Given a set P of n points in convex position in the plane, we prove that there exists a point p ∈ P such that the number of distinct distances from p is at least (13n−6)/36 . ...
In this paper we present a polynomial time algorithm for computing a Hausdorff core of a polygon with a single reflex vertex. A Hausdorff core of a polygon P is a convex polygon Q...
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...
We show that cutting shortest paths from every vertex of a convex polyhedron to a simple closed quasigeodesic, and cutting all but a short segment of the quasigeodesic, unfolds th...
Abstract. Given a simple n-sided polygon in the plane with a boundary partitioned into subchains some of which are convex and colored, we consider the following problem: Which is t...