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Other titles in the Dover Books on Mathematical & Word Recreations series:Mathematical Recreations & Essays 13TH Editionby W W Rouse Ball
Synopses & ReviewsPublisher Comments:This classic work offers scores of stimulating, mindexpanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, mapcoloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" — The Mathematics Teacher. Index. References for Further Study. Includes 150 blackandwhite line illustrations. Synopsis:Classic treasury of arithmetical and geometrical problems, chessboard recreations, cryptography, and much more.
Synopsis:This classic work offers scores of stimulating, mindexpanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, mapcoloring problems, cryptography and cryptanalysis, much more. Includes 150 blackandwhite line illustrations. About the AuthorH. S. M. Coxeter: Through the Looking Glass Harold Scott MacDonald Coxeter (19072003) is one of the greatest geometers of the last century, or of any century, for that matter. Coxeter was associated with the University of Toronto for sixty years, the author of twelve books regarded as classics in their field, a student of Hermann Weyl in the 1930s, and a colleague of the intriguing Dutch artist and printmaker Maurits Escher in the 1950s. In the Author's Own Words: "I'm a Platonist — a follower of Plato — who believes that one didn't invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered." "In our times, geometers are still exploring those new Wonderlands, partly for the sake of their applications to cosmology and other branches of science, but much more for the sheer joy of passing through the looking glass into a land where the familiar lines, planes, triangles, circles, and spheres are seen to behave in strange but precisely determined ways." "Geometry is perhaps the most elementary of the sciences that enable man, by purely intellectual processes, to make predictions (based on observation) about the physical world. The power of geometry, in the sense of accuracy and utility of these deductions, is impressive, and has been a powerful motivation for the study of logic in geometry." "Let us revisit Euclid. Let us discover for ourselves a few of the newer results. Perhaps we may be able to recapture some of the wonder and awe that our first contact with geometry aroused." — H. S. M. Coxeter Table of ContentsI ARITHEMETICAL RECREATIONS
To find a number selected by someone Prediction of the result of certain operations Problems involving two numbers Problems depending on the scale of notation Other problems with numbers in the denary scale Four fours problems Problems with a series of numbered things Arithmetical restorations Calendar problems Medieval problems in arithmetic The Josephus problem. Decimation Nim and similar games Moore's game Kayles Wythoff's game Addendum on solutions II ARITHEMETICAL RECREATIONS (continued) Arithmetical fallacies Paradoxical problems Probability problems Permutation problems Bachet's weights problem The decimal expression for 1/n Decimals and continued fractions Rational rightangled triangles Triangular and pyramidal numbers Divisibility The prime number theorem Mersenne numbers Perfect numbers Fermat numbers Fermat's Last Theorem Galois fields III GEOMETRICAL RECREATIONS Geometrical fallacies Geometrical paradoxes Continued fractions and lattice points Geometrical dissections Cyclotomy Compass problems The fivedisc problem Lebesgue's minimal problem Kakeya's minimal problem Addendum on a solution IV GEOMETRICAL RECREATIONS (continued) Statical games of position Threeinarow. Extension to pinarow Tessellation Anallagmatic pavements Polyominoes Colourcube problem Squaring the square Dynamical games of position Shunting problems Ferryboat problems Geodesic problems Problems with counters or pawns Paradromic rings Addendum on solutions V POLYHEDRA Symmetry and symmetries The five Platonic solids Kepler's mysticism "Pappus, on the distribution of vertices" Compounds The Archimedean solids Mrs. Stott's construction Equilateral zonohedra The KeplerPoinsot polyhedra The 59 icosahedra Solid tessellations Ballpiling or closepacking The sand by the seashore Regular sponges Rotating rings of tetrahedra The kaleidoscope VI CHESSBOARD RECREATIONS Relative value of pieces The eight queens problem Maximum pieces problem Minimum pieces problem Reentrant paths on a chessboard Knight's reentrant path King's reentrant path Rook's reentrant path Bishop's reentrant path Route's on a chessboard Guarini's problem Latin squares Eulerian squares Euler's officers problem Eulerian cubes VII MAGIC SQUARE Magic squares of an odd order Magic squares of a singlyeven order Magic squares of a doublyeven order Bordered squares Number of squares of a given order Symmetrical and pandiagonal squares Generalization of De la Loubère's rule Arnoux's method Margossian's method Magic squares of nonconsecutive numbers Magic squares of primes Doublymagic and treblymagic squares Other magic problems Magic domino squares Cubic and octahedral dice Interlocked hexagons Magic cubes VIII MAPCOLOURING PROBLEMS The fourcolour conjecture The Petersen graph Reduction to a standard map Minimum number of districts for possible failure Equivalent problem in the theory of numbers Unbounded surfaces Dual maps Maps on various surfaces "Pits, peaks, and passes" Colouring the icosahedron IX UNICURSAL PROBLEMS Euler's problem Number of ways of describing a unicursal figure Mazes Trees The Hamiltonian game Dragon designs X COMBINATORIAL DESIGNS A projective plane Incidence matrices An Hadamard matrix An errorcorrrecting code A block design Steiner triple systems Finite geometries Kirkman's schoolgirl problem Latin squares The cube and the simplex Hadamard matrices Picture transmission Equiangular lines in 3space Lines in higherdimensional space Cmatrices Projective planes XI MISCELLANEOUS The fifteen puzzle The Tower of Hanoï Chinese rings Problems connected with a pack of cards Shuffling a pack Arrangements by rows and columns Bachet's problem with pairs of cards Gergonne's pile problem The window reader The mouse trap. Treize XII THREE CLASSICAL GEOMETRICAL PROBLEMS The duplication of the cube "Solutions by Hippocrates, Archytas, Plato, Menaechmus, Apollonius, and Diocles" "Solutions by Vieta, Descartes, Gregory of St. Vincent, and Newton" The trisection of an angle "Solutions by Pappus, Descartes, Newton, Clairaut, and Chasles" The quadrature of the circle Origin of symbo p Geometrical methods of approximation to the numerical value of p "Results of Egyptians, Babylonians, Jews" Results of Archimedes and other Greek writers "Results of European writers, 12001630" Theorems of Wallis and Brouncker "Results of European writers, 16991873" Ap What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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