Non-Euclidean Geometry (Dover Books on Mathematics) (Paperback)

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Description


This accessible approach features two varieties of proofs: stereometric and planimetric, as well as elementary proofs that employ only the simplest properties of the plane. A short history of geometry precedes a systematic exposition of the principles of non-Euclidean geometry.
Starting with fundamental assumptions, the author examines the theorems of Hjelmslev, mapping a plane into a circle, the angle of parallelism and area of a polygon, regular polygons, straight lines and planes in space, and the horosphere. Further development of the theory covers hyperbolic functions, the geometry of sufficiently small domains, spherical and analytical geometry, the Klein model, and other topics. Appendixes include a table of values of hyperbolic functions.


Product Details
ISBN: 9780486462646
ISBN-10: 0486462641
Publisher: Dover Publications
Publication Date: February 29th, 2008
Pages: 208
Language: English
Series: Dover Books on Mathematics