The Erdős-Szekeres problem on points in convex position and its proof using Ramsey theorem are well know. The problem goes like this: For every natural number $k$ there exists a number $n(k)$ such ...
Defining the diameter of a convex polygon as the maximum possible distance between all pairs of vertices, can we conclude that the convex polygon is inscribable (i.e has all its sides as chords of a ...
In a program I'm writing I need to be able to check whether a straight line between two points is homotopic to a polyline between them. For example in the below example the first one is equivalent to ...
Are there any Heron-like formulas for convex polygons ? By Heron-like I mean formulas without angles as arguments and which takes as arguments only lenghts of sides of polygon - that is - we know no ...
Let $P$ be a convex polygon represented with a list of vertices specified by some orientation. Consider the following problem Problem. Find in linear time a diagonal of $P$ such that the absolute ...
I am trying to write an algorithm to solve a problem I have. I have a few ideas of what the algorithm might be like but I am posting to see if anyone else has a better more efficient solution or any ...