资源描述：
《0195144368.Oxford.University.Press.USA.A.Smoother.Pebble.Mathematical.Explorations.Oct.2003》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、ASmootherPebbleThispageintentionallyleftblankASmootherPebbleMathematicalExplorationsDONALDC.BENSONOXFORDUNIVERSITYPRESS2003OXPORDUNIVERSITYPRESSOxfordNewYorkAucklandBangkokBuenosAiresCapeTownChennaiDaresSalaamDelhiHongKongIstanbulKarachiKolkataKualaLumpurMadridMelbourneM
2、exicoCityMumbaiNairobiSaoPauloShanghaiTaipeiTokyoTorontoCopyright©2003byOxfordUniversityPress,Inc.PublishedbyOxfordUniversityPress,Inc.198MadisonAvenue,NewYork,NewYork10016www.oup.comOxfordisaregisteredtrademarkofOxfordUniversityPressAllrightsreserved.Nopartofthispublica
3、tionmaybereproduced,storedinaretrievalsystem,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,recording,orotherwise,withoutthepriorpermissionofOxfordUniversityPress.LibraryofCongressCataloging-in-PublicationDataBenson,DonaldC.Asmootherpebble:mathema
4、ticalexplorations/DonaldC.Benson.p.cm.Includesbibliographicalreferencesandindex.ISBN0-19-514436-81.Mathematics—History—Popularworks.I.Title.QA21.B462003510—dc21200204251598765432PrintedintheUnitedStatesofAmericaonacid-freepaperAcknowledgmentsFirst,Iwouldliketothankmywife
5、,Dorothy,forreadingtheentiremanu-scriptmanytimesandmakingmanyvaluablesuggestions.ThankstoNedBlackandDonaldChakerianforreadingpartsofthemanuscriptandmakingvaluablecomments.IwouldalsoliketoacknowledgetheassistanceandencouragementofKirkJensenatOxfordUniversityPress.Thisbook
6、wastypesetbytheauthorusingWtjiX..ManythankstotheauthorsoftheETgXpackagesusedhereandallwhohavecontributedtoCTAN,theComprehensiveTgXArchiveNetwork.ThelinedrawingsweredonebytheauthorusingMetaPostandGnu-Plot.ThispageintentionallyleftblankContentsIntroduction1IBridgingtheGap1
7、AncientFractions5TheEgyptianUnitFractions6Egyptianarithmetic8Thegreedyalgorithm13TheBabyloniansandtheSexagesimalSystem15Sexagesimalfractions162GreekGifts18TheHeresy20Magnitudes,Ratio,andProportion22Method1—proportionaccordingtoEudoxus24Method2—AttributedtoTheaetetus263Th
8、eMusicoftheRatios33Acoustics35Therotatingcircle36Waveformsandspectra39Psychoacoustics44Consonanceversus
