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# Two-dimensional spaces. Volume 1 : geometry of lengths, areas, and volumes

Author: James W Cannon Providence, Rhode Island : American Mathematical Society, [2017] ©2017 eBook : Document : EnglishView all editions and formats 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 $\pi$, 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.  Read more... (not yet rated) 0 with reviews - Be the first.

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Genre/Form: Electronic books Print version:Cannon, James W.Two-dimensional spaces.Providence, Rhode Island : American Mathematical Society, [2017](DLC) 2017024690(OCoLC)988749483 Document, Internet resource Internet Resource, Computer File James W Cannon Find more information about: James W Cannon 9781470443030 1470443031 1037838091 1 online resource (xi, 119 pages). Lengths-the Pythagorean theorem -- Consequences of the Pythagorean theorem -- Areas by slicing and scaling -- Areas by cut and paste -- Areas by counting -- Unsolvable problems in Euclidean geometry -- Does every set have a size? James W. Cannon.

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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  Read more...

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