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Volume of geometric objects was studied by ancient Greek mathematicians. In discrete geometry, a relatively new branch of geometry, volume plays a significant role in generating topics for research. 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.
List 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
About the author
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.
Summary
Volume of geometric objects was studied by ancient Greek mathematicians. In discrete geometry, a relatively new branch of geometry, volume plays a significant role in generating topics for research. 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.
