RegularNGons case visualizer

This applet helps you finding interesting theorems in regular polygons and polygrams. See a preprint for the concept. By using the applet you can set n to define the number of the sides of the polygon or polygram. Use k to explicitly define the polygon or polygram with the Schläfli symbol {n/k}. Please note that k must be a coprime to n. Interesting inputs include the following cases:
  • n=11, k=4, s=50867. Here |RS| is near 1.
  • n=11, k=3, s=40220. Here |RS| is near 5/3.
  • n=12, k=5, s=43261. Here |RS| is near π. The approximation is the same as Kochański's result (1685).
  • n=12, k=5, s=52958. Here |RS| is near π again, but this setup is simpler.
  • n=15, k=2, s=381653. Here |RS| is even closer to π, in an exact form it is , a root of the polynomial .