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	{{Infobox Philosopher \|
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	<!-- Philosopher Category -->
	region = Classical Greek philosophy \|
	era = Ancient philosophy \|
	color = #B0C4DE \|

	<!-- Image -->
	image_name = Archimedes.jpg \|

	<!-- Information -->
	name = Archimedes of Syracuse (Greek: Ἀρχιμήδης) \|
	birth = ''c''. ] (], ancient ]) \|
	death = ''c''. ] (Syracuse) \|
	school_tradition = \|]
	main_interests = ], ], ], ], and ] \|
	influences = \|
	influenced = \|
	notable_ideas = \|
	}}

	'''Archimedes''' (]: {{polytonic\|Ἀρχιμήδης}}; ''c''. ] – ]) was a ] ], ], ], ], and ], born on the seaport colony of ], ], what is now ]. Many consider him one of the greatest, if not the greatest, mathematicians in ]. ], himself frequently called the most influential mathematician of all time, modestly claimed that Archimedes was one of the three epoch-making mathematicians (the others being ] and ]). Apart from his fundamental theoretical contributions to maths, Archimedes also shaped the fields of physics and practical engineering, and has been called "the greatest scientist ever".<ref>{{cite web \| title= Archimedes (287-212 B.C.), Greatest Scientist Ever" ] \| url=http://www.idsia.ch/~juergen/archimedes.html \| accessdate=October 11 \| accessyear=2006 }}</ref>

	He was a relative of the Hiero monarchy, which was the ruling family of Syracuse, a seaport kingdom. King ], who was said to be Archimedes's uncle, commissioned him to design and fabricate a new class of ships for his navy, which were crucial for the preservation of the ruling class in Syracuse. Hiero had promised large caches of grain to the Romans in the north in return for peace. Faced with war when unable to present the promised amount, Hiero commissioned Archimedes to develop a large luxury/supply/war barge in order to serve the changing requirements of his navy. It is rumored that the Archimedes Screw was actually an invention of happenstance, as he needed a tool to remove bilge water. The ship, named ''Syracusia'', after its nation, was huge, and its construction caused stupor in the Greek world.<ref>], '']'', v, 207b.</ref>

	He is credited with many inventions and discoveries, some of which we still use today, like his ]. He was famous for his compound pulley, a system of pulleys used to lift heavy loads such as ships. He made several war machines for his patron and friend King Hiero II. He did a lot of work in geometry, which included finding the surface areas and volumes of solids accurately. The work that has made Archimedes famous is his theory of floating bodies. He laid down the laws of flotation and developed the famous ].<ref>Eminent scientists, Published by scholastic India pvt. Ltd.</ref>

	==Discoveries and inventions==

	] lifts water to higher levels for irrigation.]]

	Archimedes became a very popular figure as a result of his involvement in the defense of ] against the ] ] in the ]. He is reputed to have held the Romans at bay with war machines of his own design, to have been able to move a full-size ship complete with crew and cargo by pulling a single rope, and to have ]ed the principles of ] and ], also known as ], while taking a bath. The story goes that he then took to the streets without any clothing, being so elated with his discovery that he forgot to dress, crying "]!" ("I have found it!"). He has also been credited with the possible invention of the ] during the ]. One of his inventions used for military defense of Syracuse against the invading Romans was the ].

	]
	It is said that he prevented one Roman attack on Syracuse by using a large array of ]s (speculated to have been highly polished shields) to reflect sunlight onto the attacking ships causing them to catch fire. This popular legend, dubbed the "Archimedes's death ray", has been tested many times since the Renaissance and often discredited as it seemed the ships would have had to have been virtually motionless and very close to shore for them to ignite, an unlikely scenario during a battle. A group at the ] have performed their own tests and concluded that the mirror weapon was a possibility
	, although later tests of their system showed it to be ineffective in conditions that more closely matched the described siege . The television show ] also took on the challenge of recreating the weapon and concluded that while it was possible to light a ship on fire, it would have to be stationary at a specified distance during the hottest part of a very bright, hot day, and would require several hundred troops carefully aiming mirrors while under attack. These unlikely conditions combined with the availability of other simpler methods, such as ] with flaming bolts, led the team to believe that the heat ray was far too impractical to be used, and probably just a myth.<ref></ref>

	]
	It can be argued that even if the reflections didn't induce fire, they still could have confused, and temporarily blinded the ship crews, making it hard for them to aim and steer. Making them hot and sweaty before primary battle may have also tired them faster. The effectiveness may have simply been exaggerated.

	Archimedes also has been credited with improving accuracy, range and power of the ].

	Archimedes was killed by a Roman soldier during the sack of Syracuse during the ], despite orders from the Roman general ] that he was not to be harmed. The Greeks said that he was killed while performing a geometric construction in the sand; engrossed in his diagram and impatient with being interrupted, he is said to have muttered his ] before being slain by an enraged Roman soldier: Μη μου τους κύκλους τάραττε ("Don't disturb my circles"). The phrase is often given in ] as "''Noli turbare circulos meos''" but there is no direct evidence that Archimedes ever uttered these words. This story was sometimes told to contrast the Greek high-mindedness with Roman ham-handedness; however, it should be noted that Archimedes designed the siege engines that devastated a substantial Roman invasion force, so his death may have been out of retribution .

	In creativity and insight, Archimedes exceeded any other European mathematician prior to the European ]. In a civilization with an awkward numeral system and a language in which "a myriad" (literally "ten thousand") meant "infinity", he invented a positional numeral system and used it to write numbers up to 10<sup>64</sup>. He devised a ] method based on ] to do private calculations that we would classify today as ], but then presented rigorous ] proofs for his results. To what extent he actually had a correct version of integral calculus is debatable. He proved that the ] of a ]'s ] to its ] is the same as the ratio of the circle's area to the ] of the ]. He did not call this ratio ] but he gave a procedure to approximate it to arbitrary accuracy and gave an approximation of it as between 3 + 10/71 (approximately 3.1408) and 3 + 1/7 (approximately 3.1429). He was the first ] mathematician to introduce ]s (those traced by a moving point) as legitimate objects of study. He proved that the area enclosed by a ] and a straight line is 4/3 the area of a ] with equal base and height. (See the illustration below. The "base" is any ], not necessarily ] to the parabola's ]; "the same base" means the same "horizontal" component of the length of the base; "horizontal" means orthogonal to the axis. "Height" means the length of the segment parallel to the axis from the ] to the base. The vertex must be so placed that the two horizontal distances mentioned in the illustration are equal.)

	<div style="float:right;padding:5px;text-align:center">]<br></div>

	In the process, he calculated the earliest known example of a ] summed to infinity with the ] 1/4:

	:<math> \sum_{n=0}^\infty 4^{-n} = 1 + 4^{-1} + 4^{-2} + 4^{-3} + \cdots = {4\over 3} \; . </math>

	If the first term in this series is the area of the triangle in the ] then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines in the illustration, and so on. Archimedes also gave a quite different proof of nearly the same ] by a method using ] (see "]").

	He proved that the ] and volume of the ] are in the same ratio to the area and volume of a circumscribed straight ], a result he was so proud of that he made it his ].

	Archimedes is probably also the first ] on record, and the best before ] and ]. He invented the field of ], enunciated the law of the ], the law of ] of ], and the law of ]. He famously discovered the latter when he was asked to determine whether a wreath (often incorrectly reported as a crown -- a crown could have been melted down to determine its composition, whereas a wreath was sacred) had been made of pure gold, or gold adulterated with silver; he realized that the rise in the water level when it was immersed would be equal to the volume of the wreath, and the decrease in the weight of the wreath would be in proportion; he could then compare those with the values of an equal weight of pure gold. He was the first to identify the concept of ], and he found the centers of gravity of various geometric figures, assuming uniform ] in their interiors, including ], ]s, and ]s. Using only ] ], he also gave the equilibrium positions of floating sections of paraboloids as a function of their height, a feat that would be taxing to a modern physicist using ].

	Apart from general physics, he was also an ], and ] writes that the Roman ] ] brought two devices back to ] from the ransacked city of Syracuse. One device mapped the ] on a sphere and the other predicted the motions of the ] and the ] and the ]s (i.e., an ]). He credits ] and ] for constructing these devices. For some time this was assumed to be a legend of doubtful nature, but the discovery of the ] has changed the view of this issue, and it is indeed probable that Archimedes possessed and constructed such devices. ] of ] writes that Archimedes had written a practical book on the construction of such spheres entitled '']''.

	Archimedes's works were not widely recognized, even in ]. He and his contemporaries probably constitute the peak of Greek ]. During the ] the mathematicians who could understand Archimedes's work were few and far between. Many of his works were lost when the ] was burnt (twice) and survived only in ] or ] ]s. As a result, his '']'' was lost until around ], after the ] had been carried out successfully. We can only speculate about the effect that the "method" would have had on the development of ] had it been known in the ] to the ] centuries.

	==Writings by Archimedes==

	* ''On the Equilibrium of Planes'' (2 volumes)
	:This scroll explains the law of the lever and uses it to calculate the areas and centers of gravity of various geometric figures.
	* ''On Spirals''
	:In this scroll, Archimedes defines what is now called ]. This is the first mechanical curve (i.e., traced by a moving point) ever considered by a Greek mathematician.
	* ''On the Sphere and The Cylinder''
	:In this scroll Archimedes obtains the result he was most proud of: the relation between the area of a sphere to that of a circumscribed straight cylinder is the same as that of the volume of the sphere to the volume of the cylinder (exactly 2/3).
	* ''On Conoids and Spheroids''
	:In this scroll Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
	* ''On Floating Bodies'' (2 volumes)
	:In the first part of this scroll, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This was probably an attempt at explaining the observation made by Greek astronomers that the Earth is round. Note that his fluids are not self-gravitating: he assumes the existence of a point towards which all things fall and derives the spherical shape. One is led to wonder what he would have done had he struck upon the idea of universal ].
	:In the second part, a veritable ''tour-de-force'', he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, which is reminiscent of the way ]s float, although Archimedes probably was not thinking of this application.
	* ''The Quadrature of the Parabola''
	:In this scroll, Archimedes calculates the area of a segment of a parabola (the figure delimited by a parabola and a secant line not necessarily perpendicular to the axis). The final answer is obtained by ] the area and summing the geometric series with ratio 1/4.
	* ''Stomachion''
	:This is a Greek puzzle similar to a ]. In this scroll, Archimedes calculates the areas of the various pieces. This may be the first reference we have to this game. Recent discoveries indicate that Archimedes was attempting to determine how many ways the strips of paper could be assembled into the shape of a square. This is possibly the first use of ] to solve a problem.
	* ''Archimedes's Cattle Problem''
	:Archimedes wrote a letter to the scholars in the Library of Alexandria, who apparently had downplayed the importance of Archimedes's works. In these letters, he dares them to count the numbers of cattle in the ] by solving a number of simultaneous ] equations, some of them ] (in the more complicated version). This problem is one of the famous problems solved with the aid of a computer. The solution is a very large number, approximately 7.760271{{e\|206544}} (See the external links to the Cattle Problem.)
	* '']''
	:In this scroll, Archimedes counts the number of grains of sand fitting inside the ]. This book mentions ]' theory of the ] (concluding that "this is impossible"), contemporary ideas about the size of the Earth and the distance between various celestial bodies. From the introductory letter we also learn that Archimedes's father was an astronomer.
	* ''"]"''
	:In this work, which was unknown in the Middle Ages, but the importance of which was realised after its discovery, Archimedes pioneers the use of ]s, showing how breaking up a figure in an infinite number of infinitely small parts could be used to determine its area or volume. Archimedes probably considered these methods not mathematically precise, and he used these methods to find at least some of the areas or volumes he sought, and then used the more traditional ] to prove them. <!-- This particular work is found in what is called the ]. --> Some details can be found at ].

	==See also==

	* ]
	* ]
	* The ] on the ] which was named in his honor.

	== Notes==
	<div class="references-small"><references/></div>

	== References ==
	* ], ''Archimedes'', 1987, Princeton University Press, Princeton, ISBN 0-691-08421-1. Republished translation of the 1938 study of Archimedes and his works by an historian of science
	* Fred S. Kliner Christin J. Mamiya, "Gardener's Art Through the Ages" twelfth ed. Vol II 2005, Thompson Wadsworth- Los Angeles

	== External links ==
	{{wikiquote}}
	* at ]
	* by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
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	* {{MacTutor Biography\|id=Archimedes }}
	* web pages at the ].
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	* points out that in reality Archimedes may well have used a more subtle method than the one in the classic version of the story.
	* Translated by ].
	* Translated by ].
	* by ].
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	*{{gutenberg author\|id=Archimedes\|name=Archimedes}}
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Revision as of 18:37, 9 December 2006

fuck u