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Geometry: Euclid and Beyond - Robin Hartshorne
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Geometry: Euclid and Beyond - neues Buch

2010, ISBN: 9781441931450

ID: 128084524

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. Geometry: Euclid and Beyond Bücher > Fremdsprachige Bücher > Englische Bücher Taschenbuch 15.12.2010 Buch (fremdspr.), Springer, .201

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Geometry: Euclid and Beyond - Robin Hartshorne
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Robin Hartshorne:
Geometry: Euclid and Beyond - neues Buch

ISBN: 9781441931450

ID: 240981869

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. Geometry: Euclid and Beyond Buch (fremdspr.) Bücher>Fremdsprachige Bücher>Englische Bücher, Springer

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Geometry:  Euclid and Beyond - Robin Hartshorne
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Robin Hartshorne:
Geometry: Euclid and Beyond - neues Buch

ISBN: 9781441931450

ID: 978144193145

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, 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- to senior-level mathematics majors. Robin Hartshorne is a professor of mathematics at the University of California at Berkeley, and is the author of Foundations of Projective Geometry (Benjamin, 1967) and Algebraic Geometry (Springer, 1977). Robin Hartshorne, Books, Science and Nature, Geometry: Euclid and Beyond Books>Science and Nature, Springer New York

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Geometry: Euclid and Beyond - Robin Hartshorne
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Robin Hartshorne:
Geometry: Euclid and Beyond - Taschenbuch

ISBN: 9781441931450

ID: 9781441931450

Mathematics; Geometry Area, Euclid, Euclid's Elements, Geometry, Non-Euclidean Geometry Books Book (Paperback Initiative), Springer Science+Business Media

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Geometry: Euclid and Beyond - Robin Hartshorne
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Robin Hartshorne:
Geometry: Euclid and Beyond - Taschenbuch

2010, ISBN: 9781441931450

ID: 16197950

1st ed. Softcover of orig. ed. 2000, Softcover, Buch, [PU: Springer-Verlag New York Inc.]

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Details zum Buch
Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)
Autor:

Hartshorne, Robin

Titel:

Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)

ISBN-Nummer:

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.

Detailangaben zum Buch - Geometry: Euclid and Beyond (Undergraduate Texts in Mathematics)


EAN (ISBN-13): 9781441931450
ISBN (ISBN-10): 1441931457
Gebundene Ausgabe
Taschenbuch
Erscheinungsjahr: 2010
Herausgeber: Springer-Verlag GmbH
544 Seiten
Gewicht: 1,008 kg
Sprache: eng/Englisch

Buch in der Datenbank seit 01.04.2007 01:46:25
Buch zuletzt gefunden am 01.03.2017 10:12:45
ISBN/EAN: 9781441931450

ISBN - alternative Schreibweisen:
1-4419-3145-7, 978-1-4419-3145-0


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