Euclidean Plane and Its Relatives by Anton Petrunin - Free PDF
About this book :-
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.
Book Detail :-
Title:
Euclidean Plane and Its Relatives by Anton Petrunin - Free PDF
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
About Author :-
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.
Book Contents :-
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
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