The Four Pillars of Geometry

John Stillwell

ISBN 10: 0387255303 / ISBN 13: 9780387255309

Edité par Springer New York, Springer US Aug 2005, 2005

A propos de cet article

Neuware -Many people think there is only one ¿right¿ way to teach geometry. For two millennia, the ¿right¿ way was Euclid¿s way, and it is still good in many respects. But in the 1950s the cry ¿Down with triangles!¿ was heard in France and new geometry books appeared, packed with linear algebra but with no diagrams. Was this the new ¿right¿ way, or was the ¿right¿ way something else again, perhaps transformation groups In this book, I wish to show that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Euclid-style construction and axiomatics seem the best way to start, but linear algebra smooths the later stages by replacing some tortuous arguments by simple calculations. And how can one avoid projective geometry It not only explains why objects look the way they do; it also explains why geometry is entangled with algebra. Finally, one needs to know that there is not one geometry, but many, and transformation groups are the best way to distinguish between them. Two chapters are devoted to each approach: The rst is concrete and introductory, whereas the second is more abstract. Thus, the rst chapter on Euclid is about straightedge and compass constructions; the second is about axioms and theorems. The rst chapter on linear algebra is about coordinates; the second is about vector spaces and the inner product.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 244 pp. Englisch.

N° de réf. du vendeur 9780387255309

Détails bibliographiques

• Titre: The Four Pillars of Geometry
• Éditeur: Springer New York, Springer US Aug 2005
• Date de parution: 2005
• Langue: anglais
• ISBN à 10 chiffres: 0387255303
• ISBN à 13 chiffres: 9780387255309
• Reliure: Buch
• État de l'article: Neu
• Dimensions: 241 L x 160 H x 19 P (en millimètres) 241 millimètres de largeur par 160 millimètres de hauteur par 19 millimètres de profondeur
• Poids: 535 grammes

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Synopsis

Geometry has something for everyone, and students will find themselves building on their strengths at times, and working to overcome weaknesses at other times. This new textbook demonstrates that geometry can be developed in four fundamentally different ways, and that all should be used if the subject is to be shown in all its splendor. Two chapters are devoted to each approach, the first being concrete and introductory, while the second is more abstract. The book contains more than 100 figures, and a large selection of exercises in each chapter.