of the
Week
|
Problem
of the Week |
A diagonal in a convex polygon is a line joining two non-adjacent vertices. Take an n-sided polygon and draw all possible diagonals. Suppose that no three diagonals ever intersect at a common point. How many crossings are there in the interior of the polygon? Below is a sketch of the situation for a pentagon and a hexagon where the number of crossings, c, is five and fifteen, respectively.
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ã2002 Alberto L. Delgado