Softcover ISBN:  9781470437169 
Product Code:  MBK/110 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443078 
Product Code:  MBK/110.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9781470437169 
eBook: ISBN:  9781470443078 
Product Code:  MBK/110.B 
List Price:  $104.00 $81.50 
MAA Member Price:  $93.60 $73.35 
AMS Member Price:  $83.20 $65.20 
Softcover ISBN:  9781470437169 
Product Code:  MBK/110 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443078 
Product Code:  MBK/110.E 
List Price:  $45.00 
MAA Member Price:  $40.50 
AMS Member Price:  $36.00 
Softcover ISBN:  9781470437169 
eBook ISBN:  9781470443078 
Product Code:  MBK/110.B 
List Price:  $104.00 $81.50 
MAA Member Price:  $93.60 $73.35 
AMS Member Price:  $83.20 $65.20 

Book Details2017; 105 ppMSC: Primary 51; 53
This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2dimensional 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 spacetime. Bill Thurston showed us that nonEuclidean geometries and curvature are essential to the understanding of lowdimensional 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 nonEuclidean 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 nonEuclidean 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”)).
ReadershipGraduate and undergraduate students and researchers interested in topology.
This item is also available as part of a set: 
Table of Contents

Chapters

A graphical introduction to hyperbolic geometry

Hyperbolic geometry

Gravity as curvature

Curvature by polyhedral approximation

Curvature as a length derivative

Theorema egregium

Curvature appendix


Additional Material

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 3dimensional 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 & CohnVoseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables.
Tushar Das, MAA Reviews


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 Book Details
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This is the final volume of a three volume collection devoted to the geometry, topology, and curvature of 2dimensional 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 spacetime. Bill Thurston showed us that nonEuclidean geometries and curvature are essential to the understanding of lowdimensional 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 nonEuclidean 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 nonEuclidean 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”)).
Graduate and undergraduate students and researchers interested in topology.

Chapters

A graphical introduction to hyperbolic geometry

Hyperbolic geometry

Gravity as curvature

Curvature by polyhedral approximation

Curvature as a length derivative

Theorema egregium

Curvature appendix

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 3dimensional 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 & CohnVoseen and Rademacher and Toeplitz to my students. Now I have Cannon's trio to add to my list of giftables.
Tushar Das, MAA Reviews