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＜電子ブック＞
Geometry: Euclid and Beyond / by Robin Hartshorne
(Undergraduate Texts in Mathematics. ISSN:21975604)

版	1st ed. 2000.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	2000
本文言語	英語
大きさ	XII, 528 p : online resource
冊子体	Geometry : Euclid and beyond / Robin Hartshorne
著者標目	*Hartshorne, Robin author SpringerLink (Online service)
件　名	LCSH:Geometry FREE:Geometry
一般注記	1. Euclid’s Geometry -- 2. Hilbert’s Axioms -- 3. Geometry over Fields -- 4. Segment Arithmetic -- 5. Area -- 6. Construction Problems and Field Extensions -- 7. Non-Euclidean Geometry -- 8. Polyhedra -- Appendix: Brief Euclid -- Notes -- References -- List of Axioms -- Index of Euclid’s Propositions 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 Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-0-387-22676-7

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