Non?Euclidean Geometry and Curvature ? Two?Dimensional Spaces, Volume 3
Two-Dimensional Spaces, Volume 3
Series: Monograph Books;
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27 835 Ft (26 510 Ft + 5% VAT)
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27 835 Ft
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Estimated delivery time: In stock at the publisher, but not at Prospero's office. Delivery time approx. 3-5 weeks.
Not in stock at Prospero.
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Delivery time is estimated on our previous experiences. We give estimations only, because we order from outside Hungary, and the delivery time mainly depends on how quickly the publisher supplies the book. Faster or slower deliveries both happen, but we do our best to supply as quickly as possible.
Product details:
- Publisher MP?AMM American Mathematical
- Date of Publication 30 December 2017
- Number of Volumes Paperback
- ISBN 9781470437169
- Binding Paperback
- No. of pages106 pages
- Size 254x178x19 mm
- Weight 825 g
- Language English 0
Categories
Short 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&&&39;s masters of geometric topology. The books provide perspective and insight to mathematicians at all levels who are interested in geometry and topology.
MoreLong 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&&&39;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&&&39;s original definition of curvature is extrinsic rather than intrinsic. The final two chapters show that the book&&&39;s intrinsic definition is equivalent to Gauss&&&39;s extrinsic definition (Gauss&&&39;s "Theorema Egregium" ("Great Theorem")).
