Discrete Geometry

Celebrating the work of Professor W. Kuperberg, this reference explores packing and covering theory, tilings, combinatorial and computational geometry, and convexity, featuring an extensive collection of problems compiled at the Discrete Geometry Special Session of the American Mathematical Society in New Orleans, Louisiana. Discrete Geometry analyzes packings and coverings with congruent convex bodies , arrangements on the sphere, line transversals, Euclidean and spherical tilings, geometric graphs, polygons and polyhedra, and fixing systems for convex figures. This text also offers research and contributions from more than 50 esteemed international authorities, making it a valuable addition to any mathematical library.

Table of Contents:
Transversal lines to lines and intervals, Jorge L. Arocha, Javier Bracho, and Luis Montejano; on a shortest path problem of G. Fejes, Toth Donald R. Baggett and Andras Bezdek; a short survey of (r,q)-structures, Vojtech Balint; lattice points on the boundary of the integer hull, Imre Barany and Karoly Boroczky, Jr; the Erdos-Szekeres problem for planar points in arbitrary position, Tibor Bisztriczky and Gabor Fejes Toth, separation in totally-sewn 4-polytopes, Tibor Bisztriczky and Deborah Oliveros, on a class of equifacetted polytopes, Gerd Blind and Roswitha Blind; chessboard Ramsey numbers, Jens-P. Bode, Heiko Harborth, and Stefan Krause; maximal primitive fixing systems for convex figures, Vladimir Boltyanski and Hernan Gonzalez-Aguilar; the Newton-Gregory problem revisited, Karoly Boroczky, arrangements of 13 points on a sphere Karoly Boroczky and Laszlo Szabo; on point sets without k collinear points, Peter Brass; the Beckman-Quarles theorem for rational d-spaces, d even and d> 6, Robert Connelly and Joseph Zaks; edge-antipodal convex polytopes - a proof of Talata's conjecture, Balazs Csikos; single-split tilings of the sphere with right triangles, Robert J. MacG. Dawson; vertex-unfoldings of simplicial manifolds, Erik D. Demaine, David Eppstein, Jeff Erickson, George W. Hart, and Joseph O'Rourke; view-obstruction through trajectories of co-dimension three Vishwa C. Dumir and Rajinder J. Hans-Gill; fat 4-polytopes and fatter 3-spheres, David Eppstein, Greg Kuperberg, and Gunter M. Ziegler; arbitrarily large neighbourly families of congruent symmetric convex 3-polytopes, Jeff Erickson and Scott Kim; on the non-solidity of some packings and coverings with circles, August Florian and Aladar Heppes; on the mth Petty numbers of normed spaces Karoly Bezdek, Marton Naszodi and Balazs Visy; cubic polyhedra, Chaim Goodman-Strauss and John M. Sullivan; new uniform polyhedra, Branko Grunbaum; on the existence of a convex polygon with a specified number of interior points, Kiyoshi Hosono, Gyula Karolyi and Masatsugu Urabe; on-line 2-adic covering of the unit square by boxes, Janusz Januszewski and Marek Lassak; an example of a stable, even order quadrangle which is determined by its angle function, Janos Kincses; sets with a unique extension to a set of constant width, Marton Naszodi and Balazs Visy; the number of simplices embracing the origin, Janos Pach and Mario Szegedy; Helly-type theorems on definite supporting lines for k-disjoint families of convex bodies in the plane, Sorin Revenko and Valeriu Soltan; combinatorial aperiodicity of polyhedral prototiles, Egon Schulte; sequences of smoothed polygons, G.C. Shephard; on a packing inequality, Graham, Witsenhausen and Zassenhaus, Jorg M. Wills; covering a triangle with homothetic copies, Zoltan Furedi; open problems, Andras Bezdek.