## Classical Topics in Discrete GeometryGeometry is a classical core part of mathematics which, with its birth, marked the beginning of the mathematical sciences. Thus, not surprisingly, geometry has played a key role in many important developments of mathematics in the past, as well as in present times. While focusing on modern mathematics, one has to emphasize the increasing role of discrete mathematics, or equivalently, the broad movement to establish discrete analogues of major components of mathematics. In this way, the works of a number of outstanding mathema- cians including H. S. M. Coxeter (Canada), C. A. Rogers (United Kingdom), and L. Fejes-T oth (Hungary) led to the new and fast developing eld called discrete geometry. One can brie y describe this branch of geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. This, as a classical core part, also includes the theory of polytopes and tilings in addition to the theory of packing and covering. D- crete geometry is driven by problems often featuring a very clear visual and applied character. The solutions use a variety of methods of modern mat- matics, including convex and combinatorial geometry, coding theory, calculus of variations, di erential geometry, group theory, and topology, as well as geometric analysis and number theory. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

### Common terms and phrases

affine arbitrary convex body Bezdek billiard trajectories body of constant Boltyanski boundary point closed congruent constant width convex body convex domain convex hull convex polytope convex set Corollary covering radius d-dimensional ball defined denote dihedral angles dimension dimensional Discrete Geometry disk-polygon dist(o Dodecahedral Conjecture Ed,d edge Euclidean ball Euclidean space face Fejes Tóth finishing the proof finite following theorem Geom graph Hadwiger number halfspaces hyperbolic hyperplane Illumination Conjecture illumination number implies inequality inner dihedral angles inradius integer intersection kissing number lattice Lemma Math Moreover non-overlapping o-symmetric convex body orthogonal packing of unit pairwise plane plank problem proof of Theorem ra_2 Recall refer the interested relative interior resp Rogers orthoscheme conv{o simplex space sphere packings spherical cap spherically convex spindle convex hull Springer Science+Business Media translates unit sphere upper bound vector vertex vertices vold vold(K Voronoi cell Voronoi polytope P C E wedge of type