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Geometry: Plane and Fancy

  • Textbook
  • © 1998

Overview

Authors:
  1. David A. Singer

    1. Department of Mathematics, Case Western Reserve University, Cleveland, USA

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  • This book offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies.
  • Lively exposition and off-beat approach.
  • Covers many topics in geometry not found in other introductions to the subject.
  • No calculus is assumed; book written at an elementary level.
  • Interesting problems are nicely scattered throughout.

Part of the book series: Undergraduate Texts in Mathematics (UTM)

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Table of contents (6 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Euclid and Non-Euclid

    • David A. Singer
    Pages 1-20

  3. Tiling the Plane with Regular Polygons

    • David A. Singer
    Pages 21-47

  4. Geometry of the Hyperbolic Plane

    • David A. Singer
    Pages 48-73

  5. Geometry of the Sphere

    • David A. Singer
    Pages 74-104

  6. More Geometry of the Sphere

    • David A. Singer
    Pages 105-130

  7. Geometry of Space

    • David A. Singer
    Pages 131-154

  8. Back Matter

    Pages 155-162
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Keywords

About this book

GEOMETRY: Plane and Fancy offers students a fascinating tour through parts of geometry they are unlikely to see in the rest of their studies while, at the same time, anchoring their excursions to the well known parallel postulate of Euclid. The author shows how alternatives to Euclid's fifth postulate lead to interesting and different patterns and symmetries. In the process of examining geometric objects, the author incorporates the algebra of complex (and hypercomplex) numbers, some graph theory, and some topology. Nevertheless, the book has only mild prerequisites. Readers are assumed to have had a course in Euclidean geometry (including some analytic geometry and some algebra) at the high school level. While many concepts introduced are advanced, the mathematical techniques are not. Singer's lively exposition and off-beat approach will greatly appeal both to students and mathematicians. Interesting problems are nicely scattered throughout the text. The contents of the book can be covered in a one-semester course, perhaps as a sequel to a Euclidean geometry course.

Authors and Affiliations

  • Department of Mathematics, Case Western Reserve University, Cleveland, USA

    David A. Singer

Bibliographic Information

  • Book Title: Geometry: Plane and Fancy

  • Authors: David A. Singer

  • Series Title: Undergraduate Texts in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4612-0607-1

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

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

  • Hardcover ISBN: 978-0-387-98306-6Published: 09 January 1998

  • Softcover ISBN: 978-1-4612-6837-6Published: 28 September 2012

  • eBook ISBN: 978-1-4612-0607-1Published: 06 December 2012

  • Series ISSN: 0172-6056

  • Series E-ISSN: 2197-5604

  • Edition Number: 1

  • Number of Pages: X, 162

  • Topics: Geometry

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