Non-Euclidean Geometry and Curvature: Two-Dimensional Spaces, Volume 3
- ISBN-10
- 1470437163
- ISBN-13
- 9781470437169
- Category
- Geometry
- Pages
- 105
- Language
- English
- Published
- 2017-11-08
- Publisher
- American Mathematical Soc.
- Author
- James W. Cannon
Description
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. Einstein showed how to interpret gravity as the dynamic response to the curvature of space-time. Bill Thurston showed us that non-Euclidean geometries and curvature are essential to the understanding of low-dimensional spaces. This third and final volume aims to give the reader a firm intuitive understanding of these concepts in dimension 2. The volume first demonstrates a number of the most important properties of non-Euclidean geometry by means of simple infinite graphs that approximate that geometry. This is followed by a long chapter taken from lectures the author gave at MSRI, which explains a more classical view of hyperbolic non-Euclidean geometry in all dimensions. Finally, the author explains a natural intrinsic obstruction to flattening a triangulated polyhedral surface into the plane without distorting the constituent triangles. That obstruction extends intrinsically to smooth surfaces by approximation and is called curvature. Gauss's original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book's intrinsic definition is equivalent to Gauss's extrinsic definition (Gauss's “Theorema Egregium” (“Great Theorem”)).
Get the book
Similar books
-
Cuaderno de práctica
By Prentice Hall Direct Education StaffPrentice Hall Direct Education Staff ... 1. b = 4 , h = 4 2. b = 8 , h = 2 3. b = 20 , h = 6 4. b = 40 , h = 12 5. b = 3.1 , h = 1.7 6. b = 4.8 , h = 0.8 ! ... Pearson Education Inc. , publishing as Pearson Prentice Hall . 14.
-
Connected Mathematics: Covering and Surrounding
By Prentice Hall, Glenda LappanContains a complete sixth grade mathematics curriculum with connections to other subject areas.
-
Matemática : razonamiento y aplicaciones: geometría
Matemática : razonamiento y aplicaciones: geometría
-
Center for Mathematics Education Project Geometry Practice Workbook
CME Project ((c)2009) components for Geometry. Extend learning beyond the textbook with helpful tools for every chapter and lesson of Geometry. CME Geometry Companion Website
-
Geometry: Fun with Fundamentals: Book 4, Teacher's Guide
By Newton Hawley, Patrick Suppes, George Woodward GearhartGeometry: Fun with Fundamentals: Book 4, Teacher's Guide
-
Geometry: Fun with Fundamentals: Book 2, Teacher's Guide
By Newton Hawley, Patrick Suppes, George Woodward GearhartGeometry: Fun with Fundamentals: Book 2, Teacher's Guide
-
Geometry: Fun with Fundamentals: Book 1, Teacher's Guide
By Newton Hawley, Patrick Suppes, George Woodward GearhartGeometry: Fun with Fundamentals: Book 1, Teacher's Guide
-
Geometry: Constructions and Transformations
By Johnny W. Lott, Iris Mack DayoubThese more advanced Mira exercises explore basic geometric concepts, then constructions, transformations and problem solving.
-
Geometry: Common Core. All-in-one teaching resources
By Pearson Education, IncEach volume corresponds with one chapter of the Pearson Geometry: common core textbook. Includes vocabulary support, practice problems, lesson planning resources, and standardized test prep.
-
Geometry Computer Item Generator Bk 1998c
tools for a changing world. Computer item generator Prentice-Hall, inc. • Lesson 5-1 Objective: Finding area and perimeter of squares and.