This book is a text for junior, senior, or firstyear graduate courses traditionally titled Foundations of Geometry and/or Non Euclidean Geometry. The first 29 chapters are for a semester or year course on the foundations of geometry. The remaining chap ters may then be used for either a regular course or independent study courses. Another possibility, which is also especially suited for inservice teachers of high school geometry, is to survey the the fundamentals of absolute geometry (Chapters 1 20) very quickly and begin earnest study with the theory of parallels and isometries (Chapters 21 30). The text is selfcontained, except that the elementary calculus is assumed for some parts of the material on advanced hyperbolic geometry (Chapters 31 34). There are over 650 exercises, 30 of which are 10part trueorfalse questions. A rigorous rulerandprotractor axiomatic development of the Euclidean and hyperbolic planes, including the classification of the isometries of these planes, is balanced by the discussion about this development. Models, such as Taxicab Geometry, are used exten sively to illustrate theory. Historical aspects and alternatives to the selected axioms are prominent. The classical axiom systems of Euclid and Hilbert are discussed, as are axiom systems for three and fourdimensional absolute geometry and Pieri's system based on rigid motions. The text is divided into three parts. The Introduction (Chapters 1 4) is to be read as quickly as possible and then used for ref erence if necessary.
About G. E. Martin
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Author  :  G. E. Martin 
Publisher  :  SpringerVerlag New York Inc. 
Data Published  :  06 December 2011 
ISBN  :  1461257271 
EAN  :  9781461257271 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  512 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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