Simple N-gon Counter

> To play this game, you need a Java compatible browser.

Click some points in the rectangle shown above, then click the "submit" button. The Java applet counts the number of different polygons that can be made using all those points as vertices. (A polygon is a circuit of edges connecting the vertices, where no two edges may cross.)

A famous question in the field of combinatorial geometry is:

Given n points in the plane, how many polygons are determined by those points?

If the points lie on the outside of a circle, the answer is one. If all but one of the points lie on the outside of a circle, and the last one lies on the inside, the answer is n-1. These are the smallest numbers that answer the question. The largest possible number of polygons determined by n points is unknown.

Feel free to send questions about the applet and suggestions for improvement of this page to me at burgiel@geom.umn.edu.

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