Mathematical recreations and essays

Format:

Book

Author/Creator:

Ball, W. W. Rouse (Walter William Rouse), 1850-1925.

Contributor:

Coxeter, H. S. M. (Harold Scott Macdonald), 1907-2003.

Language:

English

Subjects (All):

Mathematical recreations--Famous problems.

Mathematical recreations.

Geometry.

Cryptography.

Ciphers.

Physical Description:

1 online resource (449 pages)

1 online resource

Edition:

12th ed.

Place of Publication:

London Macmillan 1922

Language Note:

English

Summary:

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.

Contents:

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

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

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.

An Hadamard matrix

An error-correcting code

A block design

Steiner triple systems

Finite geometries

Kirkman's school-girl problem

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.

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.

Notes:

Bibliographic Level Mode of Issuance: Monograph