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Overview"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""))." Full Product DetailsAuthor: James W. CannonPublisher: American Mathematical Society Imprint: American Mathematical Society Weight: 0.825kg ISBN: 9781470437169ISBN 10: 1470437163 Pages: 105 Publication Date: 30 December 2017 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: In Print This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsA graphical introduction to hyperbolic geometry Hyperbolic geometry Gravity as curvature Curvature by polyhedral approximation Curvature as a length derivative Theorema egregium Curvature appendix BibliographyReviews"Like its predecessors, it is well written and full of exciting twists and turns, and will delight undergraduates, graduates, and those of us looking for something new to add to our geometry and topology classes."" — Alan S. McRae, Mathematical Reviews ""The reviewer likes the geometric style of the book, written by an expert in this beautiful area of mathematics...Reading this book made me want to learn more about 3-dimensional geometry."" — Joseph Malkoun, Zentralblatt MATH ""Many readers will be hooked by Cannon's aesthetics and proof exposition, where geometric intuition and topological arguments play leading roles...Cannon's books are worth every cent. I have in the past gifted Hilbert & Cohn-Voseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables."" — Tushar Das, MAA Reviews" Like its predecessors, it is well written and full of exciting twists and turns, and will delight undergraduates, graduates, and those of us looking for something new to add to our geometry and topology classes. - Alan S. McRae, Mathematical Reviews The reviewer likes the geometric style of the book, written by an expert in this beautiful area of mathematics...Reading this book made me want to learn more about 3-dimensional geometry. - Joseph Malkoun, Zentralblatt MATH Many readers will be hooked by Cannon's aesthetics and proof exposition, where geometric intuition and topological arguments play leading roles...Cannon's books are worth every cent. I have in the past gifted Hilbert & Cohn-Voseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables. - Tushar Das, MAA Reviews Author InformationJames W. Cannon, Brigham Young University, Provo, UT. Tab Content 6Author Website:Countries AvailableAll regions |