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Mathematical Recreations & Essays 13TH Edition

by

Mathematical Recreations & Essays 13TH Edition Cover

 

Synopses & Reviews

Publisher Comments:

This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. "A must to add to your mathematics library" — The Mathematics Teacher. Index. References for Further Study. Includes 150 black-and-white line illustrations.

Synopsis:

Classic treasury of arithmetical and geometrical problems, chessboard recreations, cryptography, and much more.

Synopsis:

This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. Includes 150 black-and-white line illustrations.

About the Author

H. S. M. Coxeter: Through the Looking Glass

Harold Scott MacDonald Coxeter (1907-2003) 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 Contents

I 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 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

      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

      Route's on a chess-board

      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 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

    An Hadamard matrix

    An error-corrrecting 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

    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, 1200-1630"

    Theorems of Wallis and Brouncker

    "Results of European writers, 1699-1873"

    Ap

Product Details

ISBN:
9780486253572
Author:
Coxeter, H. S. M. Mharold S.
Author:
Coxeter, H. S. M. Mharold S.
Author:
Ball, W. W. Rouse
Author:
Coxeter, H. S. M.
Author:
Ball, Walter W. Rouse
Author:
Coxeter, H. S. M. Mharold S.
Publisher:
Dover Publications
Location:
New York :
Subject:
General
Subject:
Geometry
Subject:
Puzzles
Subject:
Recreations & Games
Subject:
Mathematical recreations
Subject:
Cryptography
Subject:
Ciphers
Subject:
General Mathematics
Subject:
Mathematics-Games and Puzzles
Edition Number:
13
Edition Description:
Trade Paper
Series:
Dover Recreational Math
Series Volume:
no. 6
Publication Date:
20100531
Binding:
TRADE PAPER
Language:
English
Illustrations:
Yes
Pages:
464
Dimensions:
8.5 x 5.38 in 1.1 lb

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Mathematical Recreations & Essays 13TH Edition New Trade Paper
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Product details 464 pages Dover Publications - English 9780486253572 Reviews:
"Synopsis" by , Classic treasury of arithmetical and geometrical problems, chessboard recreations, cryptography, and much more.

"Synopsis" by ,
This classic work offers scores of stimulating, mind-expanding games and puzzles: arithmetical and geometrical problems, chessboard recreations, magic squares, map-coloring problems, cryptography and cryptanalysis, much more. Includes 150 black-and-white line illustrations.
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