5 papers
Extremal convex polygons inscribed in a given convex polygon
Csenge Lili Ködmön, Zsolt Lángi
A convex polygon is inscribed in a convex polygon if every side of contains at least one vertex of . We present algorithms for finding a minimum area and a minimum p…
On the convex hull and homothetic convex hull functions of a convex body
Ákos G. Horváth, Zsolt Lángi
The aim of this note is to investigate the properties of the convex hull and the homothetic convex hull functions of a convex body in Euclidean -space, defined as the volume…
A solution to some problems of Conway and Guy on monostable polyhedra
Zsolt Lángi
A convex polyhedron is called monostable if it can rest in stable position only on one of its faces. The aim of this paper is to investigate three questions of Conway, regarding mo…
From spherical to Euclidean illumination
Károly Bezdek, Zsolt Lángi
In this note we introduce the problem of illumination of convex bodies in spherical spaces and solve it for a large subfamily of convex bodies. We derive from it a combinatorial ve…
Centering Koebe polyhedra via Möbius transformations
Zsolt Lángi
A variant of the Circle Packing Theorem states that the combinatorial class of any convex polyhedron contains elements midscribed to the unit sphere centered at the origin, and tha…