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Convexity of Sub-polygons of Convex Polygons

Iosif Pinelis
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Abstract

A convex polygon is defined as a sequence (V_0,...,V_{n-1}) of points on a plane such that the union of the edges [V_0,V_1],..., [V_{n-2},V_{n-1}], [V_{n-1},V_0] coincides with the boundary of the convex hull of the set of vertices {V_0,...,V_{n-1}}. It is proved that all sub-polygons of any convex polygon with distinct vertices are convex. It is also proved that, if all sub-(n-1)-gons of an n-gon with n\ge5 are convex, then the n-gon is convex. Other related results are given.

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Iosif Pinelis. 2006-09-25. Convexity of Sub-polygons of Convex Polygons. https://arxiv.org/abs/math/0609698

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