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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...

2 votes
0 answers
126 views

Intersecting balls with convex regions and a bisector thereof

This question is related to my previous posting Angle subtended by the shortest segment that bisects the area of a convex polygon Let $C$ be a convex region in the plane and let $s$ be the shortest …
Tom Solberg's user avatar
8 votes
2 answers
338 views

Angle subtended by the shortest segment that bisects the area of a convex polygon

Let $C$ be a convex polygon in the plane and let $s$ be the shortest line segment (I believe this is called a "chord") that divides the area of $C$ in half. What is the smallest angle that $s$ could m …
Tom Solberg's user avatar