Regular+polygons+and+diagonals

media type="custom" key="19153400"

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?