Volumetric Discrete Geometry: 1st Edition (Hardback) book cover

Volumetric Discrete Geometry

1st Edition

By Karoly Bezdek, Zsolt Langi

Chapman and Hall/CRC

282 pages | 44 B/W Illus.

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Hardback: 9780367223755
pub: 2019-04-15
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Description

Volume of geometric objects has been studied by the ancient Greek mathematicians. Even today volume continues to play an important role in applied as well as pure mathematics. In discrete geometry, which is a relatively new branch of geometry, volume plays a significant role in generating new topics for research. The author’s goal is to demonstrate the recent aspects of volume in particular, volumetric method within discrete geometry. Part I consists of survey chapters of selected topics on volume and Part II consisting of chapters of selected proofs of theorems stated in Part I.

Table of Contents

Preface xiii

List of Figures xvii

Authors xix

Symbols xxi

I Selected Topics

1 Volumetric Properties of (m; d)-scribed Polytopes

2 Volume of the Convex Hull of a Pair of Convex Bodies

3 The Kneser-Poulsen conjecture revisited

4 Volumetric Bounds for Contact Numbers

5 More on Volumetric Properties of Separable Packings

II Selected Proofs

6 Proofs on Volume Inequalities for Convex Polytopes

7 Proofs on the Volume of the Convex Hull of a Pair of Convex

Bodies

8 Proofs on the Kneser{Poulsen conjecture

9 Proofs on Volumetric Bounds for Contact Numbers

10 More Proofs on Volumetric Properties of Separable Packings

11 Open Problems: An Overview

Bibliography

Index

About the Authors

Karoly Bezdek is a Professor and Director - Centre for Computational & Discrete Geometry, Pure Mathematics at University of Calgary. He received his Ph.D. in mathematics at the ELTE University of Budapest. He holds a first tier Canada chair, which is the highest level of research funding awarded by the government of Canada.

Zsolt Langi is an associate professor at Budapest University of Technology, and a senior research fellow at the Morphodynamics Research Group of the Hungarian Academy of Sciences. He received his Ph.D. in mathematics at the ELTE University of Budapest, and also at the University of Calgary. He is particularly interested in geometric extremum problems, and equilibrium points of convex bodies.

About the Series

Discrete Mathematics and Its Applications

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Subject Categories

BISAC Subject Codes/Headings:
MAT012000
MATHEMATICS / Geometry / General
MAT036000
MATHEMATICS / Combinatorics