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Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics) 🔍
Robin Hartshorne; Robin Hartshorene Springer New York : Imprint : Springer, Undergraduate Texts in Mathematics, Undergraduate Texts in Mathematics, 1, 2000
英语 [en] · PDF · 50.3MB · 2013 · 📘 非小说类图书 · 🚀/lgli/lgrs/nexusstc/scihub/upload/zlib · Save
描述
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.
Erscheinungsdatum: 15.12.2010
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lgli/Z:\Bibliotik_\A Library\Geometry - Euclid and Beyond [Retail] - Hartshorne.pdf
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lgrsnf/Z:\Bibliotik_\A Library\Geometry - Euclid and Beyond [Retail] - Hartshorne.pdf
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nexusstc/Geometry: Euclid and Beyond/5c126accdd2863a3f959167d9c793447.pdf
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scihub/10.1007/978-0-387-22676-7.pdf
备用文件名
zlib/Mathematics/Hartshorne, Robin/Geometry: Euclid and beyond_10997776.pdf
备用出版商
Springer; Brand: Springer
备用出版商
Springer London, Limited
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Springer Nature
备用出版商
Springer US
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Copernicus
备用出版商
Telos
备用版本
Undergraduate texts in mathematics, First edition, New York, 2010
备用版本
Undergraduate texts in mathematics, New York, NY, 2000
备用版本
Undergraduate texts in mathematics, New York, 2011
备用版本
Undergraduate texts in mathematics, 2010;2011
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United States, United States of America
备用版本
Dec 15, 2010
备用版本
1, 20131111
元数据中的注释
lg2859154
元数据中的注释
producers:
Acrobat Distiller 9.0.0 (Windows)
元数据中的注释
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元数据中的注释
Source title: Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
备用描述
This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's "Elements" leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants. Also included are complete proofs, introduction of coordinates, the theory of area, geometrical constructions and finite field extensions, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra. The text is intended for junior-senior level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California, Berkeley, and is the author of "Foundations of Projective Geometry" (Benjamin, 1967) and "Algebraic Geometry" (Springer, 1977)
备用描述
<p>This book offers a unique opportunity to understand the essence of one of the great thinkers of western civilization. A guided reading of Euclid's Elements leads to a critical discussion and rigorous modern treatment of Euclid's geometry and its more recent descendants, with complete proofs. Topics include the introduction of coordinates, the theory of area, history of the parallel postulate, the various non-Euclidean geometries, and the regular and semi-regular polyhedra.</p>
备用描述
A little after the time of Plato, but before Archimedes, in ancient Greece, a man named Euclid wrote the Elements, gathering and improving the work of his predecessors Pythagoras, Theaetetus, and Eudoxus into one magnificent edifice.
开源日期
2020-11-29
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