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0. Introduction 1. Preliminaries Part-I Euclidean geometry 2. The Axioms 3. Half-planes 4. Congruent triangles 5. Perpendicular lines 6. Similar triangles 7. Parallel lines 8. Triangle geometry Part-II Inversive geometry 9. Inscribed angles 10. Inversion Part-III Non-Euclidean geometry 11. Neutral Geometry 12. Hyperbolic plane 13. Geometry of h-plane Part-IV Additional topics 14. Affine geometry 15. Projective geometry 16. Spherical geometry 17. Projective model 18. Complex coordinates 19. Geometric constructions 20. Area
This book is about different types of flat and curved surfaces in geometry. It covers Euclidean geometry, Inversive geometry, Non-Euclidean geometry and Additional topics. It talks about flat surfaces like the ones we learn about in school. It also looks at other kinds of surfaces that are curved or different. It shows how shapes and distances can change on these surfaces. The book helps people understand different kinds of spaces in geometry. It is good for anyone who wants to learn more about shapes and how space can be different.
Title: Euclidean Plane and Its Relatives by Anton Petrunin Publisher: arXiv Year: 2017 Pages: 198 Type: PDF Language: English ISBN-10 #: 1650229674 ISBN-13 #: 978-1650229676 License: CC BY-SA 4.0 Amazon: Amazon
The author Anton Petrunin is a mathematician who studies geometry, especially different types of spaces and shapes. He’s good at explaining tricky ideas in simple ways. As a teacher and author, he shares his knowledge through books and lectures, helping people understand geometry better. His work explores how shapes behave on both flat and curved surfaces, opening new ways to think about space.
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