Professor Stewart's hoard of mathematical treasures

353 Pages·2009·2.78 MB·English

by  Ian Stewart

Professor Stewart’s
Hoard of
Mathematical Treasures
...........................................
By the Same Author
ConceptsofModernMathematics
Game,Set,andMath
DoesGodPlayDice?
AnotherFineMathYou’veGotMeInto
FearfulSymmetry(withMartinGolubitsky)
Nature’sNumbers
FromHeretoInfinity
TheMagicalMaze
Life’sOtherSecret
Flatterland
WhatShapeIsaSnowflake?
TheAnnotatedFlatland(withEdwinA.Abbott)
MathHysteria
TheMayorofUglyville’sDilemma
LetterstoaYoungMathematician
HowtoCutaCake
WhyBeautyIsTruth
TamingtheInfinite
ProfessorStewart’sCabinetofMathematicalCuriosities
withJackCohen
TheCollapseofChaos
FigmentsofReality
WhatDoesaMartianLookLike?
Wheelers(sciencefiction)
Heaven(sciencefiction)
withTerryPratchettandJackCohen
TheScienceofDiscworld
TheScienceofDiscworldII:TheGlobe
TheScienceofDiscworldIII:Darwin’sWatch
Professor Stewart’s
Hoard of
Mathematical Treasures
...........................................
Ian Stewart
A Member of the Perseus Books Group
New York
Hardcover first published in Great Britain in 2009 by
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Hardcover ISBN: 978-1-84668-292-6
Paperback ISBN: 978-0-465-01775-1
10 9 8 7 6 5 4 3 2 1
Contents
...........................................
Acknowledgements//xi
SecondDrawerDown ... //1
CalculatorCuriosity1//7
YearTurnedUpsideDown//7
LucklessLovelornLilavati//8
SixteenMatches//9
SwallowingElephants//9
MagicCircle//10
Dodgem//10
Press-the-Digit-ation//11
SecretsoftheAbacus//13
Redbeard’sTreasure//16
Hexaflexagons//18
WhoInventedtheEqualsSign?//20
StarsandSnips//20
BytheNumbersofBabylon//21
MagicHexagons//25
TheCollatz–Syracuse–UlamProblem//26
TheJeweller’sDilemma//29
WhatSeamusDidn’tKnow//30
WhyToastAlwaysFallsButtered-SideDown//31
vi//Contents
TheButteredCatParadox//31
Lincoln’sDog//32
Whodunni’sDice//33
AFlexiblePolyhedron//33
ButWhatAboutConcertinas?//34
TheBellowsConjecture//35
DigitalCubes//38
NothingWhichAppealsMuchtoaMathematician//38
WhatIstheAreaofanOstrichEgg?//40
OrderintoChaos//43
BigNumbers//44
TheDrowningMathematician//49
MathematicalPirates//49
TheHairyBallTheorem//52
CupsandDowns//53
SecretCodes//56
When2+2=0//59
SecretCodesThatCanBeMadePublic//62
CalendarMagic//66
MathematicalCats//67
TheRuleofEleven//70
DigitalMultiplication//70
CommonKnowledge//71
PickledOnionPuzzle//73
GuesstheCard//74
AndNowwithaCompletePack//75
Halloween=Christmas//75
EgyptianFractions//76
TheGreedyAlgorithm//80
HowtoMoveaTable//83
RectanglingtheSquare//83
Newton,byByron//84
XMarkstheSpot//84
Contents//vii
Whatever’stheAntimatter?//86
HowtoSeeInsideThings//91
MathematiciansMusingAboutMathematics//96
Wittgenstein’sSheep//98
LeaningTowerofPizza//99
PieThagoras’sWorld-FamousMinceπs//103
DiamondFrame//104
PourRelations//105
Alexander’sHornedSphere//105
TheSacredPrincipleofMat//107
PerfectlyAbundantlyAmicablyDeficient//109
TargetPractice//111
JustaPhaseI’mGoingThrough//112
ProofTechniques//114
SecondThoughts//116
HowDudeneyCookedLoyd//116
CookingwithWater//117
CelestialResonance//118
CalculatorCuriosity2//123
WhichisBigger?//123
SumsThatGoOnForEver//123
TheMostOutrageousProof//126
ColoradoSmithandtheSolarTemple//129
WhyCan’tIAddFractionsLikeIMultiplyThem?//131
Farey,Farey,QuiteContrary//131
PoolingResources//133
WelcometotheRep-TileHouse//133
CookingonaTorus//135
TheCatalanConjecture//136
TheOriginoftheSquareRootSymbol//138
PleaseBearwithMe//139
TheHamSandwichTheorem//139
CricketonGrumpius//143
viii//Contents
TheManWhoLovedOnlyNumbers//144
TheMissingPiece//145
TheOtherCoconut//145
WhatDoesZeno?//146
PiecesofFive//153
PiintheSky//154
TheCuriousIncidentoftheDog//155
MathematicsMadeDifficult//155
AWeirdFactaboutEgyptianFractions//157
AFourColourTheorem//157
SerpentofPerpetualDarkness//158
WhatAretheOdds?//159
APottedHistoryofMathematics//160
TheShortestMathematicalJokeEver//163
GlobalWarmingSwindle//164
NametheCards//171
WhatIsPointNineRecurring?//172
GhostofaDepartedQuantity//174
NiceLittleEarner//176
APuzzleforLeonardo//176
CongruentNumbers//177
Present-MindedSomewhereElse//179
It’sAboutTime//180
DoIAvoidKangaroos?//180
TheKleinBottle//181
AccountingtheDigits//185
MultiplyingwithSticks//186
AsLongasIGazeonLaplacianSunrise//190
AnotherTakeonMathematicalCats//191
BorderedPrimeMagicSquare//192
TheGreen–TaoTheorem//192
Peaucellier’sLinkage//195
ABetterApproximationtoπ//196
Contents//ix
StrictlyforCalculusBuffs//197
TheStatueofPallasAthene//198
CalculatorCuriosity3//199
CompletingtheSquare//200
TheLookandSaySequence//200
Non-MathematiciansMusingAboutMathematics//201
Euler’sConjecture//203
TheMillionthDigit//203
PiraticalPathways//204
TrainsThatPassintheSiding//205
PleaseMakeYourselfClear//205
Squares,ListsandDigitalSums//206
Hilbert’sHit-List//206
MatchTrick//211
WhichHospitalShouldClose?//212
HowtoTurnaSphereInsideOut//213
APieceofStringWalkedintoaBar...//218
SlicingtheCake//218
TheOriginoftheSymbolforPi//219
HallofMirrors//219
GreekandTrojanAsteroids//220
SlidingCoins//223
BeatThat!//223
Euclid’sPuzzle//224
TheInfiniteMonkeyTheorem//225
MonkeysAgainstEvolution//226
UniversalLetterofReference//228
SnakesandAdders//228
PowerfulCrossnumber//230
MagicHandkerchiefs//231
ABluffer’sGuidetoSymmetry//232
DigitalCenturyRevisited//236
AnInfinityofPrimes//237