The Four Pillars of Geometry

John Stillwell - Collection Undergraduate Texts in Mathematics

240 pages, parution le 15/09/2005

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Résumé

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.

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. In this book, two chapters are devoted to each approach, the first being concrete and introductory, while the second is more abstract.

Geometry, of all subjects, should be about taking different viewpoints, and geometry is unique among mathematical disciplines in its ability to look different from different angles. Some students prefer to visualize, while others prefer to reason or to calculate. 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 book will be suitable for a second course in geometry and contains more than 100 figures, and a large selection of exercises in each chapter.

Written for: Undergraduate and graduate math students, future high school math teachers

L'auteur - John Stillwell

John Stillwell is Professor of Mathematics at the University of San Francisco. He is the author of several highly regarded books published by Springer-Verlag, including Mathematics and Its History (Second Edition 2001), Numbers and Geometry (1997) and Elements of Algebra (1994).

Sommaire

Straightedge and compass
Euclid's approach to geometry
Coordinates
Vectors and Euclidean spaces
Perspective
Projective planes
Transformations
Non-Euclidean geometry
References

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	John Stillwell
Collection	Undergraduate Texts in Mathematics
Parution	15/09/2005
Nb. de pages	240
Format	16 x 24
Couverture	Relié
Poids	460g
Intérieur	Noir et Blanc
EAN13	9780387255309
ISBN13	978-0-387-25530-9