LEADER 03888nam 2200577 a 450 001 9910461942903321 005 20200520144314.0 010 $a1-61444-201-0 035 $a(CKB)2670000000205119 035 $a(EBL)3330369 035 $a(SSID)ssj0000577574 035 $a(PQKBManifestationID)11378673 035 $a(PQKBTitleCode)TC0000577574 035 $a(PQKBWorkID)10561943 035 $a(PQKB)11365664 035 $a(UkCbUP)CR9781614442011 035 $a(MiAaPQ)EBC3330369 035 $a(Au-PeEL)EBL3330369 035 $a(CaPaEBR)ebr10728518 035 $a(OCoLC)929120458 035 $a(EXLCZ)992670000000205119 100 $a20100421d2010 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aCharming proofs$b[electronic resource] $ea journey into elegant mathematics /$fClaudi Alsina, Roger B. Nelsen 210 $aWashington, D.C. $cMathematical Association of America$dc2010 215 $a1 online resource (320 p.) 225 0$aDolciani mathematical expositions ;$vno. 42 300 $aDescription based upon print version of record. 311 $a0-88385-348-5 320 $aIncludes bibliographical references (p. 275-287) and index. 327 $aA 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. 330 $a"Theorems and their proofs lie at the heart of mathematics. In speaking of the purely aesthetic qualities of theorems and proofs, G. H. Hardy wrote that in beautiful proofs 'there is a very high degree of unexpectedness, combined with inevitability and economy'. Charming Proofs present a collection of remarkable proofs in elementary mathematics that are exceptionally elegant, full of ingenuity, and succinct. By means of a surprising argument or a powerful visual representation, the proofs in this collection will invite readers to enjoy the beauty of mathematics, to share their discoveries with others, and to become involved in the process of creating new proofs. Charming Proofs is organized as follows. Following a short introduction about proofs and the process of creating proofs, the authors present, in twelve chapters, a wide and varied selection of proofs they consider charming, Topics include the integers, selected real numbers, points in the plane, triangles, squares, and other polygons, curves, inequalities, plane tilings, origami, colorful proofs, three-dimensional geometry, etc. At the end of each chapter are some challenges that will draw the reader into the process of creating charming proofs. There are over 130 such challenges. Charming Proofs concludes with solutions to all of the challenges, references, and a complete index. As in the authors' previous books with the MAA (Math Made Visual and When Less Is More), secondary school and college and university teachers may wish to use some of the charming proofs in their classrooms to introduce their students to mathematical elegance. Some may wish to use the book as a supplement in an introductory course on proofs, mathematical reasoning, or problem solving"--Publisher's description. 410 0$aDolciani Mathematical Expositions 606 $aProof theory 608 $aElectronic books. 615 0$aProof theory. 676 $a511.3/6 700 $aAlsina$b Claudi$0309455 701 $aNelsen$b Roger B$055994 712 02$aMathematical Association of America. 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910461942903321 996 $aCharming proofs$92041376 997 $aUNINA