Archimedes of Syracuse: Solving Problems and Applied Mathematics

17 Pages·2015·2.32 MB·English

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).