did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

9783764375171

Introduction to Classical Geometries

by ;
  • ISBN13:

    9783764375171

  • ISBN10:

    3764375175

  • Format: Paperback
  • Copyright: 2007-03-06
  • Publisher: Birkhauser

Note: Supplemental materials are not guaranteed with Rental or Used book purchases.

Purchase Benefits

  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
  • Write a Review Icon Write a Review
List Price: $59.99 Save up to $41.43
  • Rent Book $41.99
    Add to Cart Free Shipping Icon Free Shipping

    TERM
    PRICE
    DUE
    SPECIAL ORDER: 1-2 WEEKS
    *This item is part of an exclusive publisher rental program and requires an additional convenience fee. This fee will be reflected in the shopping cart.

Supplemental Materials

What is included with this book?

Summary

This book follows Kleins proposal of studying geometry by looking at the symmetries (or rigid motions) of the space in question. In this way the classical geometries are studied: Euclidean, affine, elliptic, projective and hyperbolic. For simplicity the focus is on the two-dimensional case, which is already rich enough, though some aspects of the 3 or $n$-dimensional geometries are included. Once plane geometry is well understood, it is much easier to go into higher dimensions. The book appeals to, and develops, the geometric intuition of the reader. Some basic notions of algebra and analysis are also used to get better understandings of various concepts and results.

Table of Contents

Prefacep. vii
List of Symbolsp. x
Euclidean geometryp. 1
Symmetriesp. 2
Rigid transformationsp. 15
Invariants under rigid transformationsp. 28
Cylinders and torip. 37
Finite subgroups of E(2) and E(3)p. 46
Frieze patterns and tessellationsp. 58
Affine geometryp. 75
The line at infinityp. 76
Affine transformations and their invariantsp. 83
Projective geometryp. 91
The real projective planep. 92
The Duality Principlep. 99
The shape of P[superscript 2](R)p. 103
Coordinate charts for P[superscript 2](R) (and for P[superscript 1] (C))p. 109
The projective groupp. 113
Invariance of the cross ratiop. 121
The space of conicsp. 126
Projective properties of the conicsp. 129
Poles and polarsp. 134
Elliptic geometryp. 141
Hyperbolic geometryp. 149
Models of the hyperbolic planep. 149
Transformations of the hyperbolic planep. 157
Steiner networkp. 164
The hyperbolic metricp. 168
First results in hyperbolic geometryp. 177
Surfaces with hyperbolic structurep. 183
Tessellationsp. 192
Appendicesp. 199
Differentiable functionsp. 199
Equivalence relationsp. 201
The symmetric group in four symbols: S[subscript 4]p. 202
Euclidean postulatesp. 205
Topologyp. 206
Some results on the circlep. 208
Bibliographyp. 211
Indexp. 215
Table of Contents provided by Ingram. All Rights Reserved.

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program