The Foundations of Geometry and the Non-Euclidean Plane / by George E. Martin
(Undergraduate Texts in Mathematics)
| データ種別 | 電子ブック |
|---|---|
| 出版者 | New York, NY : Springer New York |
| 出版年 | 1975 |
| 本文言語 | 英語 |
| 大きさ | XVI, 512 p : online resource |
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| 内容注記 | 1. Equivalence Relations 2 Mappings 3 The Real Numbers 4 Axiom Systems One Absolute Geometry 5 Models 6 Incidence Axiom and Ruler Postulate 7 Betweenness 8 Segments, Rays, and Convex Sets 9 Angles and Triangles 10 The Golden Age of Greek Mathematics (Optional) 11 Euclid’S Elements (Optional) 12 Pasch’s Postulate and Plane Separation Postulate 13 Crossbar and Quadrilaterals 14 Measuring Angles and the Protractor Postulate 15 Alternative Axiom Systems (Optional) 16 Mirrors 17 Congruence and the Penultimate Postulate 18 Perpendiculars and Inequalities 19 Reflections 20 Circles 21 Absolute Geometry and Saccheri Quadrilaterals 22 Saccherfs Three Hypotheses 23 Euclid’s Parallel Postulate 24 Biangles 25 Excursions Two Non-Euclidean Geometry 26 Parallels and the Ultimate Axiom 27 Brushes and Cycles 28 Rotations, Translations, and Horolations 29 The Classification of Isometries 30 Symmetry 31 HOrocircles 32 The Fundamental Formula 33 Categoricalness and Area 34 Quadrature of the Circle Hints and Answers Notation Index |
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| 一般注記 | This book is a text for junior, senior, or first-year 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 in-service 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 self-contained, 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 10-part true-or-false questions. A rigorous ruler-and-protractor 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 four-dimensional 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 |
| 著者標目 | *Martin, George E. author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Geometry FREE:Mathematics FREE:Geometry |
| 分 類 | DC23:516 |
| 巻冊次 | ISBN:9781461257257 
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| ISBN | 9781461257257 |
| URL | http://dx.doi.org/10.1007/978-1-4612-5725-7 |
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