Here are some questions that can be explored using this applet. Some are easy, some are very hard.
  1. How are the polygons named?
  2. Is there a pattern or a formula for the number of diagonals of a regular polygon with n sides?
  3. Can you tell whether n is odd or even just by looking at the polygon?
  4. What is the explanation for the ring patterns that we see when n is large?
  5. Is it possible for four diagonals to meet at a common interior point other than the center?
  6. What numbers do the perimeter and area approach as n increases?
  7. Why does the perimeter seem approach a limit more rapidly than the area does?