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Euclidean plane and its relatives

(2 reviews)

Anton Petrunin, Penn State

Pub Date: 2017

ISBN 13: 9781974214167

Publisher: Independent

Language: English

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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


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


Table of Contents


  • 1 Preliminaries

Euclidean geometry

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

Inversive geometry

  • 8 Inscribed angles
  • 9 Inversion

Non-Euclidean geometry

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

Additional topics

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


  • Hints
  • Index
  • Used resources

About the Book

This book is designed for a semester-long course in Foundations of Geometry and meant to be rigorous, conservative, elementary and minimalistic.

About the Contributors


Anton Petrunin. Professor of Mathematics at Penn State.