Non Euclidean Geometry and Curvature is popular PDF and ePub book, written by James W. Cannon in 2017-11-08, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Non Euclidean Geometry and Curvature can be Read Online from any device for your convenience.
Non Euclidean Geometry and Curvature Book PDF Summary
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”)).
Detail Book of Non Euclidean Geometry and Curvature PDF
- Author : James W. Cannon
- Release : 08 November 2017
- Publisher : American Mathematical Soc.
- ISBN : 9781470437169
- Genre : Mathematics
- Total Page : 119 pages
- Language : English
- PDF File Size : 7,9 Mb
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