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OverviewIn 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. Full Product DetailsAuthor: Robin HartshornePublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: 1st ed. Softcover of orig. ed. 2000 Dimensions: Width: 17.80cm , Height: 3.30cm , Length: 25.40cm Weight: 1.031kg ISBN: 9781441931450ISBN 10: 1441931457 Pages: 528 Publication Date: 15 December 2010 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand We will order this item for you from a manufactured on demand supplier. Table of Contents1. 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.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |