Download Book Non-Euclidean Geometry
EPUB + Converted PDF by Kulczycki, Stefan; Knapowski, Stanislaw
Information
Format: EPUB + Converted PDF Language: English Publisher: Dover Publications Publication Date of the Electronic Edition: 2008
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ISBN: 9780486462646, 9780486155012
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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.
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