Consider a polygon A_0…A_n. Why does there exist diagonal A_i A_j without intersection of polygon. It's looks obvious but why?

Aron Heath

Aron Heath

Answered question

2022-11-12

Question about polygons.
Consider a polygon A 0 A n . Why does there exist diagonal A i A j without intersection of polygon. It's looks obvious but why?

Answer & Explanation

luthersavage6lm

luthersavage6lm

Beginner2022-11-13Added 22 answers

Explanation:
A convex polygon is a non-empty intersection of convex sets (half-planes), hence it is convex. In particular, if we consider the segment joining A i and A j with | i j | > 1, such segment lies inside the polygon, since it is the convex envelope of A i and A j .

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