UID:
almafu_9959295545202883
Umfang:
1 online resource (449 pages)
,
1 online resource
Ausgabe:
12th ed.
Inhalt:
For over eighty years this delightful classic has provided entertainment through mathematical problems commonly known as recreations. This new edition upholds the original, but the terminology and treatment of problems have been updated and much new material has been added.
Anmerkung:
Bibliographic Level Mode of Issuance: Monograph
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Cover -- Contents -- Preface to the Tenth Edition -- Preface to the Eleventh Edition -- Preface to the Twelfth Edition -- I: ARITHMETICAL 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 problem -- 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: ARITHMETICAL 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 right-angled 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 five-disc problem -- Lebesgue's minimal problem -- Kakeya's minimal problem -- Addendum on a solution -- IV: GEOMETRICAL RECREATIONS (continued) -- Statical games of position -- Three-in-a-row. Extension to p-in-a-row -- Tessellation -- Anallagmatic pavements -- Polyominoes -- Colour-cube problem -- Squaring the square -- Dynamical games of position -- Shunting problems -- Ferry-boat problems -- Geodesic problems -- Problems with counters or pawns -- Paradromic rings -- Addendum on solutions -- V: POLYHEDRA -- Symmetry and symmetries -- The five Platonic solids.
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Kepler's mysticism -- Pappus, on the distribution of vertices -- Compounds -- The Archimedean solids -- Mrs. Stott's construction -- Equilateral zonohedra -- The Kepler-Poinsot polyhedra -- The 59 icosahedra -- Solid tessellations -- Ball-piling or close-packing -- The sand by the sea-shore -- Regular sponges -- Rotating rings of tetrahedra -- The kaleidoscope -- VI: CHESS-BOARD RECREATIONS -- Relative value of pieces -- The eight queens problem -- Maximum pieces problem -- Minimum pieces problem -- Re-entrant paths on a chess-board -- Knight's re-entrant path -- King's re-entrant path -- Rook's re-entrant path -- Bishop's re-entrant path -- Routes on a chess-board -- Guarini's problem -- Latin squares -- Eulerian squares -- Euler's officers problem -- Eulerian cubes -- VII: MAGIC SQUARES -- Magic squares of an odd order -- Magic squares of a singly-even order -- Magic squares of a doubly-even 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 non-consecutive numbers -- Magic squares of primes -- Doubly-magic and trebly-magic squares -- Other magic problems -- Magic domino squares -- Cubic and octahedral dice -- Interlocked hexagons -- Magic cubes -- VIII: MAP-COLOURING PROBLEMS -- The four-colour 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.
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An Hadamard matrix -- An error-correcting code -- A block design -- Steiner triple systems -- Finite geometries -- Kirkman's school-girl problem -- Latin squares -- The cube and the simplex -- Hadamard matrices -- Picture transmission -- Equiangular lines in 3-space -- Lines in higher-dimensional space -- C-matrices -- Projective planes -- XI: MISCELLANEOUS PROBLEMS -- The fifteen puzzle -- The Tower of Hanoї -- 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 symbol π -- Geometrical methods of approximation to the 'numerical value of Geometrical methods of approximation to the 'numerical value of π -- Results of Egyptians, Babylonians, Jews -- Results of Archimedes and other Greek writers -- Results of European writers, 1200-1630 -- Theorems of Wallis and Brouncker -- Results of European writers, 1699-1873 -- Approximations by the theory of probability -- XIII: CALCULATING PRODIGIES -- John Wallis, 1616-1703 -- Buxton, circ. 1707-1772 -- Fuller, 1710-1790 -- Ampère -- Gauss, Whately -- Colburn, 1804-1840 -- Bidder, 1806-1878 -- Mondeux, Mangiamele -- Dase, 1824-1861 -- Safford, 1836-1901 -- Zamebone, Diamandi, Rückle -- Inaudi, 1867- -- Types of memory of numbers -- Bidder's analysis of methods used -- Multiplication -- Digital method for division and factors -- Square roots. Higher roots -- Compound interest.
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Logarithms -- Alexander Craig Aitken -- XIV: CRYPTOGRAPHY AND CRYPTANALYSIS -- Cryptographic systems -- Transposition systems -- Columnar transposition -- Digraphs and trigraphs -- Comparison of several messages -- The grille -- Substitution systems -- Tables of frequency -- Polyalphabetic systems -- The Vigenere square -- The Playfair cipher -- Code -- Determination of cryptographic system -- A few final remarks -- Addendum: References for further study -- INDEX -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Y -- Z.
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English
Weitere Ausg.:
ISBN 9780802018441
Weitere Ausg.:
ISBN 0802018440
Weitere Ausg.:
ISBN 9780802061386
Weitere Ausg.:
ISBN 0802061389
Sprache:
Englisch
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