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**About this book :- **

**Two-dimensional Spaces, Volume 3: Non-Euclidean Geometry & Curvature ** written by
** James W. Cannon **.

This textbook is the last of a three volume set describing a very personal arc of thought that begins with earth measurement (that is, geo-metry), passes through the topology of 2-dimensional surfaces, and ends with space-time measurement (that is, geochronometry, where Einstein identifies gravity with the curvature of space-time). The volumes are (1) The Geometry of the 2- Dimensional Spaces; (2) The Topology of 2-Dimensional Spaces; and (3) An Introduction to Non Euclidean Geometry and Curvature.

Volume 3 gives a general introduction to hyperbolic non-Euclidean geometry in all dimensions, with an introduction to all of the standard models and their relationships to one another. It explains why the models are called hyperbolic. It discusses the ways in which this geometry differs from Euclidean geometry. It calculates the shortest paths in this geometry (the geodesics). It explains some of the reasons why this geometry is studied. Following the introduction to non-Euclidean geometry, Volume 3 approaches curvature in dimension 2 in a way that does not begin with the Gauss map. Instead, it begins with a natural metricinvariant definition of curvature that measures in an obvious way the difficulty of flattening a surface into the plane without distorting lengths and areas. It ends with the Gauss map and a proof of Gauss’s Theorema Egregium. This approach, which is backward to the classical approach, is intuitive; but it entails difficulties in proving that certain limits exist.

James W. Cannon

**Book Detail :- **
** Title: ** Two-dimensional Spaces, Volume 3: Non-Euclidean Geometry & Curvature
** Edition: **
** Author(s): ** James W. Cannon
** Publisher: ** American Mathematical Society
** Series: **
** Year: ** 2017
** Pages: ** 119
** Type: ** PDF
** Language: ** English
** ISBN: ** 1470437163,9781470437169
** Country: ** US

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**About Author :- **

The author **James W. Cannon ** (1943-2012) was born, in Bellefonte, Pennsylvania. James Cannon received his Ph.D. in Mathematics from the University of Utah in 1969, under the direction of C. Edmund Burgess.

He was a Professor at the University of Wisconsin, Madison from 1977 to 1985. In 1986 Cannon was appointed an Orson Pratt Professor of Mathematics at Brigham Young University. He held this position until his retirement in September 2012.

James Cannon gave an AMS Invited address at the meeting of the American Mathematical Society in Seattle in August 1977, an invited address at the International Congress of Mathematicians in Helsinki 1978, and delivered the 1982 Mathematical Association of America Hedrick Lectures in Toronto, Canada.

James Cannon was elected to the American Mathematical Society Council in 2003 with the term of service February 1, 2004, to January 31, 2007. In 2012 he became a fellow of the American Mathematical Society.

**All Famous Books of this Author :- **

Here is list all books, text books, editions, versions, solution manuals or solved notes avaliable of this author, We recomended you to download all.

** • Download PDF Two-Dimensional Spaces: Volume 1, Geometry of Lengths, Areas, and Volumes by James W. Cannon **

** • Download PDF Two-Dimensional Spaces: Volume 2, Topology as Fluid Geometry by James W. Cannon **

** • Download PDF Two-dimensional Spaces: Volume 3, Non-Euclidean Geometry & Curvature by James W. Cannon **

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**Book Contents :- **
**Two-dimensional Spaces, Volume 3: Non-Euclidean Geometry & Curvature ** written by
** James W. Cannon **
cover the following topics.

1. A Graphical Introduction to Hyperbolic Geometry

2. Hyperbolic Geometry

3. Gravity As Curvature

4. Curvature by Polyhedral Approximation

5. Curvature As a Length Derivative

6. Theorema Egregium

7. Curvature Appendix

Bibliography

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- Abstract Algebra
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- Differential Equations
- Engineering Mathematics
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