E-Book, Englisch, 112 Seiten, Web PDF
Meschkowski / Bromley / Declaris NonEuclidean Geometry
1. Auflage 2014
ISBN: 978-1-4832-5921-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
E-Book, Englisch, 112 Seiten, Web PDF
ISBN: 978-1-4832-5921-5
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark
Noneuclidean Geometry focuses on the principles, methodologies, approaches, and importance of noneuclidean geometry in the study of mathematics. The book first offers information on proofs and definitions and Hilbert's system of axioms, including axioms of connection, order, congruence, and continuity and the axiom of parallels. The publication also ponders on lemmas, as well as pencil of circles, inversion, and cross ratio. The text examines the elementary theorems of hyperbolic geometry, particularly noting the value of hyperbolic geometry in noneuclidian geometry, use of the Poincaré model, and numerical principles in proving hyperparallels. The publication also tackles the issue of construction in the Poincaré model, verifying the relations of sides and angles of a plane through trigonometry, and the principles involved in elliptic geometry. The publication is a valuable source of data for mathematicians interested in the principles and applications of noneuclidean geometry.
Autoren/Hrsg.
Weitere Infos & Material
1;Front Cover;1
2;Noneuclidean Geometry;4
3;Copyright Page;5
4;Table of Contents;8
5;Preface;6
6;CHAPTER 1. On Proofs and Definitions;10
7;CHAPTER 2. Hilbert's System of Axioms;17
7.1;I. Axioms of Connection;18
7.2;II. Axioms of Order;20
7.3;III. Axioms of Congruence;22
7.4;IV. Axioms of Continuity;28
7.5;V. The Axiom of Parallels;29
8;CHAPTER 3. From the History of the Parallel Postulate;30
9;CHAPTER 4. Lemmas;44
9.1;I. Pencil of Circles;44
9.2;II. Inversion;48
9.3;III. Cross Ratio;54
10;CHAPTER 5. The Poincaré Model;56
11;CHAPTER 6. Elementary Theorems of Hyperbolic Geometry;68
12;CHAPTER 7. Constructions;80
13;CHAPTER 8. Trigonometry;86
14;CHAPTER 9. Elliptic Geometry;98
15;CHAPTER 10. Epilog;106
16;References;108
17;Subject Index;112
