Table Of ContentORIGAMI, ELEUSIS, AND THE SOMA CUBE
For 25 of his 90 years, Martin Gard-
ner wrote “Mathematical Games and
Recreations,” a monthly column for
Scientific American magazine. These
columns have inspired hundreds of
thousands of readers to delve more
deeply into the large world of math-
ematics. He has also made signifi-
cant contributions to magic, philos-
ophy, debunking pseudoscience, and
children’s literature. He has produced
more than 60 books, including many
best sellers, most of which are still
in print. His Annotated Alice has sold
morethanamillioncopies.Hecontinuestowritearegularcolumnfor
the Skeptical Inquirer magazine. (The photograph is of the author in
1959.)
THE NEW MARTIN GARDNER MATHEMATICAL LIBRARY
EditorialBoard
DonaldJ.Albers, MenloCollege
GeraldL.Alexanderson, SantaClaraUniversity
JohnH.Conway,F.R.S., PrincetonUniversity
RichardK.Guy, UniversityofCalgary
HaroldR.Jacobs
DonaldE.Knuth, StanfordUniversity
PeterL.Renz
From 1957 through 1986 Martin Gardner wrote the “Mathematical
Games” columns for Scientific American that are the basis for these
books. Scientific American editor Dennis Flanagan noted that this
columncontributedsubstantiallytothesuccessofthemagazine.The
exchanges between Martin Gardner and his readers gave life to these
columnsandbooks.Theseexchangeshavecontinuedandtheimpact
ofthecolumnsandbookshasgrown.TheseneweditionsgiveMartin
Gardnerthechancetobringreadersuptodateonnewertwistsonold
puzzles and games, on new explanations and proofs, and on links to
recent developments and discoveries. Illustrations have been added
andexistingonesimproved,andthebibliographieshavebeengreatly
expandedthroughout.
1. Hexaflexagons,ProbabilityParadoxes,andtheTowerofHanoi:
MartinGardner’sFirstBookofMathematicalPuzzlesandGames
2. Origami,Eleusis,andtheSomaCube:MartinGardner’s
MathematicalDiversions
3. SpherePacking,LewisCarroll,andReversi:MartinGardner’sNew
MathematicalDiversions
4. KnotsandBorromeanRings,Rep-Tiles,andEightQueens:Martin
Gardner’sUnexpectedHanging
5. KleinBottles,Op-Art,andSliding-BlockPuzzles:MoreofMartin
Gardner’sMathematicalGames
6. Sprouts,Hypercubes,andSuperellipses:MartinGardner’s
MathematicalCarnival
7. NothingandEverything,Polyominoes,andGameTheory:Martin
Gardner’sMathematicalMagicShow
8. RandomWalks,Hyperspheres,andPalindromes:MartinGardner’s
MathematicalCircus
9. Words,Numbers,andCombinatorics:MartinGardnerontheTrail
ofDr.Matrix
10. Wheels,Life,andKnottedMolecules:MartinGardner’s
MathematicalAmusements
11. KnottedDoughnuts,Napier’sBones,andGrayCodes:Martin
Gardner’sMathematicalEntertainments
12. Tangrams,Tilings,andTimeTravel:MartinGardner’s
MathematicalBewilderments
13. PenroseTiles,TrapdoorCiphers,andtheOulipo:MartinGardner’s
MathematicalTour
14. FractalMusic,Hypercards,andChaitin’sOmega:MartinGardner’s
MathematicalRecreations
15. TheLastRecreations:Hydras,Eggs,andOtherMathematical
Mystifications:MartinGardner’sLastMathematicalRecreations
Origami, Eleusis, and the
Soma Cube
MARTIN GARDNER’S MATHEMATICAL
DIVERSIONS
Martin Gardner
®
TheMathematicalAssociationofAmerica
cambridgeuniversitypress
Cambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,Sa˜oPaulo,Delhi
CambridgeUniversityPress
32AvenueoftheAmericas,NewYork,NY10013-2473,USA
www.cambridge.org
Informationonthistitle:www.cambridge.org/9780521735247
(cid:1)c MathematicalAssociationofAmerica2008
Thispublicationisincopyright.Subjecttostatutoryexception
andtotheprovisionsofrelevantcollectivelicensingagreements,
noreproductionofanypartmaytakeplacewithout
thewrittenpermissionofCambridgeUniversityPress.
Firstpublished2008
FirsteditionpublishedasThe2ndSCIENTIFICAMERICANBookofMathematical
Puzzles&Diversions,SimonandSchuster,1961
PrintedintheUnitedStatesofAmerica
AcatalogrecordforthispublicationisavailablefromtheBritishLibrary.
LibraryofCongressCataloginginPublicationData
Gardner,Martin,1914–
Origami,Eleusis,andtheSomacube:MartinGardner’smathematical
diversions/MartinGardner.
p. cm.–(ThenewMartinGardnermathematicallibrary)
Includesbibliographicalreferencesandindex.
ISBN978-0-521-75610-5(hardback)
1.Mathematicalrecreations. I.Title. II.Series.
QA95.G2975 2008
793.74–dc22 2008012534
ISBN 978-0-521-75610-5hardback
ISBN 978-0-521-73524-7paperback
CambridgeUniversityPresshasnoresponsibilityfor
thepersistenceoraccuracyofURLsforexternalor
third-partyInternetWebsitesreferredtointhispublication
anddoesnotguaranteethatanycontentonsuch
Websitesis,orwillremain,accurateorappropriate.
Contents
Acknowledgments pageviii
Introduction ix
1 TheFivePlatonicSolids 1
2 Tetraflexagons 11
3 HenryErnestDudeney:England’sGreatestPuzzlist 20
4 DigitalRoots 32
5 NineProblems 39
6 TheSomaCube 51
7 RecreationalTopology 66
8 Phi:TheGoldenRatio 76
9 TheMonkeyandtheCoconuts 91
10 Mazes 98
11 RecreationalLogic 106
12 MagicSquares 117
13 JamesHughRileyShows,Inc. 129
14 NineMoreProblems 139
15 Eleusis:TheInductionGame 151
16 Origami 160
17 SquaringtheSquare 173
18 MechanicalPuzzles 194
19 ProbabilityandAmbiguity 204
20 TheMysteriousDr.Matrix 218
Index 229
vii
Acknowledgments
Martin Gardner thanks Scientific American for allowing reuse of
material from his columns in that magazine, material copyright
(cid:1)c 1958(Chapters1–7,9,17),1959(Chapters8,10–16,18,19),and
1960 (Chapter 20) by Scientific American, Inc. He also thanks the
artistswhocontributedtothesuccessofthesecolumnsandbooks
forallowingreuseoftheirwork:JamesD.Egelson(viaheirsJanand
NicholasEgelson),IrvingGeis(viaheirSandyGeis),HaroldJacobs,
AmyKasai,AlexSemenoick,andBunjiTagawa(viaDonaldGarber
for the Tagawa Estate). Artists’ names are cited where these were
known. All rights other than use in connection with these materi-
alsliewiththeoriginalartists.
PhotographofBernardinoLuini,“BoywithaToy,”EltonHallCol-
lectionisreproducedfrom“Gibeciere”vol.1,no.1andusedbyper-
mission. Photograph in Figure 51, courtesy of National Gallery of
Art,copyrighttheSalvadorDaliestate,isusedbypermission.Pho-
tograph of Albrecht Durer’s Melancolia I is courtesy of Owen Gin-
gerich.PhotographinfigureYiscourtesyofEdVogel.
viii
