The Elements of Non-Euclidean Geometry (Dover Books on Mathematics), by D. M.Y. Sommerville
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The Elements of Non-Euclidean Geometry (Dover Books on Mathematics), by D. M.Y. Sommerville
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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.
The Elements of Non-Euclidean Geometry (Dover Books on Mathematics), by D. M.Y. Sommerville- Amazon Sales Rank: #906633 in eBooks
- Published on: 2012-05-24
- Released on: 2012-05-24
- Format: Kindle eBook
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5 of 5 people found the following review helpful. The "bible"... By André Gargoura Indeed, some call this little book the "bible" of non-euclidean geometry and for good reasons.Despite some cryptic parts, it's the only attempt -- and successful --to treat both hyperbolic geometry and, even more, elliptic geometry synthetically (no quaternions, tensors and al...) , something that even Coxeter could not achieve (see my review on his "Non-Euclidean Geometry").
3 of 7 people found the following review helpful. AMAZING By PersonReviewing I looked and looked for an affordable non-eucledian geometry introduction and found this one. It is my first book on non-Euclidean geometry and though it is brief it also contains historical information about non-euclidian geometry.
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