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ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Archimedes of Syracuse: Solving Problems and Applied Mathematics WasedaUniversity,SILS, HistoryofMathematics ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics DomenicoFetti,“Archimedes,"1620. ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Outline Introduction Archimedes’Works Measurementofthecircle ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction Ancient cultures around the Mediterranean ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction Ancient Italy and Sicily, around 200 bce ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction What we know about Archimedes (c. 287-212) ▶ Hehimselftellsus,invariouswritings,thathisfatherwas anastronomerandoneofhisshortworksisaddressedto theyoungprinceofSyracuse(nowinSicily). Heis reportedtoberelatedtokingHieroII(ofSyracuse). ▶ HeapparentlylivedandworkedinSyracuseand correspondedwithothermathematicians,mostlyin Alexandria. ▶ Anumberofhismechanicalwritingsarepreservedin DoricGreek,thedialectofancientSicily. ▶ ThereareanumberofreportsthatArchimedeswaskilled, inhis70s,whentheRomansconqueredSyracuse,212bce. ▶ Therearemanylegendsabouthim,butitisdifficulttosift thetruthfromthefantasy. ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction The legend of Archimedes, 1 ▶ Alreadyinantiquity,Archimedeswasseenasthe iconographicimageofthebrilliantscientist(likeanancient Einstein). ▶ Archimedesissaidtohavebeenagiftedengineeraswell asamathematician,however,fewofhismechanicalworks survive. ▶ Heisreportedtohaveinventedaplanetariumthatcould model,orpredict,thepositionsofthesun,moonand planets. ▶ Thereisthefamousstoryofhimdiscoveringtheprinciple ofdensity(specificweight)whiletakingabath(“Eureka!"). ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction The legend of Archimedes, 2 ▶ Themostfamouslegendscirculatearoundhisdeath. ▶ WhentheRomansbesiegedSyracuse,theyaresaidtohave beenheldoffformonthsbythevariouswarmachines inventedbyArchimedes,suchasa“claw"(forcapsizing ships)anda"burningmirror"(forignitingships). ▶ AlthoughtheRomangeneralMarcellusgaveordersthat Archimedeswastobecapturedalive,hewassomehow killedwhenthecitywassacked... ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction The sources for his writings ▶ AfairnumberofhiswritingssurviveinearlymodernGreek copies(14th-15thcenturyce). ▶ Allofthecompletemedievalcopiesofhisworkshavebeen lost. ▶ But,thereisonemedievalmanuscriptofhiswritingsina palimpsest,knownasthe“ArchimedesPalimpsest."1 ▶ Therearealsohighlyliteraltranslationsofhisworksmade fromGreekintoLatinbyWilliamofMoerbeke(c. 1215–1286). 1Apalimpsestisatextmadebycleaningandreusinganoldertext. ArchimedesofSyracuse:SolvingProblemsandAppliedMathematics Introduction The Archimedes Palimpsest ▶ In1906,theDanishphilologistJohanLudvigHeiberg discoveredatextofArchimedesinamedievalpalimpsest inConstantinople(nowIstanbul). ▶ Thiswasthen“lost"duringWWI. ▶ In1998,itwassoldtoananonymousbuyerfor$2million USD,atChirstie’sAuctionHouse,London. ▶ ItisnowheldattheWaltersArtMuseuminBaltimoreand hasbeenstudiedbyscholars. ▶ Itcontains(amongothers)thefollowingtextsby Archimedes: EquilibriumofPlanes,SpiralLines,Measurement ofaCircle,OntheSphereandCylinder,OnFloatingBodies (onlycopyinGreek),Stomachion(onlycopy),TheMethodof MechanicalTheorems(onlycopy).

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Archimedes of Syracuse: Solving Problems and Applied Mathematics Introduction What we know about Archimedes (c. 287-212) He himself tells us, in various writings

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Archimedes of Syracuse: Solving Problems and Applied Mathematics Introduction What we know about Archimedes (c. 287-212) He himself tells us, in various writings

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