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Bücher Englische Bücher Wissen & Bildung Naturwissenschaft, Medizin, Informatik, Technik Mathematik Geometrie The Four Pillars of Geometry
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The Four Pillars of Geometry
John Stillwell (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.12.2010
Sprache
Englisch
EAN
9781441920638
Herausgeber
Springer US
Serien- oder Bandtitel
Undergraduate Texts in Mathematics
Sonderedition
Nein
Autor
John Stillwell
Seitenanzahl
229
Einbandart
Broschiert
Schlagwörter
Calc, DEX, Mathematica, Vector space, algebra, boundary element method, construction, diagrams, form, linear algebra, object, selection, theorem, transformation, transformation group, matrix theory
Thema-Inhalt
PBM - Geometrie
PBF - Algebra
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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