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 problems.
Part I of the text consists of survey chapters of selected topics on volume and is suitable for advanced undergraduate students. Part II has chapters of selected proofs of theorems stated in Part I and is oriented for graduate level students wishing to learn about the latest research on the topic. Chapters can be studied independently from each other.
- Provides a list of 30 open problems to promote research
- Features more than 60 research exercises
- Ideally suited for researchers and students of combinatorics, geometry and discrete mathematics
Table of Contents
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
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.