A new area-based convexity measure for polygons is described. It has the desirable properties that it is not sensitive to small boundary defects, and it is symmetric with respect ...
In [GL] it was shown that a polytope with few vertices is far from being symmetric in the Banach-Mazur distance. More precisely, it was shown that Banach-Mazur distance between su...
Abstract. We attempt a broad exploration of properties and connections between the symmetry function of a convex set S IRn and other arenas of convexity including convex functions...
In this paper, an evolutionary clustering technique is described that uses a new point symmetry-based distance measure. The algorithm is therefore able to detect both convex and n...
Let f(n) be the maximum number of unit distances determined by the vertices of a convex n-gon. Erdos and Moser conjectured that this function is linear. Supporting this conjecture...