On the number of star-shaped polygons and polyhedra
نویسنده
چکیده
We show that the maximum number of strictly star-shaped polygons through a given set of n points in the plane is (n). Our proof is constructive, i.e. we supply a construction which yields the stated number of polygons. We further present lower and upper bounds for the case of unrestricted star-shaped polygons. Extending the subject into three dimensions, we give a tight bound of (n) on the number of distinct sets of star-shaped polyhedra.
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