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I have a question regarding Convex Sets.

It seems that if a convex set S contains the vertices $A_1, A_2, ..., A_k$ of a polygon P = $A_1A_2...A_k$, it contains all points of the polygon P. But how can I prove it?

Thank you in advance.

Jane Doe
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1 Answers1

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If I am understanding it correctly , convex set contains convex hull of the points by definition and that implies convex set to contain the polygon.

Alp
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  • The convex hull of a set S is the smallest convex set that contains S. And the convex hull is in my case the polygon. But is there a mathematical way of proving it? – Jane Doe Oct 20 '13 at 22:29