LEADER 04495nam 2200805 a 450 001 9910789897403321 005 20200520144314.0 010 $a1-283-25606-1 010 $a0-691-11503-6 010 $a9786613256065 010 $a1-4008-4092-9 024 7 $a10.1515/9781400840922 035 $a(CKB)2670000000137530 035 $a(EBL)768544 035 $a(OCoLC)749265026 035 $a(SSID)ssj0000694776 035 $a(PQKBManifestationID)11427235 035 $a(PQKBTitleCode)TC0000694776 035 $a(PQKBWorkID)10670227 035 $a(PQKB)10526200 035 $a(SSID)ssj0000533695 035 $a(PQKBManifestationID)12196979 035 $a(PQKBTitleCode)TC0000533695 035 $a(PQKBWorkID)10492677 035 $a(PQKB)11001239 035 $a(SSID)ssj0001481260 035 $a(PQKBManifestationID)12624600 035 $a(PQKBTitleCode)TC0001481260 035 $a(PQKBWorkID)11497702 035 $a(PQKB)11689508 035 $a(DE-B1597)454673 035 $a(OCoLC)979624113 035 $a(OCoLC)984686758 035 $a(DE-B1597)9781400840922 035 $a(Au-PeEL)EBL768544 035 $a(CaPaEBR)ebr10496616 035 $a(CaONFJC)MIL325606 035 $a(MiAaPQ)EBC768544 035 $a(EXLCZ)992670000000137530 100 $a20030821d2004 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aAcross the board$b[electronic resource] $ethe mathematics of chessboard problems /$fJohn J. Watkins 205 $aCourse Book 210 $aPrinceton $cPrinceton University Press$dc2004 215 $a1 online resource (270 p.) 225 0 $aPrinceton Puzzlers 300 $aDescription based upon print version of record. 311 $a0-691-13062-0 311 $a0-691-15498-8 320 $aIncludes bibliographical references (p. 247-249) and index. 327 $tFrontmatter --$tContents --$tPreface --$tChapter One. Introduction --$tChapter Two. Knight's Tours --$tChapter Three. The Knight's Tour Problem --$tChapter Four. Magic Squares --$tChapter Five. The Torus and the Cylinder --$tChapter Six. The Klein Bottle and Other Variations --$tChapter Seven. Domination --$tChapter Eight. Queens Domination --$tChapter Nine. Domination on Other Surfaces --$tChapter Ten. Independence --$tChapter Eleven. Other Surfaces, Other Variations --$tChapter Twelve. Eulerian Squares --$tChapter Thirteen. Polyominoes --$tReferences --$tIndex 330 $aAcross the Board is the definitive work on chessboard problems. It is not simply about chess but the chessboard itself--that simple grid of squares so common to games around the world. And, more importantly, the fascinating mathematics behind it. From the Knight's Tour Problem and Queens Domination to their many variations, John Watkins surveys all the well-known problems in this surprisingly fertile area of recreational mathematics. Can a knight follow a path that covers every square once, ending on the starting square? How many queens are needed so that every square is targeted or occupied by one of the queens? Each main topic is treated in depth from its historical conception through to its status today. Many beautiful solutions have emerged for basic chessboard problems since mathematicians first began working on them in earnest over three centuries ago, but such problems, including those involving polyominoes, have now been extended to three-dimensional chessboards and even chessboards on unusual surfaces such as toruses (the equivalent of playing chess on a doughnut) and cylinders. Using the highly visual language of graph theory, Watkins gently guides the reader to the forefront of current research in mathematics. By solving some of the many exercises sprinkled throughout, the reader can share fully in the excitement of discovery. Showing that chess puzzles are the starting point for important mathematical ideas that have resonated for centuries, Across the Board will captivate students and instructors, mathematicians, chess enthusiasts, and puzzle devotees. 410 0$aPrinceton Puzzlers 606 $aMathematical recreations 606 $aChess 615 0$aMathematical recreations. 615 0$aChess. 676 $a793.74 700 $aWatkins$b John J$0480161 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910789897403321 996 $aAcross the board$947449 997 $aUNINA