This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system to avoid the tedium of a completely synthetic approach. The development includes properties of the isometry group of the hyperbolic plane, tilings, and applications to special relativity. Elementary techniques from complex analysis, matrix theory, and group theory are used, and some mathematical sophistication on the part of students is thus required, but a formal course in these topics is not a prerequisite.
Introduction to Hyperbolic Geometry
and over one million other books are available for Amazon Kindle.
Learn more
FREE Two-Day Shipping for students on millions of items. Learn more |
| ||||||||||||||||||||||||
|
There is a newer edition of this item:
|
Book Description
Editorial Reviews
Review
"The book is well laid out with no shortage of diagrams and with each chapter prefaced with its own useful introduction...Also well written, it makes pleasurable reading." Proceedings of the Edinburgh Mathematical Society
Product Details
Would you like to update product info or give feedback on images?
|
More About the Author
Discover books, learn about writers, read author blogs, and more.
Customer Reviews
|
There are no customer reviews yet.
|
|||
|
Video reviews
|
Inside This Book
(learn more)
First Sentence:
Over the centuries many attempts were made to prove the Parallel Postulate of Euclid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
asymptotic pencil, reverse isometry, crossbar theorem, angular defect, neutral theorems, hyperbolic axioms, hyperbolic plane geometry, congruence criteria, ideal rotation, angular excess, exterior angle theorem, direct isometry, common perpendicular, complete ordered field, hyperbolic case, isometry group, noncollinear points, parallel axiom, opposite rays, contravariant vector, hyperbolic geometry, abstract surface, unique plane, real number system, polygonal path Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclidean Approximations, New York, Exercises Show, Prove Lemma, Frederick Ungar, Sketch of the Proof New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Over the centuries many attempts were made to prove the Parallel Postulate of Euclid. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
asymptotic pencil, reverse isometry, crossbar theorem, angular defect, neutral theorems, hyperbolic axioms, hyperbolic plane geometry, congruence criteria, ideal rotation, angular excess, exterior angle theorem, direct isometry, common perpendicular, complete ordered field, hyperbolic case, isometry group, noncollinear points, parallel axiom, opposite rays, contravariant vector, hyperbolic geometry, abstract surface, unique plane, real number system, polygonal path Key Phrases - Capitalized Phrases (CAPs): (learn more)
Euclidean Approximations, New York, Exercises Show, Prove Lemma, Frederick Ungar, Sketch of the Proof New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 75
books:
See all 75 books this book cites
92
books
cite this book:
See all 92 books citing this book
- Non-Euclidean Geometry (Mathematical Association of America Textbooks) by H. S. M. Coxeter on page 118, and page 277
- A Survey of Modern Algebra (Akp Classics) by Garrett Birkhoff on page 19, and page 257
- Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups (Universitext) by Alexander J. Hahn in Front Matter
- Linear Algebra by Jin Ho Kwak in Front Matter
- Introduction to Arithmetical Functions (Universitext) by Paul J. McCarthy in Back Matter
See all 75 books this book cites
- Topics on Riemann Surfaces and Fuchsian Groups (London Mathematical Society Lecture Note Series) by E. Bujalance on page 28
- Option Theory with Stochastic Analysis: An Introduction to Mathematical Finance (Universitext) by Fred Espen Benth in Back Matter
- From Elementary Probability to Stochastic Differential Equations with MAPLE by Sasha Cyganowski in Back Matter
- Logic and Structure by Dirk van Dalen in Back Matter
- Theory and Numerics of Differential Equations by James F. Blowey in Back Matter
See all 92 books citing this book
Books on Related Topics
(learn more)
|
Tags Customers Associate with This Product(What's this?)Click on a tag to find related items, discussions, and people.
|
Customer Discussions
|
This product's forum
Active discussions in related forums
Search Customer Discussions
|
Related forums
|
