Mathematical Recreations and Essays [Print Replica] Kindle Edition

The classic treatise of W.W. Rouse Ball on various subjects in mathematics, cryptography, time, spatial dimensions, chess, puzzles, and even astrology and the occult including: Arithmetical Fallacies, Bachet’s Weights Problem, Fermat’s Theorem on Binary Powers, Fermat’s Last Theorem, Geometrical Fallacies, Geometrical Paradoxes, Physical Geography, Statical Games of Position, Three-in-a-row. Extension to p-in-a-row, Tesselation, Cross-Fours, Dynamical Games of Position, Shunting Problems, Ferry-Boat Problems, Geodesic Problems, Problems with Counters placed in a row, Problems on a Chess-board with Counters or Pawns, Guarini’s Problem, Geometrical Puzzles (rods, strings, &c.), Some Mechanical Questions, Paradoxes on Motion, Force, Inertia, Centrifugal Force, Work, Stability of Equilibrium, &c., Perpetual Motion, Models, Sailing quicker than the Wind, Boat moved by a rope inside the boat, Results dependent on Hauksbee’s Law, Flight of Birds, Curiosa Physica, Some Miscellaneous Questions, The Fifteen Puzzle, The Tower of Hano, The Eight Queens Problem, Other Problems with Queens and Chess-pieces, The Fifteen School-Girls Problem, Problems connected with a pack of cards, Gergonne’s Pile Problem, The Mouse Trap, Treize, Magic Squares, Notes on the History of Magic Squares, Construction of Odd Magic Squares, Method of Bachet, Method of Dela Hire, Construction of Even Magic Squares, First Method, Composite Magic Squares, Bordered Magic Squares, Hyper-Magic Squares, Pan-diagonal or Nasik Squares, Magic Pencils, Magic Puzzles, Card Square, Domino Squares, Euler’s Problem, Euler’s Theorems, Examples, Mazes, Rules for completely traversing a Maze, Notes on the History of Mazes, Geometrical Trees, The Hamiltonian Game, Knight’s Path on a Chess-Board, Method of DeMontmort and DeMoivre, Method of Euler, Method of Roget, Method of Moon, Method of Jaenisch, Number of possible routes, Paths of other Chess-Pieces, Medieval Course of Studies: Acts, Tripos Verses, The Duplication of the Cube, Lemma of Hippocrates, Solutions of Archytas, Plato, Menaechmus, Apollonius, and Sporus, Solutions of Vieta, Descartes, Gregory of St Vincent, and Newton, The Trisection of an Angle, Solutions of Descartes, Newton, Clairaut, and Chasles, The Quadrature of the Circle, Theorems of Wallis and Brouncker, Mersenne’s Enunciation of the Theorem, List of known results, Cases awaiting verification, History of Investigations, By trial of divisors of known forms, By indeterminate equations, Mechanical methods of Factorizing Numbers, Astrology, Two branches: natal and horary astrology, Rules for casting and reading a horoscope, Houses and their significations, Planets and their significations, Zodiacal signs and their significations, Knowledge that rules were worthless, Notable instances of horoscopy, Lilly’s prediction of the Great Fire and Plague, Flamsteed’s guess, Cardan’s horoscope of Edward VI, Cryptographs and Ciphers, A Cryptograph, A Cipher, Essential Features of Cryptographs and Ciphers, Cryptographs of Three Types, Use of broken symbols, The Scytale, Ciphers: Use of arbitrary symbols unnecessary, Ciphers of Four Types, Requisites in a good Cipher, Cipher Machines, Historical Ciphers, Hyper-space, Speculation on Hyper-space, Space of two dimensions and of one dimension, Space of four dimensions, Existence in such a world, Arguments in favour of the existence of such a world Non-Euclidean Geometries, Elliptic Geometry of two dimensions, Elliptic, Parabolic and Hyperbolic Geometries compared Non-Euclidean Geometries of three or more dimensions, Time and its Measurement, Units for measuring durations (days, weeks, months, years), Boscovich’s Hypothesis, Hypothesis of an Elastic Solid Ether: Labile Ether, Dynamical Theories, The Vortex Ring Hypothesis, The Vortex Sponge Hypothesis, The Ether-Squirts Hypothesis, The Electron Hypothesis, Conjectures as to the cause of Gravity, and Conjectures to explain the finite number of species of Atoms. Read more