
Geometry from Euclid to Knots
by Stahl, Saul-
Free Shipping on all Orders Over $35!*
*excludes Marketplace items.
Buy New
Rent Textbook
Rent Digital eBook
Downloadable: Lifetime Access
Used Textbook
We're Sorry
Sold Out
This item is being sold by an Individual Seller and will not ship from the Online Bookstore's warehouse. The Seller must confirm the order within two business days. If the Seller refuses to sell or fails to confirm within this time frame, then the order is cancelled.
Please be sure to read the Description offered by the Seller.
Summary
Table of Contents
Preface to the Dover Edition | p. xi |
Preface | p. xiii |
Other Geometries: A Computational Introduction | p. 1 |
Spherical Geometry | p. 1 |
Hyperbolic Geometry | p. 9 |
Other Geometries | p. 21 |
The Neutral Geometry of the Triangle | p. 29 |
Introduction | p. 29 |
Preliminaries | p. 34 |
Propositions 1 through 28 | p. 46 |
Postulate 5 Revisited | p. 81 |
Nonneutral Euclidean Geometry | p. 87 |
Parallelism | p. 87 |
Area | p. 99 |
The Theorem of Pythagoras | p. 112 |
Consequences of the Theorem of Pythagoras | p. 119 |
Proportion and Similarity | p. 122 |
Circles and Regular Polygons | p. 133 |
The Neutral Geometry of the Circle | p. 133 |
The Nonneutral Euclidean Geometry of the Circle | p. 141 |
Regular Polygons | p. 150 |
Circle Circumference and Area | p. 155 |
Impossible Constructions | p. 165 |
Toward Projective Geometry | p. 177 |
Division of Line Segments | p. 177 |
Collinearity and Concurrence | p. 184 |
The Projective Plane | p. 191 |
Planar Symmetries | p. 197 |
Translations, Rotations, and Fixed Points | p. 197 |
Reflections | p. 203 |
Glide Reflections | p. 210 |
The Main Theorems | p. 216 |
Symmetries of Polygons | p. 219 |
Frieze Patterns | p. 223 |
Wallpaper Designs | p. 228 |
Inversions | p. 247 |
Inversions as Transformations | p. 247 |
Inversions to the Rescue | p. 255 |
Inversions as Hyperbolic Motions | p. 259 |
Symmetry in Space | p. 269 |
Regular and Semiregular Polyhedra | p. 269 |
Rotational Symmetries of Regular Polyhedra | p. 281 |
Monstrous Moonshine | p. 288 |
Informal Topology | p. 295 |
Graphs | p. 305 |
Nodes and Arcs | p. 305 |
Traversability | p. 308 |
Colorings | p. 314 |
Planarity | p. 317 |
Graph Homeomorphisms | p. 326 |
Surfaces | p. 333 |
Polygonal Presentations | p. 333 |
Closed Surfaces | p. 346 |
Operations on Surfaces | p. 358 |
Bordered Surfaces | p. 367 |
Knots and Links | p. 379 |
Equivalence of Knots and Links | p. 379 |
Labelings | p. 385 |
The Jones Polynomial | p. 393 |
A Brief Introduction to The Geometer's Sketchpad® | p. 405 |
Summary of Propositions | p. 409 |
George D. Birkhoff's Axiomatization of Euclidean Geometry | p. 415 |
The University of Chicago School Mathematics Project's Geometrical Axioms | p. 417 |
David Hilbert's Axiomatization of Euclidean Geometry | p. 421 |
Permutations | p. 425 |
Modular Arithmetic | p. 429 |
Solutions and Hints to Selected Problems | p. 433 |
Bibliography | p. 447 |
Index | p. 451 |
Table of Contents provided by Ingram. All Rights Reserved. |
An electronic version of this book is available through VitalSource.
This book is viewable on PC, Mac, iPhone, iPad, iPod Touch, and most smartphones.
By purchasing, you will be able to view this book online, as well as download it, for the chosen number of days.
A downloadable version of this book is available through the eCampus Reader or compatible Adobe readers.
Applications are available on iOS, Android, PC, Mac, and Windows Mobile platforms.
Please view the compatibility matrix prior to purchase.