Euclidean plane and its relatives

(2 reviews)


Anton Petrunin, Penn State

Pub Date: 2017

ISBN 13: 978-1-9742141-6-7

Publisher: Independent

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Reviewed by Sarah Birdsong, Lecturer, University of North Carolina at Charlotte, on 2/2/2018.

The textbook presents a formal axiomatic system in which classical Euclidean geometry can be interpreted. However, it doesn't provide any details or … read more



Reviewed by Susan Hagen, Senior Instructor, Virginia Tech , on 2/2/2018.

As the title implies, the book is a minimalist introduction to the Euclidean plane and its relatives. Much of Euclidean geometry is covered but … 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.