© 1998

Geometry: Plane and Fancy


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

Table of contents

  1. Front Matter
    Pages i-x
  2. David A. Singer
    Pages 1-20
  3. David A. Singer
    Pages 21-47
  4. David A. Singer
    Pages 48-73
  5. David A. Singer
    Pages 74-104
  6. David A. Singer
    Pages 105-130
  7. David A. Singer
    Pages 131-154
  8. Back Matter
    Pages 155-162

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.


Non-Euclidean Geometry analytic geometry boundary element method complex number fractal graph graph theory object polygon proving symmetric relation techniques time topology transformation group

Authors and affiliations

  1. 1.Department of MathematicsCase Western Reserve UniversityClevelandUSA

Bibliographic information

  • Book Title Geometry: Plane and Fancy
  • Authors David A. Singer
  • Series Title Undergraduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 1998
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98306-6
  • Softcover ISBN 978-1-4612-6837-6
  • eBook ISBN 978-1-4612-0607-1
  • Series ISSN 0172-6056
  • Edition Number 1
  • Number of Pages X, 162
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Geometry
  • Buy this book on publisher's site