The number π

In this exercise we estimate π via regular polygons inscribed in the unit circle.

  1. Compute h1 and h2.
  2. Compute the area of ΔOAC and the area of ΔABC.
  3. Use your results from 2. to find an underestimate for π.
  4. Let M be the midpoint of the (shortest) arc from B to C. Compute the area of ΔBMC
    and find a better estimate for π. How could one improve this estimate?
Latest update 11. March 2011 by Iver Ottosen