Geometry: Euclid and Beyond:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
New York, NY
Springer New York
2000
|
| Series: | Undergraduate Texts in Mathematics
|
| Subjects: | |
| Online Access: | Volltext |
| Item Description: | In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks |
| Physical Description: | 1 Online-Ressource (XII, 528 p) |
| ISBN: | 9780387226767 9781441931450 |
| ISSN: | 0172-6056 |
| DOI: | 10.1007/978-0-387-22676-7 |
Staff View
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| isbn | 9780387226767 9781441931450 |
| issn | 0172-6056 |
| language | English |
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| spelling | Hartshorne, Robin Verfasser aut Geometry: Euclid and Beyond by Robin Hartshorne New York, NY Springer New York 2000 1 Online-Ressource (XII, 528 p) txt rdacontent c rdamedia cr rdacarrier Undergraduate Texts in Mathematics 0172-6056 In recent years, I have been teaching a junior-senior-level course on the classi cal geometries. This book has grown out of that teaching experience. I assume only high-school geometry and some abstract algebra. The course begins in Chapter 1 with a critical examination of Euclid's Elements. Students are expected to read concurrently Books I-IV of Euclid's text, which must be obtained sepa rately. The remainder of the book is an exploration of questions that arise natu rally from this reading, together with their modern answers. To shore up the foundations we use Hilbert's axioms. The Cartesian plane over a field provides an analytic model of the theory, and conversely, we see that one can introduce coordinates into an abstract geometry. The theory of area is analyzed by cutting figures into triangles. The algebra of field extensions provides a method for deciding which geometrical constructions are possible. The investigation of the parallel postulate leads to the various non-Euclidean geometries. And in the last chapter we provide what is missing from Euclid's treatment of the five Platonic solids in Book XIII of the Elements. For a one-semester course such as I teach, Chapters 1 and 2 form the core material, which takes six to eight weeks Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd rswk-swf 1\p (DE-588)4123623-3 Lehrbuch gnd-content Geometrie (DE-588)4020236-7 s 2\p DE-604 https://doi.org/10.1007/978-0-387-22676-7 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 |
| spellingShingle | Hartshorne, Robin Geometry: Euclid and Beyond Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4123623-3 |
| title | Geometry: Euclid and Beyond |
| title_auth | Geometry: Euclid and Beyond |
| title_exact_search | Geometry: Euclid and Beyond |
| title_full | Geometry: Euclid and Beyond by Robin Hartshorne |
| title_fullStr | Geometry: Euclid and Beyond by Robin Hartshorne |
| title_full_unstemmed | Geometry: Euclid and Beyond by Robin Hartshorne |
| title_short | Geometry: Euclid and Beyond |
| title_sort | geometry euclid and beyond |
| topic | Mathematics Geometry Mathematik Geometrie (DE-588)4020236-7 gnd |
| topic_facet | Mathematics Geometry Mathematik Geometrie Lehrbuch |
| url | https://doi.org/10.1007/978-0-387-22676-7 |
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