The Foundations of Geometry and the Non-Euclidean Plane:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1975
|
| Schriftenreihe: | Undergraduate Texts in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XVI, 512 p) |
| ISBN: | 9781461257257 9781461257271 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-1-4612-5725-7 |
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Martin, George E. |
| author_facet | Martin, George E. |
| author_role | aut |
| author_sort | Martin, George E. |
| author_variant | g e m ge gem |
| building | Verbundindex |
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| dewey-full | 516 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516 |
| dewey-search | 516 |
| dewey-sort | 3516 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-5725-7 |
| format | Electronic eBook |
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| spelling | Martin, George E. Verfasser aut The Foundations of Geometry and the Non-Euclidean Plane by George E. Martin New York, NY Springer New York 1975 1 Online-Ressource (XVI, 512 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 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 Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf Absolute Geometrie (DE-588)4193046-0 gnd rswk-swf Nichteuklidische Geometrie (DE-588)4042073-5 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Nichteuklidische Geometrie (DE-588)4042073-5 s 2\p DE-604 Geometrie (DE-588)4020236-7 s 3\p DE-604 Absolute Geometrie (DE-588)4193046-0 s 4\p DE-604 https://doi.org/10.1007/978-1-4612-5725-7 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 4\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Martin, George E. The Foundations of Geometry and the Non-Euclidean Plane Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd Absolute Geometrie (DE-588)4193046-0 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4193046-0 (DE-588)4042073-5 (DE-588)4123623-3 |
| title | The Foundations of Geometry and the Non-Euclidean Plane |
| title_auth | The Foundations of Geometry and the Non-Euclidean Plane |
| title_exact_search | The Foundations of Geometry and the Non-Euclidean Plane |
| title_full | The Foundations of Geometry and the Non-Euclidean Plane by George E. Martin |
| title_fullStr | The Foundations of Geometry and the Non-Euclidean Plane by George E. Martin |
| title_full_unstemmed | The Foundations of Geometry and the Non-Euclidean Plane by George E. Martin |
| title_short | The Foundations of Geometry and the Non-Euclidean Plane |
| title_sort | the foundations of geometry and the non euclidean plane |
| topic | Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd Absolute Geometrie (DE-588)4193046-0 gnd Nichteuklidische Geometrie (DE-588)4042073-5 gnd |
| topic_facet | Mathematics Geometry Mathematik Geometrie Absolute Geometrie Nichteuklidische Geometrie Lehrbuch |
| url | https://doi.org/10.1007/978-1-4612-5725-7 |
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