say).