03550nam a2200373 a 4500 ebr10728518 CaPaEBR m o u cr cn||||||||| 100421s2010 dcua sb 001 0 eng d 2010927263 0883853485 (hbk.) 9780883853481 (hbk.) 9781614442011 (e-book) CaPaEBR CaPaEBR (OCoLC)796675453 QA9.54 .A57 2010eb 511.3/6 23 Alsina, Claudi. Charming proofs [electronic resource] : a journey into elegant mathematics / Claudi Alsina, Roger B. Nelsen. Washington, D.C. : Mathematical Association of America, c2010. xxiv, 295 p. : ill. Dolciani mathematical expositions ; no. 42 Includes bibliographical references (p. 275-287) and index. A garden of integers -- Distinguished numbers -- Points in the plane -- The polygonal playground -- A treasury of triangle theorems -- The enchantment of the equilateral triangle -- The quadrilaterals' corner -- Squares everywhere -- Curves ahead -- Adventures in tiling and coloring -- Geometry in three dimensions -- Additional theorems, problems, and proofs. "Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving"--Publisher's description. Electronic reproduction. Palo Alto, Calif. : ebrary, 2013. Available via World Wide Web. Access may be limited to ebrary affiliated libraries. Proof theory. Electronic books. local Nelsen, Roger B. Mathematical Association of America. ebrary, Inc. http://site.ebrary.com/lib/rucke/Doc?id=10728518 An electronic book accessible through the World Wide Web; click to view 151431 151431