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Cover: 9780387255309 | The Four Pillars of Geometry | John Stillwell | Buch | Englisch | 2005
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The Four Pillars of Geometry
Buch von John Stillwell
Sprache: Englisch

42,75 €*

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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.
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.
Zusammenfassung

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.

Inhaltsverzeichnis
Straightedge and compass.- Euclid's approach to geometry.- Coordinates.- Vectors and Euclidean spaces.- Perspective.- Projective planes.- Transformations.- Non-Euclidean geometry.
Details
Erscheinungsjahr: 2005
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 244
Reihe: Undergraduate Texts in Mathematics
Inhalt: xi
229 S.
138 s/w Illustr.
138 Fotos
ISBN-13: 9780387255309
ISBN-10: 0387255303
Sprache: Englisch
Herstellernummer: 11364818
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Stillwell, John
Auflage: 2005
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 19 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 09.08.2005
Gewicht: 0,535 kg
preigu-id: 102300133
Zusammenfassung

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.

Inhaltsverzeichnis
Straightedge and compass.- Euclid's approach to geometry.- Coordinates.- Vectors and Euclidean spaces.- Perspective.- Projective planes.- Transformations.- Non-Euclidean geometry.
Details
Erscheinungsjahr: 2005
Fachbereich: Geometrie
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
Seiten: 244
Reihe: Undergraduate Texts in Mathematics
Inhalt: xi
229 S.
138 s/w Illustr.
138 Fotos
ISBN-13: 9780387255309
ISBN-10: 0387255303
Sprache: Englisch
Herstellernummer: 11364818
Ausstattung / Beilage: HC runder Rücken kaschiert
Einband: Gebunden
Autor: Stillwell, John
Auflage: 2005
Hersteller: Springer US
Springer New York
Undergraduate Texts in Mathematics
Maße: 241 x 160 x 19 mm
Von/Mit: John Stillwell
Erscheinungsdatum: 09.08.2005
Gewicht: 0,535 kg
preigu-id: 102300133
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