Classical topics in discrete geometry / Károly Bezdek

Auteur: Bezdek, Károly (1955-) - AuteurType de document: Livre numérique Collection: CMS books in mathematics Langue: anglaisÉditeur: New York : Springer, cop. 2010 ISBN: 9781441905994 Note: Contents: Preface; Part I. Classical topics revisited: 1. Sphere packings; 2. Finite packings by translates of convex bodies; 3. Coverings by homothetic bodies—illumination and related topics; 4. Coverings by planks and cylinders; 5. On the volume of finite arrangements of spheres; 6. Ball-polyhedra as intersections of congruent balls; Part II. Selected proofs: 7. Selected proofs on sphere packings; 8. Selected proofs on finite packings of translates of convex bodies; 9. Selected proofs on illumination and related topics; 10. Selected proofs on coverings by planks and cylinders; 11. Selected proofs on the Kneser-Poulsen conjecture; 12. Selected proofs on ball-polyhedra; References. Sujets MSC: 52-02 Convex and discrete geometry -- Research exposition (monographs, survey articles)
52A20 Convex and discrete geometry -- General convexity -- Convex sets in n dimensions (including convex hypersurfaces)
52A38 Convex and discrete geometry -- General convexity -- Length, area, volume
52B70 Convex and discrete geometry -- Polytopes and polyhedra -- Polyhedral manifolds
52C17 Convex and discrete geometry -- Discrete geometry -- Packing and covering in n dimensions
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Contents: Preface; Part I. Classical topics revisited: 1. Sphere packings; 2. Finite packings by translates of convex bodies; 3. Coverings by homothetic bodies—illumination and related topics; 4. Coverings by planks and cylinders; 5. On the volume of finite arrangements of spheres; 6. Ball-polyhedra as intersections of congruent balls; Part II. Selected proofs: 7. Selected proofs on sphere packings; 8. Selected proofs on finite packings of translates of convex bodies; 9. Selected proofs on illumination and related topics; 10. Selected proofs on coverings by planks and cylinders; 11. Selected proofs on the Kneser-Poulsen conjecture; 12. Selected proofs on ball-polyhedra; References.

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