Placing two disks in a convex polygon

Computing Two Centers of a Convex Polygon

Two-Center Problems for a Convex Polygon

Finding the Maximum Area Centrosymmetric Polygon in a Convex Polygon

On unit distances in a convex polygon

For any convex quadrilateral, the sum of the lengths of the diagonals is greater than the corresponding sum of a pair of opposite sides, and all four of its interior angles cannot be simultaneously acute. In this article, we use these two properties to estimate the number of unit distance edges in convex n-gons and we: (i) exhibit three large groups of cycles formed by unit distance edges that ...

Maximal Area Triangles in a Convex Polygon

In [12], the widely known linear time algorithm for computing the maximum area triangle in a convex polygon was found incorrect, and whether it can still be solved in linear time was proposed as an open problem. We resolved it affirmatively by presenting a new linear time algorithm. Our algorithm is simple and easy to implement, and it computes all the locally maximal triangles. 1998 ACM Subjec...