From zero to infinity: what makes numbers interesting ; fiftieth anniversary edition

210 Pages·2006·1.88 MB·English

by  Reid

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Whatmathematiciansandteacherswriteabout
FROMZEROTOINFINITY
“I read From Zero to Infinity when I was a schoolboy in Oxford,
England,andmyonlyregretisthatIwaswellintomyteens(17)
before it happened. Just last week I gave away my most recent
copytothe12-year-olddaughterofafriend. Iwillbegettingan-
othercopyformyselfassoonasIcan.”
—JohnB.Cosgrave,St.Patrick’sCollege,Dublin,Ireland
“AfterreadingFromZerotoInfinity,Iwashooked. Thisbookdis-
cussedmanybeautifulideasandfactsabouttheintegersandposed
severalinterestingproblems. Itriedtosolvethem. Ifailed. Itried
to construct counter examples. I made my own conjectures and
proved some related results. By the time I graduated from high
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sults,andcalculations.”
—NathanielDean,MathematicsDepartment,
BellCommunicationsResearch
“Constance Reid’s book From Zero to Infinity was translated into
Japanese, and I found it when I was a junior high school boy. I
wasreallyimpressedbyReid’sbook,andIreaditrepeatedly. In-
spiredbyit, IeventriedtosolveFermat’sLastTheorem. NowI
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sonsformychoiceisasentenceinReid’sbook:‘Analyticnumber
theoryissaidtobetechnicallythemostdifficultinthewholeof
mathematics.’”
—KohjiMatsumoto,studentatNagoyaUniversity
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“Yesterday,aboardaflightfromDenver,Ihadaniceconversation
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FromZerotoInfinity.Thereviewpromptedhimtobuyyourbook.
And your book inspired him to switch from teaching history to
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—Letterfromafriendwithappendednote
fromJohnMoulter:“Thankyou.Thankyou.”
“I was the sort of child who always carried a book wherever he
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ZerotoInfinity.Iwasindeedborntobeamathematician,butFrom
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—BruceReznick,UniversityofIllinoisUrbana
“Iwanttothankyouforhavingwrittensuchawonderfulbook.It
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—HughWilliams,UniversityofCalgary,Canada,
authorofEdouardLucasandPrimalityTesting
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· ·
FROM ZERO TO INFINITY
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· ·
FIFTIETH ANNIVERSARY EDITION
From Zero to Infinity
What Makes Numbers Interesting
Constance Reid
AKPeters,Ltd.
Wellesley,Massachusetts
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Editorial,Sales,andCustomerServiceOffice
AKPeters,Ltd.
888WorcesterStreet,Suite230
Wellesley,MA02482
www.akpeters.com
Copyright(cid:1)c2006byAKPeters,Ltd.
Allrightsreserved. Nopartofthematerialprotectedbythiscopyright
noticemaybereproducedorutilizedinanyform,electronicormechani-
cal,includingphotocopying,recording,orbyanyinformationstorageand
retrievalsystem,withoutwrittenpermissionfromthecopyrightowner.
Firstpublishedin1955byThomasY.CrowellCo.
Secondedition,1960byThomasY.CrowellCo.
Thirdedition,1964byThomasY.CrowellCo.
Fourthedition,1992byTheMathematicalAssociationofAmerica.
Fifthedition,2006
LibraryofCongressCataloging-in-PublicationData
Reid,Constance.
Fromzerotoinfinity:whatmakesnumbersinteresting/
ConstanceReid.–5thed.
p.cm.
ISBN-13:978-1-56881-273-1(alk.paper)
ISBN-10:1-56881-273-6(alk.paper)
1.Numerals.2.Numbertheory.I.Title.
QA93.R422006.
510--dc22 2005027860
PrintedintheUnitedStatesofAmerica
1009080706 10987654321
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· ·
I N M E M O R Y O F
JuliaBowmanRobinson
1919–1985
and
Raphael MitchelRobinson
1911–1995
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· ·
CONTENTS
ACKNOWLEDGMENTS xi
AUTHOR’S NOTE xiii
0 ZERO 1
Onlyaplace-holderuntilfinallyrecognized
asfirstofthenaturalnumbers.
1 ONE 15
Anumberthatmakesmathematicsdifferent
fromalltheothersciences.
2 TWO 27
Aprimitivenumbersystemcomesintoitsown
withtheelectroniccomputer.
3 THREE 39
Firstamongtheoddnumbersdivisibleonlyby
themselvesandone.
4 FOUR 53
Numbersmultipliedbythemselvesprovide
beautifullydifficulttheorems.
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