Read Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces)

Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces)

James W. Cannon

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Description:This is the first 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.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 Bolyai-Gerwien 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; straight-edge and compass constructions, giving complete proofs, including the transcendence of e and π, of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces). To get started finding Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

Pages: 119

Format: PDF, EPUB & Kindle Edition

Publisher: American Mathematical Society

Release: 2017

ISBN: 9781470437

Description: This is the first 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.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 Bolyai-Gerwien 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; straight-edge and compass constructions, giving complete proofs, including the transcendence of e and π, of the impossibility of squaring the circle, duplicating the cube, and trisecting the angle; and finally to a construction of the Hausdorff-Banach-Tarski paradox that shows some spherical sets are too complicated and cloudy to admit a well-defined notion of area.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces). To get started finding Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces), you are right to find our website which has a comprehensive collection of manuals listed.
Our library is the biggest of these that have literally hundreds of thousands of different products represented.

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Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces)

Two-Dimensional Spaces(Volume 1: Geometry of Lengths, Areas, and Volumes Two-Dimensional Spaces)

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