- 288 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
eBook - ePub
The Elements of Non-Euclidean Geometry
About this book
This volume became the standard text in the field almost immediately upon its original publication. Renowned for its lucid yet meticulous exposition, it can be appreciated by anyone familiar with high school algebra and geometry. Its arrangement follows the traditional pattern of plane and solid geometry, in which theorems are deduced from axioms and postulates. In this manner, students can follow the development of non-Euclidean geometry in strictly logical order, from a fundamental analysis of the concept of parallelism to such advanced topics as inversion and transformations.
Topics include elementary hyperbolic geometry; elliptic geometry; analytic non-Euclidean geometry; representations of non-Euclidean geometry in Euclidean space; and space curvature and the philosophical implications of non-Euclidean geometry. Additional subjects encompass the theory of the radical axes, homothetic centers, and systems of circles; inversion, equations of transformation, and groups of motions; and the classification of conics.
Although geared toward undergraduate students, this text treats such important and difficult topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, Gauss’ proof of the defect-area theorem, geodesic representation, and other advanced subjects. In addition, its 136 problems offer practice in using the forms and methods developed in the text.
Topics include elementary hyperbolic geometry; elliptic geometry; analytic non-Euclidean geometry; representations of non-Euclidean geometry in Euclidean space; and space curvature and the philosophical implications of non-Euclidean geometry. Additional subjects encompass the theory of the radical axes, homothetic centers, and systems of circles; inversion, equations of transformation, and groups of motions; and the classification of conics.
Although geared toward undergraduate students, this text treats such important and difficult topics as the relation between parataxy and parallelism, the absolute measure, the pseudosphere, Gauss’ proof of the defect-area theorem, geodesic representation, and other advanced subjects. In addition, its 136 problems offer practice in using the forms and methods developed in the text.
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Please note we cannot support devices running on iOS 13 and Android 7 or earlier. Learn more about using the app.
Yes, you can access The Elements of Non-Euclidean Geometry by D. M.Y. Sommerville in PDF and/or ePUB format, as well as other popular books in Mathematics & Geometry. We have over one million books available in our catalogue for you to explore.
Information
Table of contents
- Title Page
- Copyright Page
- PREFACE
- Table of Contents
- CHAPTER I. - HISTORICAL.
- CHAPTER II. - ELEMENTARY HYPERBOLIC GEOMETRY.
- CHAPTER III. - ELLIPTIC GEOMETRY.
- CHAPTER IV. - ANALYTICAL GEOMETRY.
- CHAPTER V. - REPRESENTATIONS OF NON-EUCLIDEAN GEOMETRY IN EUCLIDEAN SPACE.
- CHAPTER VI. - “ SPACE - CURVATURE ” AND THE PHILOSOPHICAL BEARING OF NON-EUCLIDEAN GEOMETRY.
- CHAPTER VII. - RADICAL AXES, HOMOTHETIC CENTRES, AND SYSTEMS OF CIRCLES.
- CHAPTER VIII. - INVERSION AND ALLIED TRANSFORMATIONS.
- CHAPTER IX. - THE CONIC.
- INDEX