# Archimedes

Archimedes of Syracuse
Ἀρχιμήδης
Archimedes Thoughtful
by Domenico Fetti (1620)
Bornc. 287 BC
Diedc. 212 BC (aged approximately 75)
Syracuse, Sicily
Known for
Scientific career
FieldsMathematics
Physics
Astronomy
Mechanics
Engineering
InfluencesEudoxus
InfluencedApollonius[2]
Hero
Pappus
Eutocius

Archimedes of Syracuse (/ˌɑːrkɪˈmdz/;[3][a] c. 287 – c. 212 BC) was a Greek mathematician, physicist, engineer, astronomer, and inventor from the ancient city of Syracuse in Sicily.[4] Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Considered the greatest mathematician of ancient history, and one of the greatest of all time,[5] Archimedes anticipated modern calculus and analysis by applying the concept of the infinitely small and the method of exhaustion to derive and rigorously prove a range of geometrical theorems.[6][7] These include the area of a circle, the surface area and volume of a sphere, the area of an ellipse, the area under a parabola, the volume of a segment of a paraboloid of revolution, the volume of a segment of a hyperboloid of revolution, and the area of a spiral.[8][9]

Archimedes' other mathematical achievements include deriving an approximation of pi, defining and investigating the Archimedean spiral, and devising a system using exponentiation for expressing very large numbers. He was also one of the first to apply mathematics to physical phenomena, working on statics and hydrostatics. Archimedes' achievements in this area include a proof of the law of the lever,[10] the widespread use of the concept of center of gravity,[11] and the enunciation of the law of buoyancy or Archimedes' principle.[12] He is also credited with designing innovative machines, such as his screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder that Archimedes requested be placed there to represent his mathematical discoveries.

Unlike his inventions, Archimedes' mathematical writings were little known in antiquity. Mathematicians from Alexandria read and quoted him, but the first comprehensive compilation was not made until c. 530 AD by Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes by Eutocius in the 6th century 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 and again in the 17th century,[13][14] while the discovery in 1906 of previously lost works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.[15][16][17][18]

1. ^ Knorr, Wilbur R. (1978). "Archimedes and the spirals: The heuristic background". Historia Mathematica. 5 (1): 43–75. doi:10.1016/0315-0860(78)90134-9. "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." (p. 48)
2. ^ Heath, T. L. (1896). Apollonius of Perga: Treatise on Conic Sections with Introductions Including an Essay on Earlier History of the Subject. pp. lxiix, lxxxi, xlii–xliii, cxxii. Archived from the original on 24 June 2021. Retrieved 25 June 2021.
3. ^ "Archimedes". Collins Dictionary. n.d. Archived from the original on 3 March 2016. Retrieved 25 September 2014.
4. ^ "Archimedes (c. 287 – c. 212 BC)". BBC History. Archived from the original on 19 April 2012. Retrieved 7 June 2012.
5. ^ *John M. Henshaw (10 September 2014). An Equation for Every Occasion: Fifty-Two Formulas and Why They Matter. JHU Press. p. 68. ISBN 978-1-4214-1492-8. Archived from the original on 21 October 2020. Retrieved 17 March 2019. Archimedes is on most lists of the greatest mathematicians of all time and is considered the greatest mathematician of antiquity.
6. ^ Cite error: The named reference `:2` was invoked but never defined (see the help page).
7. ^ Jullien, V. (2015), J., Vincent (ed.), "Archimedes and Indivisibles", Seventeenth-Century Indivisibles Revisited, Science Networks. Historical Studies, Cham: Springer International Publishing, vol. 49, pp. 451–457, doi:10.1007/978-3-319-00131-9_18, ISBN 978-3-319-00131-9
8. ^ O'Connor, J.J.; Robertson, E.F. (February 1996). "A history of calculus". University of St Andrews. Archived from the original on 15 July 2007. Retrieved 7 August 2007.
9. ^ Heath, Thomas L. 1897. Works of Archimedes.
10. ^ Goe, G. (1972). "Archimedes' theory of the lever and Mach's critique". Studies in History and Philosophy of Science Part A. 2 (4): 329–345. Bibcode:1972SHPSA...2..329G. doi:10.1016/0039-3681(72)90002-7.
11. ^ Berggren, J. L. (1976). "Spurious Theorems in Archimedes' Equilibrium of Planes: Book I". Archive for History of Exact Sciences. 16 (2): 87–103. doi:10.1007/BF00349632. ISSN 0003-9519. JSTOR 41133463. S2CID 119741769.
12. ^ Cite error: The named reference `:7` was invoked but never defined (see the help page).
13. ^ Hoyrup, J. (2019). Archimedes: Knowledge and lore from Latin Antiquity to the outgoing European Renaissance. Selected Essays on Pre- and Early Modern Mathematical Practice. pp. 459–477.
14. ^ Leahy, A. (2018). "The method of Archimedes in the seventeenth century". The American Monthly. 125 (3): 267–272. doi:10.1080/00029890.2018.1413857. S2CID 125559661. Archived from the original on 14 July 2021. Retrieved 20 March 2021.
15. ^ "Works, Archimedes". University of Oklahoma. 23 June 2015. Archived from the original on 15 August 2017. Retrieved 18 June 2019.
16. ^ Paipetis, Stephanos A.; Ceccarelli, Marco, eds. (8–10 June 2010). The Genius of Archimedes – 23 Centuries of Influence on Mathematics, Science and Engineering: Proceedings of an International Conference held at Syracuse, Italy. History of Mechanism and Machine Science. Vol. 11. Springer. doi:10.1007/978-90-481-9091-1. ISBN 978-90-481-9091-1.
17. ^ "Archimedes – The Palimpsest". Walters Art Museum. Archived from the original on 28 September 2007. Retrieved 14 October 2007.
18. ^ Flood, Alison. "Archimedes Palimpsest reveals insights centuries ahead of its time". The Guardian. Archived from the original on 15 May 2021. Retrieved 10 February 2017.

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