Euclidean plane and its relatives

Format:

Book

Author/Creator:

Petrunin, Anton, author.

Language:

English

Subjects (All):

Mathematics--Textbooks.

Mathematics.

Physical Description:

1 online resource

Place of Publication:

Centre County, Pennsylvania Anton Petrunin 2021.

Language Note:

In English.

Summary:

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.

Contents:

Introduction

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

References

Hints

Index

Used resources

Notes:

Description based on print resource