The Four Pillars of Geometry (Undergraduate Texts in

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The Four Pillars of Geometry (Undergraduate Texts in Mathematics)

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.

Country	USA
Author	John Stillwell
Binding	Kindle Edition
Edition	1
EISBN	9780387290522
Format	Kindle eBook
Label	Springer New York
Manufacturer	Springer New York
NumberOfPages	228
PublicationDate	2005-12-30
Publisher	Springer New York
ReleaseDate	2005-12-30
Studio	Springer New York

The Four Pillars of Geometry (Undergraduate Texts in Mathematics)

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