Mathematics and the Imagination


Anyone who gambles, plays cards, loves puzzles, or simply seeks an intellectual challenge will love this amusing and thought-provoking book. With wit and clarity, the authors deftly progress from simple arithmetic to calculus and non-Euclidean geometry. "Charming and exciting."  — Saturday Review of Literature. Includes 169 figures.

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Mathematics and the Imagination

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Anyone who gambles, plays cards, loves puzzles, or simply seeks an intellectual challenge will love this amusing and thought-provoking book. With wit and clarity, the authors deftly progress from simple arithmetic to calculus and non-Euclidean geometry. "Charming and exciting."  — Saturday Review of Literature. Includes 169 figures.

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Editorial Reviews

Saturday Review of Literature
Charming and exciting.
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Product Details

  • ISBN-13: 9780486417035
  • Publisher: Dover Publications
  • Publication date: 3/28/2001
  • Pages: 400
  • Sales rank: 464,879
  • Product dimensions: 5.40 (w) x 8.40 (h) x 0.80 (d)

Table of Contents

    Easy words for hard ideas
    Non-simple curve
    Simple curve
    Simple group
    Bolsheviks and giraffes
    Turns and slides
    Circles and cycles
    Hexagons and parhexagons
    "Radicals, hyperradicals, and ultraradicals (nonpolitical)"
    New numbers for the nursery
    Googol and googolplex
    Miracle of the rising book
    The mathescope
    Counting?the language of number
    "Counting, matching, and "Going to Jerusalem"
    Cardinal numbers
    Cosmic chess and googols
    The sand reckoner
    Mathematical induction
    The infinite and its progeny
    Puzzles and quarrels
    Galileo's puzzle
    Measuring the measuring rod
    The whole is no greater than some of its parts
    The first transfinite?Alepho
    Arithmetic for morons
    Common sense hits a snag
    Cardinality madman
    The tortoise unmasked
    Motionless motion
    Private life of a number
    The house that Cantor built
III. "Pie, i, e (PIE)"
    Chinamen and chandeliers
    Twilight of common sense
    "Pie, i, e"
    Squaring the circle and its cousins
    Mathematical impossibility
    "Silk purse, sow's ear, ruler and compass"
    Rigor mortis
    Algebraic equations and transcendental numbers
    Galois and Greek epidemics
    Cube duplicators and angle trisectors
    Biography of pie
    "Infancy: Archimedes, the Bible, the Egyptians"
    "Adolescence: Vieta, Van Ceulen"
    "Maturity: Wallis, Newton, Leibniz"
    "Old Age: Dase, Richter, Shanks"
    Victim of schizophrenia
    Boon to insurance companies
    Logarithms or tricks of the trade
    Mr. Briggs is surprised
    Mr. Napier explains
    "Biography of e; or e, the banker's boon"
    Pituitary gland of mathematics: the exponential function
    "Humpty Dumpty, Doctor or Semantics"
    Imaginary numbers
    "The v-1, or "Where am I?" "
    "Biography of i, the self-made amphibian"
    "Omar Khayyám, Cardan, Bombelli, and Gauss"
    i and Soviet Russia
    Program music of mathematics
    "Breakfast in bed; or, How to become a great mathematician"
    Analytic geometry
    Geometric representation of i
    Complex plane
    "A famous formula, faith, and humility"
    The talking fish and St. Augustine
    A new alphabet
    High priests and mumbo jumbo
    Pure and applied mathematics
    Euclid and Texas
    Mathematical tailors
    Geometry?a game
    "Ghosts, table-tipping, and the land of the dead"
    Fourth-dimension flounders
    Henry More to the rescue
    Fourth-dimension?a new gusher
    A cure for arthritis
    Syntax suffers a setback
    The physicist's delight
    Dimensions and manifolds
    Distance formulae
    Scaling blank walls
    Four-dimensional geometry defined
    Moles and tesseracts
    A four-dimensional fancy
    Romance of flatland
    Three-dimensional cats and two-dimensional kings
    Gallant Gulliver and the gloves
    Beguiling voices and strange footprints
    Non-Euclidean geometry
    Space credos and millinery
    Private and public space
    Rewriting our textbooks
    The prince and the Boethians
    The flexible fifth
    The mathematicians unite?nothing to lose but their chains
    Lobachevsky breaks a link
    Riemann breaks another
    Checks and double checks in mathematics
    The tractrix and the pseudosphere
    Great circles and bears
    The skeptic persists?and is stepped on
    Seventh Day Adventists
    Lobachevskian Eiffel Towers and Riemannian Holland Tunnels
    Puzzle acorns and mathematical oaks
    Charlemagne and crossword puzzles
    "Mark Twain and the "farmer's daughter"
    The syntax of puzzles
    Carolyn Flaubert and the cabin boy
    "A wolf, a goat, and a head of cabbage"
    Brides and cuckolds
    I'll be switched
    "Poisson, the misfit"
    "High finance; or, The international beer wolf"
    Lions and poker players
    The decimal system
    Casting out nines
    "Buddha, God, and the binary scale"
    "The march of culture; or, Russia, the home of the binary system"
    The Chinese rings
    The tower of Hanoi
    "The ritual of Benares: or, Charley horse in the Orient"
    "Nim, Sissa Ben Dahir, and Josephus"
    Bismarck plays the boss
    The 15 puzzle plague
    The spider and the fly
    A nightmare of relatives
    The magic square
    Take a number from 1 to 10
    Fermat's last theorem
    Mathematics' lost legacy
    Great paradoxes and distant relatives
    Three species of paradox
    Paradoxes strange but true
    Wheels that move faster on top than on bottom
    The cycloid family
    "The curse of transportation; or, How locomotives can't make up their minds"
    Reformation of geometry
    Ensuing troubles
    Point sets?the Arabian Nights of mathematics
    Hausdorff spins a tall tale
    Messrs. Banach and Tarski rub the magic lamp
    Baron Munchhausen is stymied by a pea
    Mathematical fallacies
    "Trouble from a bubble; or, Dividing by zero"
    The infinite?troublemaker par excellence
    Geometrical fallacies
    Logical paradoxes?the folk tales of mathematics
    Deluding dialectics of the poacher and the prince; of the introspective barber; of the number 111777; of this book and Confucius; of the Hon. Bertrand Russell
    "Scylla and Charybdis; or, What shall poor mathematics d
    "Twits Napoleon, who does"
    The Marquis de Condorcet has high hopes
    M. le Marquis omits a factor and loses his head
    Fourier of the Old Guard
    Dr. Darwin of the New
    The syllogism scraps a standby
    Mr. Socrates may not die
    "Ring out the old logic, ring in the new"
    Seven bridges over a stein of beer
    Euler shivers
    Is warmed by news from home
    Invents topology
    Dissolves the dilemma of Sunday strollers
    Babies' cribs and Pythagoreans
    Talismen and queer figures
    Position is everything in topology
    Da Vinci and Dali
    The immutable derby
    "Competition for the caliph's cup; or, Sifting out the suitors by science"
    Mr. Jordan's theorem
    Only seems idiotic
    Deformed circles
    Old facts concerning Times Square and a balloonist's head
    Eccentric deportment of several distinguished gentlemen at Princeton
    Their passion for pretzels
    Their delving in doughnuts
    Enforced modesty of readers and authors
    The ring
    Lachrymose recital around a Paris pissoir
    "Who staggered how many times around the walls of what?"
    In and out the doughnut
    Gastric surgery?from doughnut to sausage in a single cut
    N-dimensional pretzels
    The Möbius strip
    Just as black as it is painted
    Foments industrial discontent
    Never takes sides
    Bane of painter and paintpot alike
    The iron rings
    "Mathematical cotillion; or, How on earth do I get rid of my partner?"
    "Topology?the pinnacle of perversity; or, Removing your vest without your coat"
    Down to earth?map coloring
    Four-color problem
    Euler's theorem
    The simplest universal law
    Brouwer's puzzle
    The search for invariants
    The calculus and cement
    Meaning of change and rate of change
    Zeno and the movies
    "Flying Arrow" local?stops at all points"
    Geometry and genetics
    The arithmetic men dig pits
    Lamentable analogue of the boomerang
    History of the calculus
    Story of the great rectangle
    Newton and Leibniz
    Archimedes and the limit
    "Shrinking and swelling; or, "Will the circle go the limit?"
    Brief dictionary of mathematics and physics
    "Military idyll; or, The speed of the falling bomb"
    The calculus at work
    The derivative
    Higher derivatives and radius of curvature
    Laudable scholarship of automobile engineers
    The third derivative as a shock absorber
    The derivative finds its mate
    Kepler and the bungholes
    "Measuring lengths; or, The yawning regress"
    Methods of approximation
    Measuring areas under curves
    Method of rectangular strips
    The definite
    On the inverse of the other
    "The outline of history and the descent of man: or, y=ex"
    Sickly curves and orchidaceous ones
    The snowflake
    Infinite perimeters and postage stamps
    Super-colossal pathological specimen?the curve that fills space
    The unbelievable crisscross
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