Noneuclidean Geometry

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. Content: ACADEMIC PAPERBACKS, Page ii Front Matter, Page iii Copyright, Page iv Preface, Page v CHAPTER 1 - On Proofs and Definitions, Pages 1-7 CHAPTER 2 - Hilbert's System of Axioms, Pages 8-20 CHAPTER 3 - From the History of the Parallel Postulate, Pages 21-34 CHAPTER 4 - Lemmas, Pages 35-46 CHAPTER 5 - The Poincaré Model, Pages 47-58 CHAPTER 6 - Elementary Theorems of Hyperbolic Geometry, Pages 59-70 CHAPTER 7 - Constructions, Pages 71-76 CHAPTER 8 - Trigonometry, Pages 77-88 CHAPTER 9 - Elliptic Geometry, Pages 89-96 CHAPTER 10 - Epilog, Pages 97-98 References, Pages 99-101 Subject Index, Pages 103-104