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ArchimedesResearchPaper

ArchimedeswasborninSyracuse,Italyin287BCtoamathematician/astronomerinSicily.Some believethathisfamilybelongedtothenobleclassofItalywhilesomebelievethattheyarerelatedto KingHieroIIofSyracuse;however,thereislittleinformationabouttheearlylifeofthefamous mathematicianArchimedes.Archimedes'lifeandresearchintothefieldofmathematicsgavethe worldmanyprincipalsthatarestillinpopularusetodayandareacceptedascorrectapplicationsof mathandequationstosolveforbothcomplexandeverydayproblems.LivinginSyracuse,oneof theculturalhubsoftheworldduringthattime,Archimedesgrewcuriousofsolvingproblemsand learningasmuchaspossibleintheculture,arts,andsciencesHowever,evenlivinginashow morecontent...

Hewantedtocalculatethisinordertochallengehimselfsincehehadalreadymasteredtheother aspectsofmathematicsthatwereknownduringthattimeHeusedprinciplesfoundin"integral calculusthatwouldnotbefoundedforanother1800years(FamousScientists)".Archimedesbegan thiscalculationbyimaginingaspheredissectedinto"twohemisphereswhichwouldbeplacedona flatsurface,thenenclosedbyacylinder.Nextheimaginedmakingtwoverticalslicesdownthe sidesofthecylinderandmultipliedthenumberofblueringsfromthecylinderbytheirdepthtofind thevolume(FamousScientists)"IfArchimedeshadconsideredaninfinitenumberofbluerings,he wouldhaveinventedintegralcalculus1800yearsbeforeIsaacNewton.Usingtheinformationthat heknewalreadyaboutthevolumeofacylinderandhisnewknowledgeoftherelativitybetweena cylinderandasphere,hewasabletocomeupwithaformulatosolvethevolumeofasphere.He believedthiswashisgreatestachievementtosuchanextentthathe"requestedaspherewitha cylinderplacedonhistombstone(Famous

ArchimedesResearchPaper

ArchimedesofSyracuseisnotonlyknownforhisworkasamathematician,buthewasalsoknown forallhisinventions.However,Archimedesisknownasoneofmostsignificantmathematiciansof alltimes.Heisresponsiblefornineextanttreatises.OneofthemajorinventionsbyArchimedesare theIntegralCalculus,Exponentsandanaccurateapproximationofpi.Asoftoday,theinventions donebyArchimedeshavechangedandevolvedthebasisofmathematicsAlthoughmanypeople knowArchimedestobeanengineer,inreality,Archimedeswasoneofthegreatestmathematician ofalltimes.Heinventedoneofthegreatestchangesinmathematics,integralcalculus.Integral calculusisamathematicaltheorythatinvolvessubjectsuch

Honordefinition:1.Highrespect;esteem.2.aprivilege.Honoristocarryontradition;torespect peopleandtheirboundaries,tocontributeorgive.Honorisnotaspoeticasitseemsitcouldbe losingacouplehundredlivestosavethousandsormillions.Archimedeswasamathematician, physicist,engineer,inventorandanastronomerbutoverallhecontributedextremelyimportant informationtothescientificcommunityHeinventedthewaterraising"Archimedesscrew"healso helpedimprovesimimodernwarfarebyinventingweaponsthatgaveadvantageoverenemies.The discoveriesthatArchimedesmadeinmyopinionweremorerecognizedafterhisdeath.Hediedin 212BCwhenhewasunawareofromansstormingthecityhecalledhomeHeshowmore content...

Hediedashisinventionsdefendedthecityhetookhomein.Peoplehavemanydifferentperceptions ofhonor;honoristogiveyourselfforothers.Archimedesgavehisliveandintelligencetothe pursuitofknowledge.Afterhisdeathhisworkcontinuestoeducateandinspirepeople.His discoveriesinwarfarehelpedtodefendhiscountryandfurtherweaponmakingHecreatedasystem ofmirrorsthatwouldlightenemyshipsablazewithafocusedpointoflight.Healsocreatedasteam cannon,itwouldfireclayprojectilesfilledwithincendiarypropelledbyrapidlyheatedwatervapor. Thearchimedesclawwasanotherweaponhecreated;itworkedlikeacranethatwouldfireropes withgrapplinghooklikefeaturesontheendofthemtogripthebowofshipsofshipstosinkthem. ArchimedesishonorablebecausesciencewashislifeHepouredhimselfintohisworkandwas passionateaboutiteveniftheworldaroundhimdeemedhimcrazy.Hepursuedhisgoalevenwith theprobabilityofimpossibility.Hisperseverancemakeshimhonorable.Likesoldierswhowatch bulletsflyaroundthemtheyperseverejustasarchimedessawpeoplewhodisapprovedhisideasand thethingshedidyethe

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WhyWasArchimedesImportant

Archimedes,consideredonofthegreatestmindsoftheancientworldwasbornontheislandof SicilyintheGreekcityofSyracuseintheyear287B.C..Syracuseatthetimewasanindependent Greekcity–statewitha500–yearhistory.HewasthesonofPhidiaswhowasaGreekAstronomer andMathematician.AllthatweknowaboutArchimedescomesfromhisexistingmanuscripts,and fromancienthistorianssuchasPlutarchandCiceroamongotherscenturiesafterhisdeath ConsideringthelengthoftimebetweenArchimedesdeathandthehistorians'accounts,alongwith thenonuniformityoftheirwritings,somedetailsofhislifehavetobesubjecttoquestion.For example,PlutarchhasbeenstatedsayingthatArchimedeswasrelatedtoshowmorecontent HecorrectlydeterminedthatthevalueofPiissomewherebetween3.1408and3.1428.Alongthe sameplanehedeterminedthatacircle'sareacouldbedeterminedbyusingtheformulaPI(r^2). InthebookOntheSphereandCylinderArchimedesdealtwiththetopicofsolidgeometrycontains severalfamousdiscoveries,includinghistheorythatthevolumeofasphereisequalto4/3Pi(r^3).

Healsoshowedinhisworkthataslongasthecylinder'sheightandwidthisequaltothesphere's diameter,andthevolumeofthespherewillbe2/3thevolumeofthecylindersurroundingit.Hewas soproudofthisdiscoverythathehadthesymboletchedintohistombstone.

QuadratureofaParaboladiscussesarefinedversionofthemethodofexhaustionwhichwas originallydevelopedbytheEgyptians.Archimedesdevelopedthetechniquefordeterminingthe areaunderacurve,whichiselaboratedaboutinalatervolume,TheMethodInthebookThe MethoditshowsthatArchimedeshastheorizedthedevelopmentofintegralcalculusbytwo thousandyears.OftheseveralessaysthatArchimedeshaswrittenTheSandReckoningistheonly onethatremainsTheessayproposedtheproblemofdeterminingthenumberofgrainsofsandin theuniverse,containingaspecialnotationforestimatingandexpressingverylargenumbers.The numericalsystemheusesisbasedonunitsof10,000,becauseinancientGreece10,000wasthe largestnumberthey

TheLifeOfArchimedesEssay

ThelifeofArchimedesimpactedmanypeopleofhistimebecausehisinventionsbroughtanew leveltoancientwarfare.Hewasalsowellknownforbeingamathematicianandforhisscientific writings,manyofwhichstillsurvivetoday

ArchimedeswasborninSyracuse,Sicily,andhelivedtobeseventy–fiveyearsold.Thisputsthe dateofhisbirtharound287B.C.,andthedateofhisdeatharound362B.C.Hisfatherwasan astronomer,andhemayhavebeenrelatedtoHieroII,kingofSyracuse("Archimedes")Wedonot knowmuchabouthischildhood,butwedoknowthathestudiedwithEuclidinAlexandria,Egypt. Afterhisstudies,hereturnedtoSyracuseandmadethemanyinventionsthatstillimpactustoday ("ArchimedesBiography").showmorecontent

WhenwritingaboutArchimedes'invention,DiodorusSiculus,aGreekhistorian,saidthatthe Archimedesscrewcouldtakeinwater"withatriflingamountoflabor"(qtdinGow78)The Archimedesscrewisstillinusetoday,butisnowmadeofmetalandisoperatedbymorepowerful machines("ModernUsesoftheArchimedes'ScrewPump").OneofArchimedes'mostinteresting inventionswastheheatray,commonlyknownasthe"deathray"Itwasusedinwartodefend Syracuse.Theheatrayconsistedofmanypolishedbronzemirrorsfocusedonanenemyshipinthe harborThesun'srayswouldreflectfromthemirrorstotheship,promptlycausingittoburstinto flames("DidArchimedes'SolarPoweredDeathRayExist?").

Althoughtheheatrayseemslikeagoodidea,thereisstillcontroversyaboutwhetherornottheheat raywouldhaveworked,orevenexistedFortheheatraytowork,theenemyshipwouldhavehadto bestillenoughthatthemirrorswouldbeabletofocusononeconcentratedspace,andthesunwould havehadtobeout("File:ArchimedesHeatRayconceptualdiagram").Archimedesalsowouldhave onlyhadaccesstomaterialsofhistimeperiod,sothemirrorswouldhavemostlikelybeenmadeof bronze("Archimedes").

ArchimedeslefthislegacythroughhisscientificwritingsInabout1200AD,theArchimedes PalimpsestwasfoundbyChristian ...Getmorecontent...

Archimedes'Principle

Archimedes'PrincipleAbstractThepurposeofthisexperimentwastoinvestigatetheArchimedes' Principleforobjectsofdifferentdensitiesandusetheprincipletodeterminethedensityofagolf ball.Theweightofrubberstopperandthewoodcubeweremeasuredintheairbyusingtheforce sensor.Whentheobjectsweresubmergedinthewater,theapparentweightoftheobjectswas measurewiththeforcesensorandthevolumeofthedisplacedwaterweremeasurewithagraduated cylinder.Thesesameprocedurewasusedtoobtainweightandapparentweightofthegolfball.The weightofthedisplacedwaterwhentherubberstopperwassubmergedwas1.94N.Buoyantforce obtainedwas196Nand214Nwithapercentdiscrepancyofshowmorecontent

TheArchimedes'principlestatesthatanyobjectsubmergedinafluid,isbuoyedupbyaforceequal totheweightofthefluiddisplacedbytheobject.Consideringthisprinciple,anobjectfloatsorsinks inwaterisbasedontheamountofwateritdisplacesandnotontheobject'sweight.Accordingtothe Archimedes'Principle,theweightofthewaterdisplacedisdirectlyproportionaltothebuoyantforce thatactontheobjectsubmergedinwhichthisconceptwasseenwhentwodifferentobjectwere submergedwater.Theweightofthedisplacedwaterwhentherubberstopperwassubmergedwas 1.94N.Inthissituationtherubberstopperwasdenserthanwater.Twoequationswereusedto calculatebuoyantforce.Whenusingthevolumeofwaterdisplacedbytheobjectthebuoyantforce obtainedwas1.96Nwithapercentdiscrepancyof0.97%.Thebuoyantforceusingtheapparent weightandweightoftheobjectonairwas214Nwithapercentdiscrepancyof930%Thispercent discrepancywasslightlyhighwhichmightbeduetofactorssuchasair.Thepercentdiscrepancies arewithinthe

ArchimedesLifeAndAccomplishments

Archimedeswasoneofthegreatestinventorsandmathematiciansinhistory.Helivedinancient GreeceduringthethirdcenturyB.C.Heenjoyedphysics,engineering,andmechanics.Attimes Archimedeswouldbesofocusedonhiswork,hewouldabsolutelyforgettoeatandsleep. Archimedeswasborn287B.C.inSyracuse,Sicily.Hisfather,Phidias,wasanintelligent astronomerThereforeArchimedesgrewupinahomethatwascenteredaroundscienceandmath Likeallotherboysofhistime,Archimedeswenttoschoolwhenhewaseight.Helearnedreading, writing,religion,andhistory.Hewasalsorequiredtomemorizeandrecitepoetry.Attheageof fourteenArchimedesjourneyedtoAlexandria,thecapitolofEgypt,tostudyArchimedes

Archimedes,anamecommonlyassociatedwiththebeginningofscience,wasanengineerandone ofthegreatestmathematiciansinhistory.Hisimpactonmodernsciencerestsonhisuseof experimentandinventiontotestideasandhisusemathematicstodescribethebasicprinciplesof physicalphenomena.

KnowledgeofthelivesofancientphilosopherslikeArchimedesisnotprevalent.Weknowfromhis writingsthathegrewupandspentmuchofhislifeinSyracuse,aSicilianportontheIonianSea. Hislifespanned(approximately)theyears287BCto212BCHisfatherwastheastronomer Phidiasandhealsomentionedhisfriendandpossiblykinsman,KingHieronII(rulerofSicilyfrom about270B.C.).Accordingtootherauthors,showmorecontent

TherearenineknownworksofArchimedesinexistence.Thelastwasdiscoveredina10thcentury manuscriptin1906.

OntheSphereandCylinder

Thoughttobehisfirstbook,thisworkshowsthatthesurfaceareaofasphereisfourtimesthatofa greatcircle(alineofshortestdistanceonasphere).Hefindsawaytocalculatetheareaofany segmentofasphereThisbookalsodiscussingoneofhismoreimportantdiscoveries:thatthe volumeofasphereistwo–thirdsthevolumeofacircumscribedcylinder,andthatthesurfaceofthe sphereistwo–thirdsthesurfaceofthecylinder.Thesetopicsbroughthimclosetoinventingcalculus andwereveryusefultoNewtonandLeibnizintheseventeenthcentury

OntheMeasurementoftheCircle

InthisworkArchimedesmadediscoveriesregardingthevalueofpi.SeeArchimedes'Constant.

OntheEquilibriumofPlanes

InthistreatiseArchimedesdiscussesfundamentalprinciplesofmathematicsusinggeometric properties.Hediscoveredimportanttheoremsregardingthecenter

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EssayonArchimedes

TheExperiment:Archimedes'PrincipleEssay

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Archimedes'Principle

Abstract

Theprimaryaimofthislabistoinvestigatethebuoyantforceandconditionsnecessaryforanobject tofloat.First,themassandweightofvariousmaterials,i.e.acylinder,ablock,andanirregular shapewerenotedSubsequently,anexperimentwascarriedouttoobtaintherelevantdataThedata collectedwaspresentedintabularformandlaterusedtogenerateaninformedanalysis.Most importantly,relevanttheoremsandequationswereappliedtocalculatethedensityandspecific gravityofthematerials.Althoughtheprimaryobjectivesofthelabweremet,thedataanalysis proveddifficultduetosomeerrorsencounteredduringtheexperiment.

Introduction

Archimedes'principlestatesthatanobjectisbuoyeduporexperiencesaforce(buoyedup)thatis equaltotheweightofthefluiddisplacedbytheobjectwhenpartiallyorwhollyimmersedinafluid. Ineffect,itbecomespossibletocalculatethebuoyancyoftheseobjectsPractically,weightisthe downwardforcethatactsonanobject.Ontheotherhand,thebuoyantorupwardforceactingonan objectiswhatisdefinedinArchimedes'principle.Typically,thedifferencebetweentheweightand buoyantforcegivesthenetupwardforceontheobject.Anetpositiveforcemakestheobjecttorise whileanet

ArchimedesAccomplishments

Theyearis287B.C.E,AlexandertheGreatHasbeendeadforfiftyyearsandthekingdomheleftto hisgeneralshasbeguntofracture.Around300B.C.EthePunicWarsbegan,throwingGreeceinto disarray.TheHellenisticAgeiscomingtoaclose.However,atleastonegoodthingcameofthis year.Oneofthegreatestengineersinhistoryisborn.HisnameisArchimedesandhewillchange theworldArchimedeslife,achievements,andeffectonthemodernworldofengineeringmakehim oneofthemostprominentandimportantfiguresintheancientworld.Unfortunatelylittleisknown aboutthelifeofArchimedes.In287B.C.EhewasborninSyracuse.Hisfatherwasanastronomer namedPheidiasandasamanhetraveledtoAlexandriatostudyshowmorecontent

TheLawoftheLeverisoneofArchimedesmoreprestigiousdiscoveries.Whenhemadehis discoverythefulcrumwasalreadyinuse.HoweverArchimedeswasthefirsttodiscoverthata longerlevermadeliftingeasier.StoryssaythatArchimedesoncesaid,"Givemealeverandaplace tostand,andIwillmovetheworld."AnotherextremelyimportantinnovationbyArchimedeswas thepulleyHecreatedacomplexsystemofpulleysthatallowedhimtoliftalmostanythingAnother storysaysthatateamofmen,aftergreateffortdraggedatriremeontothebeach.Themenall boardedtheshipalongwiththeiranimalsandArchimedeswasabletolifttheshipandmoveit easilybyhimself.TheArchimedesScrewwasanotherimpressiveinventionbyArchimedes.The screwismassiveandcapableofliftingwaterfromtheground.Itisstillusedtodayinsomethird–worldcountriesOtherinventionsbyArchimedesincluded,theconceptofbuoyancyHeprovedthat, whenbuildingboats,thematerialdoesnotmattersomuchashowspreadoutitis.Archimedeswas alsothefirstpersontoaccuratelyestimatethevalueofpi.TheseareonlyafewofArchimedesmost prestigiousachievementsAspreviouslystated,manyoftheworksofArchimedeshavebeenlost, howeverimaginewhatotherincrediblefeatsofengineeringthismanmayhave

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ArchimedesResearchPaper

Istherepurposeinmathematics?Archimedes'liferevolvedaroundmathematics.Archimedeswasa famousmathematicianandinventor.HewasborninSyracuse,Italyandlivedfrom287BCto212 BC.Archimedesismostknownforhisfamilyandculture,scientificinventionsandhowhechanged theworldwithhisinnovations.FamilyandculturewerehugemotivatorsforArchimedes. Archimedes'father,Phidias,whowasanastronomer,hadamassiveimpactonhisson'slifeHigh standardswerealwaysexpected.ArchimedeswasfortunatelybornintotheGreekscientificculture. Originally,helivedinSyracuseformostofhislife,butthenbranchedouthiseducationin Alexandria,EgyptSinceArchimedeswasraisedwithanastronomerashisfatherand

ArchimedesResearchPapers

GreekMathematicianBacktomanycenturiesago,thereweremanymathematicians;especially Greekmathematicians.Tilltoday,theyareimportantbecausetheyhavecausedasignificantimpact onhowweusemathandanyothersubjects.ArchimedeswasoneofthemanyancientGreek mathematiciansknownfromancienthistory,hewasconsideredthegreatestmathematicianof ancienttimesAsidefrombeingaGreekmathematician,Archimedeswasalsoaphysicist,inventor, engineer,andanastronomer.Oneofhismanyinventionswasthathehaddeterminedthevolumeof anobjectwithanirregularshape.ArchimedeswasborninthecityofSyracuse,fromtherehe traveledtoEgypttostudyinAlexandriaAfterhisstudiesinAlexandria,hereturnedtoSyracuseto pursuealifeofinventions.Uponhisarrival,ArchimedesstartedtoengagewithKingHiero,he wouldprovidesolutionstoproblemsthatdispleasetheking.KingHierowasuncertainofacrownhe hadorderedhisgoldsmithtomake,hehadthoughtsthatthegoldsmithhadreplacedsomeofthe goldthatwasgoingtobeusedtocreatethecrown,withsilver.HeaskedArchimedestodetermineif theshowmorecontent

Ashewastheonewhoaccomplishedtheformulaforacylinderandacircumscribedsphere.When hebegan,hestartedbycuttingfromtopofthecylinderofamathematicalsalamitothebottom.As henoticedthatthehemisphereissmallfromthefirstslice.Bythisobservationhecalculated,atfirst, thattheradiusissmall.Fromthefirsttopslice,hehadcutanotherslicealittlebitlowerthroughthe cylinderandhemisphere,thatslicewaslargerThecylinderstayedthesamesizewhilethe hemispherewasenlarging.Afterthatobservation,hethencutdownthecylinder.Assoonashehad allofthesalamipieceshethencalculatedtheareasoftheslicesandmultipliedthembytheirdepths tofindthevolumeThevolumewouldrepresenttheallofthesalamislicesput

ArchimedeswasaGreekmathematicianandscientist.HewasborninSyracuse,Sicilyintheyear 287B.C.HewaseducatedinAlexandria,Egypt.DuetothelackofinformationaboutGreek mathematics,manyGreekmathematiciansandtheirworksarehardlyknown.Archimedesisthe exception.Archimedeswasverypreoccupiedwithmathematics.Forinstance,heoftenforgottoeat andbathebecauseofhisalwayswantedtosolveproblems

Hefoundareasandvolumesofspheres,cylindersandplainshapes.Heshowedthatthevolumeofa sphereistwo–thirdsofthevolumeofthesmallestcylinderthatcancontainthesphereArchimedes wassoproudofthisconceptthatherequestedthatacylinderenclosedasphere,withanexplanation ofthisshowmorecontent

ThismachinewasbuiltforraisingwatertohighlandareasinEgyptthatcouldnotreceivewater directlyfromtheNileRiver.Thisdeviceisstillusedtodayforirrigationpurposesevenissome countriestoday

ThemostfamousstoryofArchimedeslifeinvolvesthediscoveryofArchimedes'Principle.The storybeginswhenKingHieronaskingagoldsmithtoconstructagoldwreathtotheimmortalgods. Aftersometime,thekingcametosuspectthatthewreathwasnotpuregoldbutratherfilledwith silverInordertoendhissuspicion,thekingaskedArchimedestodeterminewhetherthewreath waspuregoldorfilledwithgoldwithoutdestroyingit.Archimedesagreedtotrytosolvetheking's problem.Thenoneday,whilehewastakingabath,Archimedesnoticedthatthewaterlevelrosein thebathasheenteredthewaterArchimedeswassoexcitedbythisdiscoverythathejumpedoutof hisbathandrannakedthroughthestreetsyelling,"Eureka,Eureka!!"meaning,Ihavefound it.Archimedeshaddiscoveredthatabodyimmersedinafluiddisplacesitsweightoffluid.This principleinturnhelpedArchimedesprovethatthegoldwreathwasnotsolidgold.

Archimedeswasprobablymostfamousduringthetimehelivedbecausehedevelopedtechniques defensesforSyracuseagainsttheRomans.Syracusewasabletoholdofftheinvasionforthreeyears duetoArchimedes'sinventions.Heinventedcatapults,whichhurled

ArchimedesEssay

Istherepurposeinmath?Archimedesliferevolvedaroundmathematics.Archimedeswasafamous mathematicianandinventor.HewasborninSyracuse,Italy.Helivedfrom287BCto212BC. Archimedesismostknownforhisfamilyandculture,scientificinventionsandhowhechangedthe worldinmanyextraordinaryways.ThereisonethingthatmotivatedArchimedesandhiswork, whichwashisfamilyandcultureArchimedesfather,Phidias,whowasanastronomer,hada massiveimpactonArchimedeslife.ThestandardsweresethighforArchimedes.Originally, ArchimedeswasbornintotheGreekscientificculture.Although,helivedinSyracuseformostof hislife,hebranchedouthiseducationinAlexandria,EgyptDuringthe16thand17thcentury

HowDidArchimedesInfluenceHisWork

ArchimedesResearchPaper

ArchimedeswasborninSyracuseontheIslandofSicilyin287BC.Hisfather'snamewasPhidias andwasbelievedtobesomewhatrelatedtothekingofSyracuse,HeiroII.Archimedesisfamously knownasmultiplethingsincludingamathematician,inventor,engineer,andastronomer.Movingto Alexandriainhislaterlife,hestudiedataschoolestablishedbyEuclid.Afterwardshereturnedto Syracuse,spendingthemajorityofhislifesolvingmathematicalproblemsandmakingnew inventionsfortheking.In212BC,SyracusewasovertakenbyoneofArchimedesenemies.Whena soldiercametoArchimedesdemandingthathegowithhim,Archimedesrefused,sayingthathe neededtofirstfinishhismathematicalequationUponhearingthis,thesoldier

Inthecity–stateofSyracuse,SicilyaGreekmathematicianwhowouldsoonmakehistorywasborn: ArchimedesFromhisbirthtohisadulthood,heprovedjusthowmuchofadifferenceonemancould make.Throughtheuseofscienceandmathematics,Archimedeswasabletoleaveamajorimpacton ancientsociety.Duringhisyouth,Archimedeswasanambitiouslearner.Hisfather,Phidias,would makeArchimedessolvenumerousmathproblemsHesolvedmostofthemcorrectly,provingtohis fatherthathewasworthyofasolideducation(Zannos21).HestudiedinAlexandria,Egyptunder theguidanceofEuclid.Besidesmath,PhidiaswouldoftentakeArchimedesforwalksatnight.

Duringthosewalks,Archimedeswasintriguedbythestarsoftheshowmorecontent KingHeironhadjustreceivedhiscrownfromthegoldsmithandaskedArchimedestotestifitwas puregold.Usingthedensityofgoldandlawsofhydrostatics,Archimedesdeterminedthatitwasnot puregoldandthatsomeofithadinfactbeenreplacedbyacheapermetal.Thegoldsmithhad cheatedtheking(Hoffman32).WithoutArchimedes,thekingwouldhaveneverknownthetruth.In thefieldofMathematics,Archimedeswasabletomakethemostadvancesinthesubjectof Geometry.TohelppeoplehaveabettergriponwhatexactlyGeometrywas,Archimedeswrotea fewbooks.HisthreemostnotablenovelswereMeasurementofaCircle,OnSpirals,andOnthe SphereandCylinder.Inhisbooks,Archimedesdidn'tjusttellthereaderhowGeometryworked; instead,heexplainedhistheoremsthroughcarefulreasoning(Gow12).Archimedesmadetwomore theoreticaldiscoveriesaboutGeometryHediscoveredtherelationshipbetweenvolumesofspheres andcylinderswiththeequivalentradius.Notonlythat,buthealsofoundmoreaccurate measurementsofPi(Gow7).PeoplebelievethatArchimedesenjoyedtheoreticaldiscoveriesmuch moreoverpracticaldiscoveriesGeometrywasallabouttheoryHisloveandpassionforthesetypes offindingsallowedhimtodiscovermoreandmoreaboutGeometry.Archimedesdid

EssayonArchimedes

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TheLifeandWorkofArchimedes

Archimedeswasaveryintelligentandagreatman.Heisthoughtofasoneofthethreegreatest mathematiciansofalltime,alongwithNewtonandGauss.Inhistimehewasreferredtobysuch greataliasesas"Thewiseone","TheMaster",and"TheGreatGeometer"Andhisworkhasyetto havebeenforgotten.HewasindubitablywasoneofthelastofthegreatGreekmathematicalminds thatthisworldhaseverseen.IwillattempttoshowyouwhatthemerepresenceofArchimedesin ourhistoryhasmeanttomathematicsandeventhecolonyofSyracuseitselfWewouldnotbethe sameifitwasn'tforthemansimplyknownasArchimedes.

Lifeandfamilyshowmorecontent

Archimedesalsogaveanaccurateapproximationtopandshowedthathecouldapproximatesquare rootsaccuratelyHeinventedasystemforexpressinglargenumbersHeconsideredhismost significantaccomplishmentswerethoseconcerningacylindercircumscribingasphere,andtheratio betweenthembeing2:3.Hismostfamousthermogivestheweightofabodyimmersedinaliquid, surprisinglycalledArchimedes'principle.Hisworksthathavesurvivedinclude:Onplane equilibriums(twobooks),Quadratureoftheparabola,Onthesphereandcylinder(twobooks),On spirals,Onconoidsandspheroids,Onfloatingbodies(twobooks),Measurementofacircle,and TheSandreckoner.Hisdiscoverieswereverywellwelcomedamonghispeers,somuchthatmanya timespeoplewouldclaimhisaccomplishmentsastheirown,sothegeniusthatwasArchimedes, cameoutwithsomephonydiscoveriesandwhenitwasfoundoutthatthattheywerefalsethe copyingprettymuchstoppedfromthereon.Themainreasonwhyhisdiscoverieswereaccepted amonghispeoplewasbecausehehadalreadyinventedsomanymachinesthatwereusedfor defenseofSyracuse,thattheyprettymuchjustlistenedtowhateverhehadtosay.Hisimpacton mathematicswashuge,forcryingoutloudheinventedanentirefieldof

EssayaboutTheLifeandWorkofArchimedes

ArchimedesofSyracuse(278B.C.E.–212B.C.E.)

"TheimportanceoftheroleplayedbyArchimedesinthehistoryofsciencecanscarcelybe exaggerated.Hewasemulatedandadmiredinhisowndayandatsuccessiveperiodsinlatertimes" (Clagett,1).

DuringthetimeperiodbeforeArchimedes,Aristotlehadalreadyeffectivelydrawnalinebetween philosophyandmathematics.Afterhisdatephilosophyiscarriedonwithoutmathematical inspirationThereisanoutbreak,knownastheGoldenAgeofGreekmathematics,thatjusthappens tooccurinAlexandriaduringtheperiod300to200B.C.E..Thisperiodlastedonlyashorttime howeverbecausephilosophicfaithinmathematicsgraduallydisappeared.Philosopherswere moreshowmorecontent

Thepeopleofhisdayweremoreinterestedinpracticalpurposesratherthantheirphysicalor mathematicalimplicationsAstoldinabookconcerningGreekhistory"Archimedesemergedasa figurelargerthanlifeinthepopularimagination,legendaryfortheseemingmiraclesheperformed throughhismechanicalinventions"(Brunschwig,544).Asidefromthecreationoftheseweapons Archimedesachievedmanyadvancesinthevariousfieldsinwhichhewasinvolved.Oneexample ofthisisArchimedes'useofanexhaustionmethod,cuttingupshapesintoinfinitelysmallpiecesto discovertheirvolumesThismethodpavedthewayforwhatwenowcallintegralcalculus,which waslaterperfectedby16thand17thcenturyscientistssuchasKeplerandNewton(Grande,240). Manyofhisexploitsandachievementshavebeenpasseddownforgenerationsandoftentimesfind themselvesbeingretoldincolorfulandimaginativestories,someofwhicharenotentirelytruthful

WhenstudyingancientGreekmathematicians"theinformationavailableaboutthelivesofthose whowereengagedinitspursuitisoneoftheweakestpoints"(Dijksterhuis,9).Theperiodsinwhich theylivedandworkedare,forthemostpart,onlyeducatedestimations.ThestoryofArchimedes ...Getmorecontent...

ArchimedesofSyracuseEssay

Peoplehavebeenawareofobjectsfloatingonwaterorsinkingsincebeforerecordedhistory.Itwas notuntilArchimedesofSyracusecamealong,thatthetheoryofflotationandthebuoyancyprinciple weredefined.ArchimedeswasbornatSyracuseontheislandofSicilyin287BC.Hisfather, Phidias,isthoughttohavebeenanastronomerwhodiscoveredthesizeanddistancesofthesunand moonArchimedesmighthavebeenrelatedtoKingHieronthesecond,KingHierondefinitely favoredArchimedesashisfirstphilosopher.Asayoungboy,Archimedesdevelopedalife–long interestinthestudyoftheheavens.AsateenhetraveledtoEgyptwherehestudiedatthegreat LibraryofAlexandria,possiblyunderthefollowersofEuclidshowmorecontent It'ssaidthatArchimedeshaddiscoverybuoyancymuchearlierinhistory,butitwaslosttoagreat gustofwind.

Archimedesdiscoveriesaremany,withouthimthemoderndayworldwouldn'tbeasmathematical advanced.OnesuchdiscoverywashiscalculationofPi,forhismathematicalconstant¼represents theratioofacircle'scircumferencetoitsdiameterThewordPipronouncedas"pie"isthe lowercaseoftheGreekletterto"p"fromtheRomanalphabet.Archimedesusedgeometricformulas outlinedbyEuclid,tomakehiscomputingareasandvolumesbythemethodofexhaustion.His theorycametwo–thousandyearsbeforeitwassupposedlyinventedbySirIsaacNewtonandhe fellowGottfriedWilhelmvonLeibniz.Thatdiscoverywastheneardevelopmentoftoday'sCalculus usedinmathematics,physics,andengineeringtodayAnotherdiscoverywastherelationship betweenvolumeandsurfaceofasphereanditscircumferencecylinder.Hediscoveredthiswithtwo sphereswhichhebuilthimself,withsomefurthercalculationheprovedaformulathatisusedin today'sOntheSphereandtheCylinderAlso,thereisalegendthatArchimedesmadeadiscoveryof buoyancywhileinabathtub.Whenhewentforabath,hefoundhisprinciple(Archimedes Principal)whichstatesanobjectputintoafluidwillexperienceabuoyantforcethatisequalin magnitude

ArchimedesEssayexamples

Archimedesisonethemostfamousandancientscientistswhohelpedshapetheworldasitistoday. Hewasbornin287B.C.inSyracuse.Whilegrowingup,Archimedesbecameinterestedinproblem solvingandlaterwenttostudyattheRoyalLibraryofAlexandria.Heinventedthescrew,pi,and foundedtheprincipleofArchimedes.ManyofthethingsandaccomplishmentsofArchimedes helpedpeopleinthepastandcontinuetobethebasisofmanymoderntechnologicalthingstoday

OneofArchimedes'greatestaccomplishmentsisthescrewpumpwhichisusedeverywhere,incars andpumpsOneofthemostusesforthescrewpumpisformakingmoreadvancedscrewsAllofthe modernmadescrewsarebasedonArchimedes'screwpump.Anothergreataccomplishmentby Archimedesishisdiscoveryoftheabilitytomeasurecircles,findthecircumferenceofacircleand thenumberofPi.Weshowmorecontent

Peoplewhohavejobssuchasconstructionorengineeringarebeginningwithsomebasicpartsofhis inventions,andexpandingthemintonewbuildings,structures,orotheradvancementsCars,toys, pumps,andmodernscrewseachhavepartsthataresimilartothingsthatArchimedesinventedwhen hefirstmadediscoveries.Archimedes'inventionsmadetheworldabetterplace.Modernengineers wereabletocomeupwithnewwaystotravelsuchascars,bicycles,andairplanes.Inotherareas, Archimedes'discoveriessuchastheArchimedesprinciplemadeitpossibleforpeopletocreate entertainmentparkssuchasHurricaneHarborDesignersandengineersusedthebasicsinorderto figureouthowtomakewaterslidesbalancecorrectly,whattheappropriatevolumeofthewateris beingchanneledin,andholdtheweightoftherider.Withoutthediscoveriesandinventionsof Archimedes,manythingsthatwehaveinthemodernworldwouldn'thavebeencreatedinthe

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