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Strange Phenomena in Convex and Discrete Geometry

  • Textbook
  • © 1996

Overview

Authors:
  1. Chuanming Zong

    1. Institute of Mathematics, The Chinese Academy of Sciences, Beijing, PR China

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Editors:
  1. James J. Dudziak

    1. Department of Mathematics, Bucknell University, Lewisburg, USA

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Part of the book series: Universitext (UTX)

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-x
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  2. Borsuk’s Problem

    • Chuanming Zong, James J. Dudziak
    Pages 1-13

  3. Finite Packing Problems

    • Chuanming Zong, James J. Dudziak
    Pages 15-35

  4. The Venkov-McMullen Theorem and Stein’s Phenomenon

    • Chuanming Zong, James J. Dudziak
    Pages 37-54

  5. Local Packing Phenomena

    • Chuanming Zong, James J. Dudziak
    Pages 55-82

  6. Category Phenomena

    • Chuanming Zong, James J. Dudziak
    Pages 83-98

  7. The Busemann-Petty Problem

    • Chuanming Zong, James J. Dudziak
    Pages 99-122

  8. Dvoretzky’s Theorem

    • Chuanming Zong, James J. Dudziak
    Pages 123-142

  9. Back Matter

    Pages 143-158
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Keywords

About this book

Convex and discrete geometry is one of the most intuitive subjects in mathematics. One can explain many of its problems, even the most difficult - such as the sphere-packing problem (what is the densest possible arrangement of spheres in an n-dimensional space?) and the Borsuk problem (is it possible to partition any bounded set in an n-dimensional space into n+1 subsets, each of which is strictly smaller in "extent" than the full set?) - in terms that a layman can understand; and one can reasonably make conjectures about their solutions with little training in mathematics.

Authors, Editors and Affiliations

  • Department of Mathematics, Bucknell University, Lewisburg, USA

    James J. Dudziak

  • Institute of Mathematics, The Chinese Academy of Sciences, Beijing, PR China

    Chuanming Zong

Bibliographic Information

  • Book Title: Strange Phenomena in Convex and Discrete Geometry

  • Authors: Chuanming Zong

  • Editors: James J. Dudziak

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4613-8481-6

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag New York, Inc. 1996

  • Softcover ISBN: 978-0-387-94734-1Published: 25 June 1996

  • eBook ISBN: 978-1-4613-8481-6Published: 06 December 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: VI, 158

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Geometry

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