Euclidean Plane and its Relatives

(0 reviews)

star01star02star03star04star05

Anton Petrunin, Penn State

Pub Date: 2015

ISBN 13:

Publisher: Independent

Read This Book

Conditions of Use

Attribution-ShareAlike
CC BY-SA

Reviews

  All reviews are licensed under a CC BY-ND license.

Learn more about reviews.

There are no reviews for this book






Table of Contents

Introduction 

  • 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 Absolute plane 
  • 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 

References

  • 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

Author(s)

Anton Petrunin. Professor of Mathematics at Penn State.