| field = {{hlist|[[Mathematics]]|[[Physics]]|[[Engineering]]|[[Astronomy]]|[[Invention]]}}
| works =
| known_for = {{hlist|[[Archimedes' principle]]|[[Archimedes' screw]]|[[Fluid statics|hydrostatics]]|[[lever]]s|[[Archimedes' use of infinitesimals|infinitesimals]]|[[Neusis construction|Neuseis constructions]]<ref>{{cite journal| last= Knorr| first=Wilbur R. | title=Archimedes and the spirals: The heuristic background| journal=[[Historia Mathematica]] | year=1978| volume=5| issue=1|pages=43–75|publisher=[[Elsevier]]|quote="To be sure, Pappus does twice mention the theorem on the tangent to the spiral [IV, 36, 54]. But in both instances the issue is Archimedes' inappropriate use of a "solid neusis," that is, of a construction involving the sections of solids, in the solution of a plane problem. Yet Pappus' own resolution of the difficulty [IV, 54] is by his own classification a "solid" method, as it makes use of conic sections." (page 48)}}</ref>}}
| patrons = [[Duke Ferdinando I Gonzaga]]
| influenced by = [[Caravaggio]], [[Peter Paul Rubens]]
| influenced = [[Pietro della Vecchia]]<br/>[[Sebastiano Mazzone]]
| awards =
}}
}}
[[File:Accademia - La Meditazione by Domenico Fetti 1618.jpg|thumb|''Magdalene in Meditation'' ([[Accademia, Venice]])]]
'''Archimedes of Syracuse''' ({{IPAc-en|ˌ|ɑːr|k|ᵻ|ˈ|m|iː|d|iː|z}};<ref name="Collins">{{cite web|url=http://www.collinsdictionary.com/dictionary/english/archimedes?showCookiePolicy=true|title=Archimedes
[[File:Domenico Fetti (Italian - Portrait of a Man with a Sheet of Music - Google Art Project.jpg |thumb |''Portrait of a Man with a Sheet of Music'' ([[Getty Museum]])]]
|accessdate=25 September 2014|publisher=Collins Dictionary|date=n.d.}}</ref> {{lang-grc-gre|[[wikt:Ἀρχιμήδης|Ἀρχιμήδης]]}}; {{circa|287|212{{nbsp}}BC}}) was a [[Greeks|Greek]] [[Greek mathematics|mathematician]], [[physics|physicist]], [[engineering|engineer]], [[inventor]], and [[astronomy|astronomer]].<ref>{{cite web|title=Archimedes (c.287 - c.212 BC)|url=http://www.bbc.co.uk/history/historic_figures/archimedes.shtml|work=BBC History|accessdate=2012-06-07}}</ref> Although few details of his life are known, he is regarded as one of the leading [[scientist]]s in [[classical antiquity]]. Generally considered the greatest mathematician of antiquity and one of the greatest of all time,<ref>{{cite book |last=Calinger |first=Ronald |title=A Contextual History of Mathematics |year=1999 |publisher=Prentice-Hall |isbn=0-02-318285-7 |page=150 |quote=Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse (ca. 287 212 BC), the most original and profound mathematician of antiquity.}}</ref><ref>{{cite web |url=http://www-history.mcs.st-and.ac.uk/Biographies/Archimedes.html |title=Archimedes of Syracuse |accessdate=2008-06-09 |publisher=The MacTutor History of Mathematics archive |date=January 1999}}</ref> Archimedes anticipated modern [[calculus]] and [[mathematical analysis|analysis]] by applying concepts of [[infinitesimals]] and the [[method of exhaustion]] to derive and rigorously prove a range of [[geometry|geometrical]] [[theorem]]s, including the [[area of a circle]], the [[surface area]] and [[volume]] of a [[sphere]], and the area under a [[parabola]].<ref>{{cite web|title = A history of calculus |author1=O'Connor, J.J. |author2=Robertson, E.F.|publisher = [[University of St Andrews]]| url = http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html |date=February 1996|accessdate= 2007-08-07| archiveurl= https://web.archive.org/web/20070715191704/http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/The_rise_of_calculus.html| archivedate= 15 July 2007 <!--DASHBot-->| deadurl= no}}</ref>
Other mathematical achievements include deriving an accurate approximation of [[pi]], defining and investigating the [[Archimedes spiral|spiral]] bearing his name, and creating a system using [[exponentiation]] for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, founding [[Fluid statics|hydrostatics]] and [[statics]], including an explanation of the principle of the [[lever]]. He is credited with designing innovative [[machine]]s, such as his [[Archimedes' screw|screw pump]], [[block and tackle|compound pulleys]], and defensive war machines to protect his native [[Syracuse, Sicily|Syracuse]] from invasion.
Archimedes died during the [[Siege of Syracuse (214–212 BC)|Siege of Syracuse]] when he was killed by a [[Roman Republic|Roman]] soldier despite orders that he should not be harmed. [[Cicero]] describes visiting the tomb of Archimedes, which was surmounted by a [[sphere]] and a [[cylinder (geometry)|cylinder]], which Archimedes had requested be placed on his tomb to represent his mathematical discoveries.
Unlike his inventions, the mathematical writings of Archimedes were little known in antiquity. Mathematicians from [[Alexandria]] read and quoted him, but the first comprehensive compilation was not made until {{circa|530{{nbsp}}AD}} by [[Isidore of Miletus]] in [[Byzantine]] Constantinople, while commentaries on the works of Archimedes written by [[Eutocius of Ascalon|Eutocius]] in the sixth century AD opened them to wider readership for the first time. The relatively few copies of Archimedes' written work that survived through the [[Middle Ages]] were an influential source of ideas for scientists during the [[Renaissance]],<ref>{{cite web|title=Galileo, Archimedes, and Renaissance engineers |author=Bursill-Hall, Piers |publisher=sciencelive with the University of Cambridge |url=http://www.sciencelive.org/component/option,com_mediadb/task,view/idstr,CU-MMP-PiersBursillHall/Itemid,30 |accessdate=2007-08-07 |archiveurl=https://web.archive.org/web/20070929034534/http://www.sciencelive.org/component/option%2Ccom_mediadb/task%2Cview/idstr%2CCU-MMP-PiersBursillHall/Itemid%2C30 |archivedate=2007-09-29 |deadurl=yes |df= }}</ref> while the discovery in 1906 of previously unknown works by Archimedes in the [[Archimedes Palimpsest]] has provided new insights into how he obtained mathematical results.<ref>{{cite web|title=Archimedes – The Palimpsest |publisher=[[Walters Art Museum]] |url=http://www.archimedespalimpsest.org/palimpsest_making1.html |accessdate=2007-10-14 |archiveurl=https://web.archive.org/web/20070928102802/http://www.archimedespalimpsest.org/palimpsest_making1.html |archivedate=2007-09-28 |deadurl=yes |df= }}</ref>
==Biography==
Archimedes was born ''c''. 287 BC in the seaport city of [[Syracuse, Sicily]], at that time a self-governing [[Colonies in antiquity|colony]] in [[Magna Graecia]], located along the coast of [[Southern Italy]]. The date of birth is based on a statement by the [[Byzantine Greeks|Byzantine Greek]] historian [[John Tzetzes]] that Archimedes lived for 75 years.<ref>[[T. L. Heath|Heath, T. L.]], ''Works of Archimedes'', 1897</ref> In ''[[The Sand Reckoner]]'', Archimedes gives his father's name as Phidias, an [[astronomer]] about whom nothing else is known. [[Plutarch]] wrote in his ''[[Parallel Lives]]'' that Archimedes was related to King [[Hiero II of Syracuse|Hiero II]], the ruler of Syracuse.<ref>{{cite web|title = ''Parallel Lives'' Complete e-text from Gutenberg.org|author=[[Plutarch]]|publisher = [[Project Gutenberg]]| url = http://www.gutenberg.org/etext/674|accessdate=2007-07-23}}</ref> A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.<ref name="mactutor">{{cite web |author1=O'Connor, J.J. |author2=Robertson, E.F.|url = http://www-history.mcs.st-andrews.ac.uk/Biographies/Archimedes.html|title = Archimedes of Syracuse|publisher = University of St Andrews|accessdate = 2007-01-02| archiveurl= https://web.archive.org/web/20070206082010/http://www-history.mcs.st-andrews.ac.uk/Biographies/Archimedes.html| archivedate= 6 February 2007 <!--DASHBot-->| deadurl= no}}</ref> It is unknown, for instance, whether he ever married or had children. During his youth, Archimedes may have studied in [[Alexandria]], [[Ancient Egypt|Egypt]], where [[Conon of Samos]] and [[Eratosthenes|Eratosthenes of Cyrene]] were contemporaries. He referred to Conon of Samos as his friend, while two of his works (''[[Archimedes' use of infinitesimals|The Method of Mechanical Theorems]]'' and the ''[[Archimedes' cattle problem|Cattle Problem]]'') have introductions addressed to Eratosthenes.{{Ref_label|A|a|none}}
[[File:Death of Archimedes.png|thumb|upright=1.1|''The Death of Archimedes'' (1815) by [[Thomas Degeorge]]<ref>{{cite web|title=The Death of Archimedes: Illustrations|url=https://www.math.nyu.edu/~crorres/Archimedes/Death/DeathIllus.html|website=math.nyu.edu|publisher=[[New York University]]|ref=harv}}</ref>]]
Archimedes died ''c''. 212 BC during the [[Second Punic War]], when Roman forces under General [[Marcus Claudius Marcellus]] captured the city of Syracuse after a two-year-long [[siege]]. According to the popular account given by [[Plutarch]], Archimedes was contemplating a [[mathematical diagram]] when the city was captured. A Roman soldier commanded him to come and meet General Marcellus but he declined, saying that he had to finish working on the problem. The soldier was enraged by this, and killed Archimedes with his sword. Plutarch also gives a {{nowrap|lesser-known}} account of the death of Archimedes which suggests that he may have been killed while attempting to surrender to a Roman soldier. According to this story, Archimedes was carrying mathematical instruments, and was killed because the soldier thought that they were valuable items. General Marcellus was reportedly angered by the death of Archimedes, as he considered him a valuable scientific asset and had ordered that he not be harmed.<ref name="death">{{cite web |first=Chris |last=Rorres|url = http://www.math.nyu.edu/~crorres/Archimedes/Death/Histories.html|title = Death of Archimedes: Sources|publisher = [[Courant Institute of Mathematical Sciences]]|accessdate = 2007-01-02| archiveurl= https://web.archive.org/web/20061210060235/http://www.math.nyu.edu/~crorres/Archimedes/Death/Histories.html| archivedate= 10 December 2006| deadurl= no}}</ref> Marcellus called Archimedes "a geometrical [[Hekatonkheires#Hesiod|Briareus]]".<ref>Mary Jaeger. Archimedes and the Roman Imagination, p. 113.</ref>
The last words attributed to Archimedes are "Do not disturb my circles", a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. This quote is often given in [[Latin]] as "''[[Noli turbare circulos meos]]''," but there is no reliable evidence that Archimedes uttered these words and they do not appear in the account given by Plutarch. [[Valerius Maximus]], writing in ''Memorable Doings and Sayings'' in the 1st century AD, gives the phrase as "''...sed protecto manibus puluere 'noli' inquit, 'obsecro, istum disturbare'''" - "... but protecting the dust with his hands, said 'I beg of you, do not disturb this.{{'"}} The phrase is also given in [[Katharevousa Greek]] as "μὴ μου τοὺς κύκλους τάραττε!" (''Mē mou tous kuklous taratte!'').<ref name="death"/>
[[File:Cicero Discovering the Tomb of Archimedes by Benjamin West.jpeg|thumb|right|upright=1.1|''Cicero Discovering the Tomb of Archimedes'' (1805) by [[Benjamin West]]]]
The tomb of Archimedes carried a sculpture illustrating his favorite mathematical proof, consisting of a [[sphere]] and a [[cylinder (geometry)|cylinder]] of the same height and diameter. Archimedes had proven that the volume and surface area of the sphere are two thirds that of the cylinder including its bases. In 75 BC, 137 years after his death, the Roman [[orator]] [[Cicero]] was serving as [[quaestor]] in [[Sicily]]. He had heard stories about the tomb of Archimedes, but none of the locals were able to give him the location. Eventually he found the tomb near the Agrigentine gate in Syracuse, in a neglected condition and overgrown with bushes. Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.<ref>{{cite web|first=Chris |last=Rorres |url=http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html |title=Tomb of Archimedes: Sources |publisher=Courant Institute of Mathematical Sciences |accessdate=2007-01-02 |archiveurl=https://web.archive.org/web/20061209201723/http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html |archivedate=9 December 2006 |deadurl=no |df= }}</ref> A tomb discovered in the courtyard of the Hotel Panorama in Syracuse in the early 1960s was claimed to be that of Archimedes, but there was no compelling evidence for this and the location of his tomb today is unknown.<ref>{{cite web |first=Chris |last=Rorres|url = http://www.math.nyu.edu/~crorres/Archimedes/Tomb/TombIllus.html|title = Tomb of Archimedes – Illustrations|publisher = Courant Institute of Mathematical Sciences|accessdate = 2011-03-15}}</ref>
The standard versions of the life of Archimedes were written long after his death by the historians of Ancient Rome. The account of the siege of Syracuse given by [[Polybius]] in his ''Universal History'' was written around seventy years after Archimedes' death, and was used subsequently as a source by Plutarch and [[Livy]]. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in order to defend the city.<ref>{{cite web| first=Chris |last=Rorres|url = http://www.math.nyu.edu/~crorres/Archimedes/Siege/Polybius.html|title = Siege of Syracuse| publisher = Courant Institute of Mathematical Sciences|accessdate = 2007-07-23| archiveurl= https://web.archive.org/web/20070609013114/http://www.math.nyu.edu/~crorres/Archimedes/Siege/Polybius.html| archivedate= 9 June 2007| deadurl= no}}</ref>
