1st Edition

Volumetric Discrete Geometry

By Karoly Bezdek, Zsolt Langi Copyright 2019
306 Pages 44 B/W Illustrations
by Chapman & Hall

306 Pages 44 B/W Illustrations
by Chapman & Hall

306 Pages 44 B/W Illustrations
by Chapman & Hall

Volume of geometric objects plays an important role in applied and theoretical mathematics. This is particularly true in the relatively new branch of discrete geometry, where volume is often used to find new topics for research. Volumetric Discrete Geometry demonstrates the recent aspects of volume, introduces problems related to it, and presents methods to apply it to other geometric... Read more



I Selected Topics



Volumetric Properties of (m, d)-scribed Polytopes



Volume of the Convex Hull of a Pair of Convex Bodies



The Kneser-Poulsen conjecture revisited



Volumetric Bounds for Contact Numbers



More on Volumetric Properties of Separable Packings





 



II Selected Proofs



Proofs on Volume Inequalities for Convex Polytopes



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



Proofs on the Kneser-Poulsen conjecture



Proofs on Volumetric Bounds for Contact Numbers



More Proofs on Volumetric Properties of Separable Packings



Open Problems: An Overview

Biography

Károly 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 Lángi 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.