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A Geometrical Picture Book

  • Book
  • © 1998

Overview

Authors:
  1. Burkard Polster

    1. Department of Pure Mathematics, The University of Adelaide, Adelaide, Australia

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Part of the book series: Universitext (UTX)

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Table of contents (21 chapters)

  1. Front Matter

    Pages i-xx
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  2. Finite Geometries

    1. Front Matter

      Pages 1-1
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    2. Introduction via the Fano Plane

      • Burkard Polster
      Pages 3-17

    3. Designs

      • Burkard Polster
      Pages 19-26

    4. Configurations

      • Burkard Polster
      Pages 27-38

    5. Generalized Quadrangles

      • Burkard Polster
      Pages 39-66

    6. The Smallest Three-Dimensional Projective Space

      • Burkard Polster
      Pages 67-91

    7. The Projective Plane of Order 3

      • Burkard Polster
      Pages 93-105

    8. The Projective Plane of Order 4

      • Burkard Polster
      Pages 107-116

    9. The Projective Plane of Order 5

      • Burkard Polster
      Pages 117-124

    10. Stargazing in Affine Planes up to Order 8

      • Burkard Polster
      Pages 125-134

    11. Biplanes

      • Burkard Polster
      Pages 135-154

    12. Semibiplanes

      • Burkard Polster
      Pages 155-160

    13. The Smallest Benz Planes

      • Burkard Polster
      Pages 161-171

    14. Generalized Polygons

      • Burkard Polster
      Pages 173-184

    15. Colour Pictures and Building the Models

      • Burkard Polster
      Pages 185-196

    16. Some Fun Games and Puzzles

      • Burkard Polster
      Pages 197-202

  3. Geometries on Surfaces

    1. Front Matter

      Pages 203-203
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    2. Introduction via Flat Affine Planes

      • Burkard Polster
      Pages 205-218

    3. Flat Circle Planes-An Overview

      • Burkard Polster
      Pages 219-222
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Keywords

About this book

How do you convey to your students, colleagues and friends some of the beauty of the kind of mathematics you are obsessed with? If you are a mathematician interested in finite or topological geometry and combinatorial designs, you could start by showing them some of the (400+) pictures in the "picture book". Pictures are what this book is all about; original pictures of everybody's favorite geometries such as configurations, projective planes and spaces, circle planes, generalized polygons, mathematical biplanes and other designs which capture much of the beauty, construction principles, particularities, substructures and interconnections of these geometries. The level of the text is suitable for advanced undergraduates and graduate students. Even if you are a mathematician who just wants some interesting reading you will enjoy the author's very original and comprehensive guided tour of small finite geometries and geometries on surfaces This guided tour includes lots of sterograms of the spatial models, games and puzzles and instructions on how to construct your own pictures and build some of the spatial models yourself.

Authors and Affiliations

  • Department of Pure Mathematics, The University of Adelaide, Adelaide, Australia

    Burkard Polster

Bibliographic Information

  • Book Title: A Geometrical Picture Book

  • Authors: Burkard Polster

  • Series Title: Universitext

  • DOI: https://doi.org/10.1007/978-1-4419-8526-2

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 1998

  • Softcover ISBN: 978-1-4612-6426-2Published: 13 September 2012

  • eBook ISBN: 978-1-4419-8526-2Published: 17 September 2012

  • Series ISSN: 0172-5939

  • Series E-ISSN: 2191-6675

  • Edition Number: 1

  • Number of Pages: XX, 292

  • Topics: Combinatorics, Geometry

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