Softcover ISBN:  9781470437145 
Product Code:  MBK/108 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443030 
Product Code:  MBK/108.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470437145 
eBook: ISBN:  9781470443030 
Product Code:  MBK/108.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $102.60 $77.85 
AMS Member Price:  $91.20 $69.20 
Softcover ISBN:  9781470437145 
Product Code:  MBK/108 
List Price:  $59.00 
MAA Member Price:  $53.10 
AMS Member Price:  $47.20 
eBook ISBN:  9781470443030 
Product Code:  MBK/108.E 
List Price:  $55.00 
MAA Member Price:  $49.50 
AMS Member Price:  $44.00 
Softcover ISBN:  9781470437145 
eBook ISBN:  9781470443030 
Product Code:  MBK/108.B 
List Price:  $114.00 $86.50 
MAA Member Price:  $102.60 $77.85 
AMS Member Price:  $91.20 $69.20 

Book Details2017; 119 ppMSC: Primary 51
This is the first 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.
The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the BolyaiGerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straightedge and compass constructions, giving complete proofs, including the transcendence of \(e\) and \(\pi\), of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the HausdorffBanachTarski paradox that shows some spherical sets are too complicated and cloudy to admit a welldefined notion of area.
ReadershipUndergraduate and graduate students and researchers interested in topology.
This item is also available as part of a set: 
Table of Contents

Chapters

Lengths—The Pythagorean theorem

Consequences of the Pythagorean theorem

Areas

Areas by slicing and scaling

Areas by cut and paste

Areas by counting

Unsolvable problems in Euclidean geometry

Does every set have a size?


Additional Material

Reviews

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 
The presentation is accessible, generously illustrated, and supported by exercises.
Viktor Blasjö, Mathematical Reviews


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This is the first 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.
The first volume begins with length measurement as dominated by the Pythagorean Theorem (three proofs) with application to number theory; areas measured by slicing and scaling, where Archimedes uses the physical weights and balances to calculate spherical volume and is led to the invention of calculus; areas by cut and paste, leading to the BolyaiGerwien theorem on squaring polygons; areas by counting, leading to the theory of continued fractions, the efficient rational approximation of real numbers, and Minkowski's theorem on convex bodies; straightedge and compass constructions, giving complete proofs, including the transcendence of \(e\) and \(\pi\), of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the HausdorffBanachTarski paradox that shows some spherical sets are too complicated and cloudy to admit a welldefined notion of area.
Undergraduate and graduate students and researchers interested in topology.

Chapters

Lengths—The Pythagorean theorem

Consequences of the Pythagorean theorem

Areas

Areas by slicing and scaling

Areas by cut and paste

Areas by counting

Unsolvable problems in Euclidean geometry

Does every set have a size?

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 
The presentation is accessible, generously illustrated, and supported by exercises.
Viktor Blasjö, Mathematical Reviews