The Elements of Non-Euclidean Geometry

ISBN: 9780486442228
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Overview

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.

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Product Details

Author:
D. M.Y. Sommerville
Format:
Paperback
Pages:
288
Publisher:
Dover Publications (April 12, 2005)
Language:
English
ISBN-13:
9780486442228
ISBN-10:
0486442225
Weight:
11.52oz
Dimensions:
5.38" x 8.5"
Case Pack:
28
Series:
Dover Books on Mathematics
File:
Dover-Dover_02032018_complete_onix21-20180203.xml
Folder:
Dover
As low as:
$11.70
List Price:
$16.95
Publisher Identifier:
P-DOVER
Discount Code:
D
Pub Discount:
65

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