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.
Author(s): Herbert Meschkowski, D. Allan Bromley, Nicholas Declaris and W. Magnus (Auth.)
Publisher: Elsevier Inc
Year: 1964
Language: English
Pages: 107
Cover
Title Page
Copyright Page
Preface
CHAPTER I On Proofs and Definitions
CHAPTER 2 Huberts System of Axioms
I. Axioms of Connection
II. Axioms of Order
III. Axioms of Congruence
IV. Axioms of Continuity
V. The Axiom of Parallels
CHAPTER 3 From the History of the Parallel Postulate
CHAPTER 4 Lemmas
I. Pencil of Circles
II. Inversion
III . Cross Ratio
CHAPTER 5 The Poincaré Model
CHAPTER 6 Elementary Theorems of Hyperbolic Geometry
CHAPTER 7 Constructions
CHAPTER 8 Trigonometry
CHAPTER 9 Elliptic Geometry
CHAPTER 10 Epilog
References
Subject Index
