Mathematics and the Imagination

Häftad, Engelska, 2003

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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.

Produktinformation

Utgivningsdatum2003-03-28
Mått140 x 220 x 25 mm
Vikt400 g
FormatHäftad
SpråkEngelska
SerieDover Books on Mathema 1.4tics
Antal sidor400
FörlagDover Publications Inc.
ISBN9780486417035

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IntroductionI. NEW NAMES FOR OLDEasy words for hard ideasTranscendentalNon-simple curveSimple curveSimple groupBolsheviks and giraffesTurbinesTurns and slidesCircles and cyclesPatho-circlesClocksHexagons and parhexagons"Radicals, hyperradicals, and ultraradicals (nonpolitical)"New numbers for the nurseryGoogol and googolplexMiracle of the rising bookThe mathescopeII. BEYOND THE GOOGOLCounting?the language of number"Counting, matching, and "Going to Jerusalem"Cardinal numbersCosmic chess and googolsThe sand reckonerMathematical inductionThe infinite and its progenyZenoPuzzles and quarrelsBolzanoGalileo's puzzleCantorMeasuring the measuring rodThe whole is no greater than some of its partsThe first transfinite?AlephoArithmetic for moronsCommon sense hits a snagCardinality madmanThe tortoise unmaskedMotionless motionPrivate life of a numberThe house that Cantor builtIII. "Pie, i, e (PIE)"Chinamen and chandeliersTwilight of common sense"Pie, i, e"Squaring the circle and its cousinsMathematical impossibility"Silk purse, sow's ear, ruler and compass"Rigor mortisAlgebraic equations and transcendental numbersGalois and Greek epidemicsCube duplicators and angle trisectorsBiography of pie"Infancy: Archimedes, the Bible, the Egyptians""Adolescence: Vieta, Van Ceulen""Maturity: Wallis, Newton, Leibniz""Old Age: Dase, Richter, Shanks"Victim of schizophreniaBoon to insurance companies(e)Logarithms or tricks of the tradeMr. Briggs is surprisedMr. Napier explains"Biography of e; or e, the banker's boon"Pituitary gland of mathematics: the exponential function(i)"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 RussiaProgram music of mathematics"Breakfast in bed; or, How to become a great mathematician"Analytic geometryGeometric representation of i Complex plane"A famous formula, faith, and humility"IV. ASSORTED GEOMETRIES?PLANE AND FANCYThe talking fish and St. AugustineA new alphabetHigh priests and mumbo jumboPure and applied mathematicsEuclid and TexasMathematical tailorsGeometry?a game"Ghosts, table-tipping, and the land of the dead"Fourth-dimension floundersHenry More to the rescueFourth-dimension?a new gusherA cure for arthritisSyntax suffers a setbackThe physicist's delightDimensions and manifoldsDistance formulaeScaling blank wallsFour-dimensional geometry definedMoles and tesseractsA four-dimensional fancyRomance of flatlandThree-dimensional cats and two-dimensional kingsGallant Gulliver and the glovesBeguiling voices and strange footprintsNon-Euclidean geometrySpace credos and millineryPrivate and public spaceRewriting our textbooksThe prince and the BoethiansThe flexible fifthThe mathematicians unite?nothing to lose but their chainsLobachevsky breaks a linkRiemann breaks anotherChecks and double checks in mathematicsThe tractrix and the pseudosphere Great circles and bearsThe skeptic persists?and is stepped onGeodesicsSeventh Day AdventistsCurvatureLobachevskian Eiffel Towers and Riemannian Holland TunnelsV. PASTIMES OF PAST AND PRESENT TIMESPuzzle acorns and mathematical oaksCharlemagne and crossword puzzles"Mark Twain and the "farmer's daughter"The syntax of puzzlesCarolyn Flaubert and the cabin boy"A wolf, a goat, and a head of cabbage"Brides and cuckoldsI'll be switched"Poisson, the misfit""High finance; or, The international beer wolf"Lions and poker playersThe decimal systemCasting out nines"Buddha, God, and the binary scale""The march of culture; or, Russia, the home of the binary system"The Chinese ringsThe tower of Hanoi"The ritual of Benares: or, Charley horse in the Orient""Nim, Sissa Ben Dahir, and Josephus"Bismarck plays the bossThe 15 puzzle plagueThe spider and the flyA nightmare of relativesThe magic squareTake a number from 1 to 10Fermat's last theoremMathematics' lost legacyVI. PARADOX LOST AND PARADOX REGAINEDGreat paradoxes and distant relativesThree species of paradoxParadoxes strange but trueWheels that move faster on top than on bottomThe cycloid family"The curse of transportation; or, How locomotives can't make up their minds"Reformation of geometryEnsuing troublesPoint sets?the Arabian Nights of mathematicsHausdorff spins a tall taleMessrs. Banach and Tarski rub the magic lampBaron Munchhausen is stymied by a peaMathematical fallacies"Trouble from a bubble; or, Dividing by zero"The infinite?troublemaker par excellenceGeometrical fallaciesLogical paradoxes?the folk tales of mathematicsDeluding 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 hopesM. le Marquis omits a factor and loses his headFourier of the Old GuardDr. Darwin of the NewThe syllogism scraps a standbyMr. Socrates may not die"Ring out the old logic, ring in the new"VIII. RUBBER-SHEET GEOMETRYSeven bridges over a stein of beerEuler shiversIs warmed by news from homeInvents topologyDissolves the dilemma of Sunday strollersBabies' cribs and PythagoreansTalismen and queer figuresPosition is everything in topologyDa Vinci and DaliInvariantsTransformationsThe immutable derby"Competition for the caliph's cup; or, Sifting out the suitors by science"Mr. Jordan's theoremOnly seems idioticDeformed circlesOld facts concerning Times Square and a balloonist's headEccentric deportment of several distinguished gentlemen at PrincetonTheir passion for pretzelsTheir delving in doughnutsEnforced modesty of readers and authorsThe ringLachrymose recital around a Paris pissoir"Who staggered how many times around the walls of what?"In and out the doughnutGastric surgery?from doughnut to sausage in a single cutN-dimensional pretzelsThe Möbius stripJust as black as it is paintedFoments industrial discontentNever takes sidesBane of painter and paintpot alikeThe 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 coloringFour-color problemEuler's theoremThe simplest universal lawBrouwer's puzzleThe search for invariantsIX. CHANGE AND CHANGEABILITYThe calculus and cementMeaning of change and rate of changeZeno and the movies"Flying Arrow" local?stops at all points"Geometry and geneticsThe arithmetic men dig pitsLamentable analogue of the boomerangHistory of the calculusKeplerFermatStory of the great rectangleNewton and LeibnizArchimedes 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 workThe derivative Higher derivatives and radius of curvatureLaudable scholarship of automobile engineersThe third derivative as a shock absorberThe derivative finds its mateIntegrationKepler and the bungholes"Measuring lengths; or, The yawning regress"Methods of approximationMeasuring areas under curvesMethod of rectangular stripsThe definite IndefiniteOn the inverse of the other"The outline of history and the descent of man: or, y=ex"Sickly curves and orchidaceous onesThe snowflakeInfinite perimeters and postage stampsAnti-snowflakeSuper-colossal pathological specimen?the curve that fills spaceThe unbelievable crisscrossEPILOGUE. MATHEMATICS AND THE IMAGINATION