Read more about Euclidean plane and its relatives

Euclidean plane and its relatives

(2 reviews)

Anton Petrunin, Penn State

Copyright Year: 2017

Last Update: 2021

ISBN 13: 9781974214167

Publisher: Anton Petrunin

Language: English

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Reviewed by Susan Hagen, Senior Instructor, Virginia Tech on 2/1/18

As the title implies, the book is a minimalist introduction to the Euclidean plane and its relatives. Much of Euclidean geometry is covered but through the lens of a Metric Space. The approach allows a faster progression through familiar Euclidean... read more

Reviewed by Sarah Birdsong, Lecturer, University of North Carolina at Charlotte on 2/1/18

The textbook presents a formal axiomatic system in which classical Euclidean geometry can be interpreted. However, it doesn't provide any details or even examples of the classical (eg: Hilbert, etc) axioms. The few examples and discussions that... read more

Table of Contents


  • 1 Preliminaries

Euclidean geometry

  • 2 The Axioms
  • 3 Half-planes
  • 4 Congruent triangles
  • 5 Perpendicular lines
  • 6 Similar triangles
  • 7 Parallel lines
  • 8 Triangle geometry

Inversive geometry

  • 9 Inscribed angles
  • 10 Inversion

Non-Euclidean geometry

  • 11 Neutral Geometry
  • 12 Hyperbolic plane
  • 13 Geometry of h-plane

Additional topics

  • 14 Affine geometry
  • 15 Projective geometry
  • 16 Spherical geometry
  • 17 Projective model
  • 18 Complex coordinates
  • 19 Geometric constructions
  • 20 Area


  • Hints
  • Index
  • Used resources

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  • About the Book

    This book is meant to be rigorous, conservative, elementary and minimalist. At the same time it includes about the maximum what students can absorb in one semester. Approximately one-third of the material used to be covered in high school, but not any more.The present book is based on the courses given by the author at the Pennsylvania State University as an introduction to the foundations of geometry. The lectures were oriented to sophomore and senior university students. These students already had a calculus course. In particular,they are familiar with the real numbers and continuity. It makes it possible to cover the material faster and in a more rigorous way than it could be done in high school.

    About the Contributors


    Anton Petrunin. Professor of Mathematics at Penn State.

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