NonEuclidean Geometry
Published on 12. May 2014
112 pages
978-1-4832-5921-5 (ISBN)
Description
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.
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Content
PrefaceChapter 1 On Proofs and DefinitionsChapter 2 Hilbert's System of Axioms I. Axioms of Connection II. Axioms of Order III. Axioms of Congruence IV. Axioms of Continuity V. The Axiom of ParallelsChapter 3 From the History of the Parallel PostulateChapter 4 Lemmas I. Pencil of Circles II. Inversion III. Cross RatioChapter 5 The Poincaré ModelChapter 6 Elementary Theorems of Hyperbolic GeometryChapter 7 ConstructionsChapter 8 TrigonometryChapter 9 Elliptic GeometryChapter 10 EpilogReferencesIndex
