Overview
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.
Full Product Details
Author: James W. Cannon
Publisher: American Mathematical Society
Imprint: American Mathematical Society
Weight: 0.252kg
ISBN: 9781470437145
ISBN 10: 1470437147
Pages: 119
Publication Date: 30 December 2017
Audience:
Professional and scholarly
,
Professional & Vocational
Format: Paperback
Publisher's Status: Active
Availability: In Print
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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 & 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 The presentation is accessible, generously illustrated, and supported by exercises. - Viktor Blasjoe, Mathematical 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 & 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 ""The presentation is accessible, generously illustrated, and supported by exercises."" — Viktor Blasjö, Mathematical 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 & 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 ""The presentation is accessible, generously illustrated, and supported by exercises."" — Viktor Blasjö, Mathematical Reviews
Author Information
James W. Cannon, Brigham Young University, Provo, UT.
