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Encyclopedia > Archimedes
Classical Greek philosophy
Ancient philosophy
Archimedes Thoughtful by Fetti (1620)

Name Archimedes was a celebrated mathematician and engineer of ancient Greece. ... Image File history File linksMetadata Size of this preview: 450 × 600 pixel Image in higher resolution (1364 × 1818 pixel, file size: 548 KB, MIME type: image/jpeg) Archimedes Thoughtful by Domenico Fetti, 1620 Alte Meister Museum, Dresden (Germany/Deutschland) Source/Quelle: http://archimedes2. ... Domenico Fetti (c1589-1624) was an Italian painter born in Rome. ...

Archimedes of Syracuse (Greek: Άρχιμήδης)

Birth

c. 287 BC (Syracuse, Sicily, Magna Graecia) Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... Magna Graecia around 280 b. ...

Death

c. 212 BC (Syracuse)

School/tradition

Euclid of Alexandria
Natural philosophy Euclid Euclid of Alexandria (Greek: ) (ca. ... Natural philosophy or the philosophy of nature, known in Latin as philosophia naturalis, is a term applied to the objective study of nature and the physical universe that was regnant before the development of modern science. ...

Main interests

mathematics, physics, engineering, astronomy For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Engineering is the discipline of acquiring and applying knowledge of design, analysis, and/or construction of works for practical purposes. ... For other uses, see Astronomy (disambiguation). ...

Notable ideas

Hydrostatics, Levers,
Infinitesimals Hydrostatics, also known as fluid statics, is the study of fluids at rest. ... For the Portuguese town and parish, see Lever, Portugal. ... The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ...

Archimedes of Syracuse (Greek: Άρχιμήδης c. 287 BC – c. 212 BC) was an ancient Greek mathematician, physicist, astronomer and engineer. Although little is known of his life, he is regarded as one of the leading scientists in classical antiquity. In addition to making discoveries in the fields of mathematics and geometry, he is credited with designing innovative machines. He laid the foundations of hydrostatics, and explained the principle of the lever. His early advances in calculus included the first known summation of an infinite series with a method that is still used today.[1] The historians of Ancient Rome showed a strong interest in Archimedes and wrote accounts of his life and works, while the relatively few copies of his treatises that survived through the Middle Ages were an influential source of ideas for scientists during the Renaissance.[2] The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ... Not to be confused with physician, a person who practices medicine. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... Look up engineer in Wiktionary, the free dictionary. ... This article is about the profession. ... Classical antiquity is a broad term for a long period of cultural history centered on the Mediterranean Sea, which begins roughly with the earliest-recorded Greek poetry of Homer (7th century BC), and continues through the rise of Christianity and the fall of the Western Roman Empire (5th century AD... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... For other uses, see Geometry (disambiguation). ... This article is about devices that perform tasks. ... Hydrostatics, also known as fluid statics, is the study of fluids at rest. ... For the Portuguese town and parish, see Lever, Portugal. ... For other uses, see Calculus (disambiguation). ... Sum redirects here. ... In mathematics, a series is a sum of a sequence of terms. ... Ancient Rome was a civilization that grew from a small agricultural community founded on the Italian Peninsula circa the 9th century BC to a massive empire straddling the Mediterranean Sea. ... The Middle Ages formed the middle period in a traditional schematic division of European history into three ages: the classical civilization of Antiquity, the Middle Ages, and modern times, beginning with the Renaissance. ... This article is about the European Renaissance of the 14th-17th centuries. ...


Archimedes died during the Siege of Syracuse, when he was killed by a Roman soldier despite orders that he should not be harmed. At his request, his tomb carried a carving of his favorite mathematical proof. Modern experiments have tested claims that he built a "death ray" capable of setting ships on fire at a distance, and that he constructed a device that could sink ships by lifting them out of the water. [3] The discovery of previously unknown works by Archimedes in the Archimedes Palimpsest has provided new insights into how he obtained mathematical results.[4] The Siege of Syracuse was fought from 214 BC to 212 BC between the rebellious city of Syracuse, and a Roman army under Marcellus sent to put down the citys rebellion. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ...


Carl Friedrich Gauss is said to have remarked that Archimedes was one of the three epoch-making mathematicians, with the others being Sir Isaac Newton and Ferdinand Eisenstein.[5] Johann Carl Friedrich Gauss or Gauß ( ; Latin: ) (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, electrostatics, astronomy, and optics. ... Sir Isaac Newton in Knellers portrait of 1689. ... Ferdinand Gotthold Max Eisenstein (April 16, 1823 - October 11, 1852) was a German mathematician. ...

Contents

Biography

This bronze statue of Archimedes is at the Archenhold Observatory in Berlin. It was sculpted by Gerhard Thieme and unveiled in 1972.

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a colony of Magna Graecia. The date of birth is based on an assertion by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years.[6] In The Sand Reckoner, Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse.[7] A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure.[8] It is unknown, for instance, whether he ever married or had children. Archimedes probably spent part of his youth in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were contemporaries. He referred to Conon of Samos as his friend, while two of his works (The Sand Reckoner and the Cattle Problem) have introductions addressed to Eratosthenes.[a] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... This article does not cite any references or sources. ... This article is about the capital of Germany. ... Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... Magna Graecia around 280 b. ... Byzantine Greeks or Byzantines, is a conventional term used by modern historians to refer to the medieval Greek or Hellenized citizens of the Byzantine Empire, centered mainly in Constantinople, southern Balkans, the Greek islands, the coasts of Asia Minor (modern Turkey) and the large urban centres of Near East and... John Tzetzes, was a Byzantine poet and grammarian, known to have lived at Constantinople during the 12th century. ... The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ... An astronomer or astrophysicist is a person whose area of interest is astronomy or astrophysics. ... Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ... Wikisource has original text related to this article: Plutarch in Greek Plutarchs Lives of the Noble Greeks and Romans is a series of biographies of famous men, arranged in tandem to illuminate their common moral virtues or failings. ... Grave monument of Hiëro II in Syracuse Hiero II, tyrant of Syracuse from 270 to 215 BC, was the illegitimate son of a Syracusan noble, Hierocles, who claimed descent from Gelo. ... This article is about the city in Egypt. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Archimedes cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. ...


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 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 had ordered him not to be harmed.[9] Combatants Roman Republic Carthage Commanders Publius Cornelius Scipio†, Tiberius Sempronius Longus Publius Cornelius Scipio Africanus, Gaius Flaminius†, Fabius Maximus, Claudius Marcellus†, Lucius Aemilius Paullus†, Gaius Terentius Varro, Marcus Livius Salinator, Gaius Claudius Nero, Gnaeus Cornelius Scipio Calvus†, Masinissa, Minucius†, Servilius Geminus† Hannibal Barca, Hasdrubal Barca†, Mago Barca†, Hasdrubal Gisco†, Syphax... Marcus Claudius Marcellus (ca. ... A siege is a military blockade of a city or fortress with the intent of conquering by force or attrition, often accompanied by an assault. ...


The last words attributed to Archimedes are "Do not disturb my circles" (Greek: μή μου τούς κύκλους τάραττε), 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.[9] For other uses, see Latin (disambiguation). ...

Μη μου τους κύκλους τάραττε – Do not disturb my circles Image File history File links Archimedes_circles. ...

Listen to the last words attributed to Archimedes.

Problems listening to the file? See media help.

The sphere has 2/3 the surface area and volume of the circumscribing cylinder. A sphere and cylinder were carved on the tomb of Archimedes at his request.

The tomb of Archimedes had a carving of his favorite mathematical diagram, which was a sphere inside a cylinder of the same height and diameter. Archimedes had proved that the volume and surface area of the sphere would be two thirds that of the cylinder. 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 was 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.[10] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... For other uses, see Sphere (disambiguation). ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... Look up orator in Wiktionary, the free dictionary. ... For other uses, see Cicero (disambiguation). ... Quaestores were elected officials of the Roman Republic who supervised the treasury and financial affairs of the state, its armies and its officers. ... Sicily ( in Italian and Sicilian) is an autonomous region of Italy and the largest island in the Mediterranean Sea, with an area of 25,708 km² (9,926 sq. ...


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.[11] Polybius (c. ... A portrait of Titus Livius made long after his death. ...


Discoveries and inventions

The most commonly related anecdote about Archimedes tells how he invented a method for measuring the volume of an object with an irregular shape. According to Vitruvius, a new crown in the shape of a laurel wreath had been made for King Hiero II, and Archimedes was asked to determine whether it was of solid gold, or whether silver had been added by a dishonest goldsmith.[12] Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its density as a cube, which would have been the simplest solution. While taking a bath, he noticed that the level of the water rose as he got in. He realized that this effect could be used to determine the volume of the crown, and therefore its density after weighing it. The density of the crown would be lower if cheaper and less dense metals had been added. He then took to the streets naked, so excited by his discovery that he had forgotten to dress, crying "Eureka!" "I have found it!" (Greek: "εύρηκα!")[13] An anecdote is a short tale narrating an interesting or amusing biographical incident. ... Marcus Vitruvius Pollio (born ca. ... A laurel wreath decorating a memorial at the Folketing, the national parliament of Denmark. ... Grave monument of Hiëro II in Syracuse Hiero II, tyrant of Syracuse from 270 to 215 BC, was the illegitimate son of a Syracusan noble, Hierocles, who claimed descent from Gelo. ... GOLD refers to one of the following: GOLD (IEEE) is an IEEE program designed to garner more student members at the university level (Graduates of the Last Decade). ... This article is about the chemical element. ... For other uses, see Density (disambiguation). ... For other uses, see Volume (disambiguation). ... Eureka (Eureka!, or Heureka; Greek (later ); IPA: (modern Greek), (ancient Greek, both former and later forms), Anglicised as ) is a famous exclamation attributed to Archimedes. ...


The story about the golden crown does not appear in the known works of Archimedes, but in his treatise On Floating Bodies he gives the principle known in hydrostatics as Archimedes' Principle. This states that a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.[14] Hydrostatics, also known as fluid statics, is the study of fluids at rest. ... In physics, buoyancy is an upward force on an object immersed in a fluid (i. ...


While Archimedes did not invent the lever, he wrote the earliest known rigorous explanation of the principle involved. According to Pappus of Alexandria, his work on levers caused him to remark: "Give me a place to stand on, and I will move the Earth." (Greek: "δος μοι πα στω και ταν γαν κινάσω")[15] Plutarch describes how Archimedes designed block and tackle pulley systems, allowing sailors to use the principle of leverage to lift objects that would otherwise have been too heavy to move.[16] For the Portuguese town and parish, see Lever, Portugal. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... This block and tackle on a davit of the Mercator is used to help lower a boat. ... For the band, see Pulley (band). ... Leverage is related to torque; leverage is a factor by which lever multiplies a force. ...

The Archimedes' screw was operated by hand and could raise water efficiently.

A large part of Archimedes' work in engineering arose from fulfilling the needs of his home city of Syracuse. The Greek writer Athenaeus of Naucratis described how King Hieron II commissioned Archimedes to design a huge ship, the Syracusia, which could be used for luxury travel, carrying supplies, and as a naval warship. The Syracusia is said to have been the largest ship built in classical antiquity.[17] According to Athenaeus, it was capable of carrying 600 people and included garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite among its facilities. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes' screw was purportedly developed in order to remove the bilge water. The screw was a machine with a revolving screw shaped blade inside a cylinder. It was turned by hand, and could also be used to transfer water from a low-lying body of water into irrigation canals. Versions of the Archimedes' screw are still in use today in developing countries. The Archimedes' screw described in Roman times by Vitruvius may have been an improvement on a screw pump that was used to irrigate the Hanging Gardens of Babylon.[18][19][20] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Archimedes screw. ... Athenaeus (ca. ... The Greek ship Syracusia had a length of 55 meters (180. ... The gymnasium functioned as a training facility for competitors in public games. ... The Birth of Venus, (detail) by Sandro Botticelli, 1485 For other uses, see Aphrodite (disambiguation). ... Archimedes screw. ... Hanging Gardens redirects here. ...


The Claw of Archimedes is another weapon that he is said to have designed in order to defend the city of Syracuse. Also known as "the ship shaker", the claw consisted of a crane-like arm from which a large metal grappling hook was suspended. When the claw was dropped on to an attacking ship the arm would swing upwards, lifting the ship out of the water and possibly sinking it. There have been modern experiments to test the feasibility of the claw, and in 2005 a television documentary entitled Superweapons of the Ancient World built a version of the claw and concluded that it was a workable device.[21][22] The Claw of Archimedes was an ancient weapon devised by Archimedes to defend the seaward portion of Syracuses city wall against amphibious assault. ...


Archimedes has also been credited with improving the power and accuracy of the catapult, and with inventing the odometer during the First Punic War. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled.[23] Replica catapult at Château des Baux, France For the handheld Y-shaped weapon, see slingshot. ... A modern non-digital odometer A Smiths speedometer from the 1920s showing odometer and trip meter An odometer is a device used for indicating distance traveled by an automobile or other vehicle. ... Osama was here and he doesnt enjoy this site???? the red sox won and i am one happy camper. ...


Cicero (106 BC–43 BC) mentions Archimedes briefly in his dialogue De re publica, which portrays a fictional conversation taking place in 129 BC. After the capture of Syracuse c. 212 BC, General Marcus Claudius Marcellus is said to have taken back to Rome two mechanisms used as aids in astronomy, which showed the motion of the Sun, Moon and five planets. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome. Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus, who described it thus: For other uses, see Cicero (disambiguation). ... For other uses, see Dialogue (disambiguation). ... De re publica is a work by Cicero, written in six books 54-51 BC, in the format of a Socratic dialogue, that is to say: Scipio Africanus Minor (who had died a few decades before Cicero was born) takes the role of wise old man, that is an obligatory... Marcus Claudius Marcellus (ca. ... For the Defense and Security Company, see Thales Group. ... Another article concerns Eudoxus of Cyzicus. ... Gaius Sulpicius Gallus, Roman general, statesman and orator. ... Lucius Furius Philus was a consul of ancient Rome in 136 BC. He was a member of the Scipionic circle, and particularly close to Scipio Aemilianus. ...

Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. – When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.[24][25]

This is a description of a planetarium or orrery. Pappus of Alexandria stated that Archimedes had written a manuscript (now lost) on the construction of these mechanisms entitled On Sphere-Making. Modern research in this area has been focused on the Antikythera mechanism, another device from classical antiquity that was probably designed for the same purpose. Constructing mechanisms of this kind would have required a sophisticated knowledge of differential gearing. This was once thought to have been beyond the range of the technology available in ancient times, but the discovery of the Antikythera mechanism in 1902 has confirmed that devices of this kind were known to the ancient Greeks.[26][27] For the song by Ai Otsuka, see Planetarium (song) // A planetarium is a theatre built primarily for presenting educational and entertaining shows about astronomy and the night sky, or for training in celestial navigation. ... A small orrery showing earth and the inner planets An orrery is a mechanical device that illustrates the relative positions and motions of the planets and moons in the solar system in heliocentric model. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... On Sphere-Making is the title of a lost work by Archimedes, mentioned by Pappus of Alexandria. ... The Antikythera mechanism (main fragment). ... In an automobile and other four-wheeled vehicles, a differential is a device, usually consisting of gears, that allows each of the driving wheels to rotate at different speeds, while supplying equal torque to each of them. ...


"Death ray"

Archimedes may have used mirrors acting as a parabolic reflector to burn ships attacking Syracuse
Archimedes may have used mirrors acting as a parabolic reflector to burn ships attacking Syracuse

Lucian wrote that during the Siege of Syracuse (c. 214–212 BC), Archimedes repelled an attack by Roman forces with a burning glass.[28] The device was used to focus sunlight on to the approaching ships, causing them to catch fire. This claim, sometimes called the "Archimedes death ray", has been the subject of ongoing debate about its credibility since the Renaissance. René Descartes rejected it as false, while modern researchers have attempted to recreate the effect using only the means that would have been available to Archimedes.[29] It has been suggested that a large array of highly polished bronze or copper shields acting as mirrors could have been employed to focus sunlight on to a ship. This would have used the principle of the parabolic reflector in a manner similar to a solar furnace. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ... Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... Lucian. ... The Siege of Syracuse was fought from 214 BC to 212 BC between the rebellious city of Syracuse, and a Roman army under Marcellus sent to put down the citys rebellion. ... A burning-glass is a large convex lens that can concentrate the suns rays onto a small area, heating up the area and thus resulting in ignition of the surface exposed. ... Descartes redirects here. ... This article is about the metal alloy. ... For other uses, see Copper (disambiguation). ... A parabolic reflector (also known as a parabolic dish or a parabolic mirror) is a reflective device formed in the shape of a paraboloid of revolution. ... solar oven A solar oven or solar furnace is a way of harnessing the suns power to cook food. ...


In October 2005 a group of students from the Massachusetts Institute of Technology carried out an experiment with 127 one-foot (30 cm) square mirror tiles, focused on a mocked-up wooden ship at a range of around 100 feet (30 m). Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes. It was concluded that the weapon was a feasible device under these conditions. The MIT group repeated the experiment for the television show MythBusters, using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame. In order to catch fire, wood needs to reach its flash point, which is around 300 degrees Celsius (570 °F), and this is hotter than the maximum temperature produced by a domestic oven.[30] When Mythbusters broadcast the result of the San Francisco experiment in January 2006, the claim was placed in the category of "busted" (or "failed") due to of the length of time and ideal weather conditions required for combustion to occur. [31] “MIT” redirects here. ... MythBusters is an American popular science television program on the Discovery Channel starring special effects experts Adam Savage and Jamie Hyneman, who use basic elements of the scientific method to test the validity of various rumors and urban legends in popular culture. ... This page is a candidate for speedy deletion. ... For other uses, see Flash point (disambiguation). ...


A similar test of the "Archimedes death ray" was carried out in 1973 by the Greek scientist Ioannis Sakkas. The experiment took place at the Skaramagas naval base outside Athens. On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet (1.5 by 1 m). The mirrors were pointed at a plywood mock-up of a Roman warship at a distance of around 160 feet (50 m). When the mirrors were focused accurately, the ship burst into flames within a few seconds. The plywood ship had a coating of tar paint, which is flammable and may have aided combustion.[32] Skaramagas, Skaramanga, Skaramaga, Skaramangas or Skaramagkas (Greek: Σκαραμαγκά or Σκαραμαγκάς) older forms Skaramangas and Scaramanga is a small town in the western part of Athens, Greece. ... This article is about the capital of Greece. ... Ewer from Iran, dated 1180-1210CE. Composed of brass worked in repoussé and inlaid with silver and bitumen. ...


Mathematics

While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics. Plutarch wrote: “He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life.”[33] Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ...

Archimedes used the method of exhaustion to approximate the value of π.
Archimedes used the method of exhaustion to approximate the value of π.

Archimedes was able to use infinitesimals in a way that is similar to modern integral calculus. By assuming a proposition to be true and showing that this would lead to a contradiction, he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay. This technique is known as the method of exhaustion, and he employed it to approximate the value of π (Pi). He did this by drawing a larger polygon outside a circle and a smaller polygon inside the circle. As the number of sides of the polygon increases, it becomes a more accurate approximation of a circle. When the polygons had 96 sides each, he calculated the lengths of their sides and showed that the value of π lay between 3 + 1/7 (approximately 3.1429) and 3 + 10/71 (approximately 3.1408). He also proved that the area of a circle was equal to π multiplied by the square of the radius of the circle. Image File history File links Archimedes_pi. ... Image File history File links Archimedes_pi. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... In mathematics, an infinitesimal, or infinitely small number, is a number that is greater in absolute value than zero yet smaller than any positive real number. ... This article deals with the concept of an integral in calculus. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... When a circles diameter is 1, its circumference is Ï€. Pi or Ï€ is the ratio of a circles circumference to its diameter in Euclidean geometry, approximately 3. ... Look up polygon in Wiktionary, the free dictionary. ... Circle illustration This article is about the shape and mathematical concept of circle. ... This article is about the physical quantity. ... For other uses, see Square. ... This article is about an authentication, authorization, and accounting protocol. ...


In The Measurement of a Circle, Archimedes gives the value of the square root of 3 as being more than 265/153 (approximately 1.732) and less than 1351/780 (approximately 1.7320512). The actual value is around 1.7320508076, making this a very accurate estimate. He introduced this result without offering any explanation of the method used to obtain it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results."[34] In mathematics, a square root of a number x is a number r such that , or in words, a number r whose square (the result of multiplying the number by itself) is x. ... John Wallis John Wallis (November 22, 1616 - October 28, 1703) was an English mathematician who is given partial credit for the development of modern calculus. ...


In The Quadrature of the Parabola, Archimedes proved that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He expressed the solution to the problem as a geometric series that summed to infinity with the ratio 1/4: Image File history File links No higher resolution available. ... A parabolic segment. ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. ... For other uses, see Infinity (disambiguation). ... This article is about the mathematical concept. ...

sum_{n=0}^infty 4^{-n} = 1 + 4^{-1} + 4^{-2} + 4^{-3} + cdots = {4over 3}. ;

If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines, and so on. This proof is a variation of the infinite series 1/4 + 1/16 + 1/64 + 1/256 + · · · which sums to 1/3. A secant line of a curve is a line that intersects two or more points on the curve. ... In mathematics, a series is a sum of a sequence of terms. ... Archimedes figure with a = 3/4 In mathematics, the infinite series 1/4 + 1/16 + 1/64 + 1/256 + · · · is an example of one of the first infinite series to be summed in the history of mathematics; it was used by Archimedes circa 250-200 BC.[1] Its sum is...


In The Sand Reckoner, Archimedes set out to calculate the number of grains of sand that the universe could contain. In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo (Gelo II, son of Hiero II), who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." To solve the problem, Archimedes devised a system of counting based around the myriad. The word is based on the Greek for uncountable, murious, and was also used to denote the number 10,000. He proposed a number system using powers of myriad myriads (100 million) and concluded that the number of grains of sand required to fill the universe would be 8×1063 in modern notation.[35] The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ... Hiero II, tyrant of Syracuse from 270 to 215 BC, was the illegitimate son of a Syracusan noble, Hierocles, who claimed descent from Gelo. ... For other uses, see Myriad (disambiguation). ...


Writings

Archimedes is said to have remarked about the lever: "Give me a place to stand on, and I will move the Earth."
Archimedes is said to have remarked about the lever: "Give me a place to stand on, and I will move the Earth."
  • On the Equilibrium of Planes (two volumes)
The first book is in fifteen propositions with seven postulates, while the second book is in ten propositions. In this work Archimedes explains the Law of the Lever, stating:
Equal weights at equal distances are in equilibrium, and equal weights at unequal distances are not in equilibrium but incline towards the weight which is at the greater distance.
Archimedes uses the principles derived to calculate the areas and centers of gravity of various geometric figures including triangles, paraboloids, and hemispheres. [36]
  • On the Measurement of the Circle
This is a short work consisting of three propositions. It is written in the form of a correspondence with Dositheus of Pelusium, who was a student of Conon of Samos. In Proposition II, Archimedes shows that the value of π (Pi) is greater than 223/71 and less than 22/7. The latter figure was used as an approximation of π throughout the Middle Ages and is still used today when a rough figure is required.
  • On Spirals
This work of 28 propositions is also addressed to Dositheus. The treatise defines what is now called the Archimedean spiral. It is the locus of points corresponding to the locations over time of a point moving away from a fixed point with a constant speed along a line which rotates with constant angular velocity. Equivalently, in polar coordinates (r, θ) it can be described by the equation
with real numbers a and b. This is an early example of a mechanical curve (a curve traced by a moving point) considered by a Greek mathematician.
  • On the Sphere and the Cylinder (two volumes)
In this treatise addressed to Dositheus, Archimedes obtains the result of which he was most proud, namely the relationship between a sphere and a circumscribed cylinder of the same height and diameter. The volume is 4/3πr³ for the sphere, and 2πr³ for the cylinder; the surface area is 4πr² for the sphere, and 6πr² for the cylinder, where r is the radius. The sphere will have two thirds of the volume and surface area of the cylinder. A carving of this proof was used on the tomb of Archimedes at his request.
  • On Conoids and Spheroids
This is a work in 32 propositions addressed to Dositheus. In this treatise Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.
  • On Floating Bodies (two volumes)
In the first part of this treatise, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This may have been an attempt at explaining the theory of contemporary Greek astronomers such as Eratosthenes that the Earth is round. The fluids described by Archimedes are not self-gravitating, since he assumes the existence of a point towards which all things fall in order to derive the spherical shape.
Archimedes is commemorated on a Greek postage stamp from 1983.
Archimedes is commemorated on a Greek postage stamp from 1983.
In the second part, 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, similar to the way that icebergs float. Archimedes' principle of buoyancy is given in the work, stated as follows:
Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced.
  • The Quadrature of the Parabola
A work of 24 propositions addressed to Dositheus. In this treatise Archimedes proves by two methods that the area enclosed by a parabola and a straight line is 4/3 multiplied by the area of a triangle with equal base and height. He achieves this by calculating the value of a geometric series that sums to infinity with the ratio 1/4.
  • Stomachion
This is a dissection puzzle similar to a Tangram, and the treatise describing it was found in more complete form in the Archimedes Palimpsest. Archimedes calculates the areas of the 14 pieces which can be assembled to form a square. Research published by Dr. Reviel Netz of Stanford University in 2003 argued that Archimedes was attempting to determine how many ways the pieces of paper could be assembled into the shape of a square. The figure given by Dr. Netz is that the pieces can be made into a square in 17,152 ways. The number of arrangements is 536 when solutions that are equivalent by rotation and reflection have been excluded. The Stomachion represents an example of an early problem in combinatorics. Stomachion is the Greek word for stomach, στομάχιον; the reason for the name is unknown.[37][38]
This work was discovered by Gotthold Ephraim Lessing in a Greek manuscript consisting of a poem of 44 lines, in the Herzog August Library in Wolfenbüttel, Germany in 1773. It is addressed to Eratosthenes and the mathematicians at the University of Alexandria. Archimedes challenges them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations. There is a more difficult version of the problem in which some of the answers are required to be square numbers. This version of the problem was first solved by a computer in 1965, and the answer is a very large number, approximately 7.760271×10206544.[39]
In this treatise, Archimedes counts the number of grains of sand that will fit inside the universe. This book mentions the heliocentric theory of the solar system proposed by Aristarchus of Samos (concluding that "this is impossible"), contemporary ideas about the size of the Earth and the distance between various celestial bodies. By using a system of numbers based on powers of the myriad, Archimedes concludes that the number of grains of sand required to fill the universe is 8×1063 in modern notation. The introductory letter states that Archimedes' father was an astronomer named Phidias. The Sand Reckoner or Psammites is the only surviving work in which Archimedes discusses his views on astronomy.[40]
  • The Method of Mechanical Theorems
This treatise was thought lost until the discovery of the Archimedes Palimpsest in 1906. In this work Archimedes uses infinitesimals, and shows how breaking up a figure into an infinite number of infinitely small parts can be used to determine its area or volume. Archimedes may have considered this method lacking in formal rigor, so he also used the method of exhaustion to derive the results. As with The Cattle Problem, The Method of Mechanical Theorems was written in the form of a letter to Eratosthenes in Alexandria.

Image File history File linksMetadata No higher resolution available. ... Image File history File linksMetadata No higher resolution available. ... This article or section does not adequately cite its references or sources. ... In physics, the center of mass of a system of particles is a specific point at which, for many purposes, the systems mass behaves as if it were concentrated. ... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... Paraboloid of revolution Hyperbolic paraboloid In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation: (elliptic paraboloid), or (hyperbolic paraboloid). ... For other uses, see Sphere (disambiguation). ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... Lower-case pi The mathematical constant Ï€ is a real number which may be defined as the ratio of a circles circumference (Greek περιφέρεια, periphery) to its diameter in Euclidean geometry, and which is in common use in mathematics, physics, and engineering. ... An Archimedean spiral is a curve which in polar coordinates (r, θ) can be described by the equation with real numbers a and b. ... In mathematics, a locus (Latin for place, plural loci) is a collection of points which share a common property. ... Angular velocity describes the speed of rotation and the orientation of the instantaneous axis about which the rotation occurs. ... This article describes some of the common coordinate systems that appear in elementary mathematics. ... Please refer to Real vs. ... In mathematics, the concept of a curve tries to capture the intuitive idea of a geometrical one-dimensional and continuous object. ... A spatial point is an entity with a location in space but no extent (volume, area or length). ... For other uses, see Sphere (disambiguation). ... A black circle circumscribed by a red square In geometry, a circumscribed planar shape or solid is one that encloses and fits snugly around another geometric shape or solid. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... DIAMETER is a computer networking protocol for AAA (Authentication, Authorization and Accounting). ... A 3-D view of a beverage-can stove with a cross section in yellow. ... This article is about the geometric object, for other uses see Cone. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A parabolic segment. ... A parabola A graph showing the reflective property, the directrix (light blue), and the lines connecting the focus and directrix to the parabola (blue) In mathematics, the parabola (from the Greek: παραβολή) (IPA pronunciation: ) is a conic section generated by the intersection of a right circular conical surface and a plane... For alternate meanings, such as the musical instrument, see triangle (disambiguation). ... In mathematics, a geometric progression is a sequence of numbers such that the quotient of any two successive members of the sequence is a constant called the common ratio of the sequence. ... This article is about the mathematical concept. ... A dissection puzzle, also called a transformation puzzle is a tiling puzzle where a solver is given a set of pieces that can be assembled in different ways to produce two or more distinct geometric shapes. ... A typical tangram construction Tangram (Chinese: ; Pinyin: ; literally seven boards of cunning) is a Dissection puzzle. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... For other uses, see Square. ... Stanford redirects here. ... Combinatorics is a branch of pure mathematics concerning the study of discrete (and usually finite) objects. ... Archimedes cattle problem (or the problema bovinum or problema Archimedis) is a problem in Diophantine analysis, the study of polynomial equations with integer solutions. ... Gotthold Ephraim Lessing (22 January 1729 – 15 February 1781), writer, philosopher, publicist, and art critic, was one of the most outstanding German representatives of the Enlightenment era. ... Wolfenbüttel is a town in Lower Saxony, Germany. ... Alexandria University is a university in Alexandria, Egypt. ... In mathematics, a Diophantine equation is an indeterminate polynomial equation that allows the variables to be integers only. ... In mathematics, a square number, sometimes also called a perfect square, is a positive integer that can be written as the square of some other integer. ... The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ... In astronomy, heliocentrism is the theory that the Sun is at the center of the Universe and/or the Solar System. ... This article is about the Solar System. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... For other uses, see Myriad (disambiguation). ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ... The method of exhaustion is a method of finding the area of a shape by inscribing inside it a sequence of polygons whose areas converge to the area of the containing shape. ... This article is about the city in Egypt. ...

Apocryphal works

Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in Arabic. The scholars T. L. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author. The Lemmas may be based on an earlier work by Archimedes that is now lost.[41] Arabic can mean: From or related to Arabia From or related to the Arabs The Arabic language; see also Arabic grammar The Arabic alphabet, used for expressing the languages of Arabic, Persian, Malay ( Jawi), Kurdish, Panjabi, Pashto, Sindhi and Urdu, among others. ... Sir Thomas Little Heath (October 5, 1861 - March 16, 1940) was a mathematician, classical scholar, historian of ancient Greek mathematics, and translator. ... Marshall Clagett (January 23, 1916 - October 21, 2005) was an American scholar who specialized in the history of science. ...


It has also been claimed by the Arab scholar Abu'l Raihan Muhammed al-Biruni that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes.[c] However, the first reliable reference to the formula is given by Heron of Alexandria in the 1st century  AD.[42] A triangle with sides a, b, and c. ... Hero (or Heron) of Alexandria (Greek: Ήρων ο Αλεξανδρεύς) (c. ...


Archimedes Palimpsest

Main article: Archimedes Palimpsest

The written work of Archimedes has not survived as well as that of Euclid, and seven of his treatises are known to exist only through references made to them by other authors. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra, while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica.[b] The writings of Archimedes were collected by the Byzantine architect Isidore of Miletus (c. 530 AD), while translations into Arabic and Latin made during the Middle Ages helped to keep his work alive. Archimedes' work was translated into Arabic by Thābit ibn Qurra (836–901 AD), and Latin by Gerard of Cremona (c. 1114–1187 AD). During the Renaissance, the Editio Princeps (First Edition) was published in Basel in 1544 by Johann Herwagen with the works of Archimedes in Greek and Latin.[43] Around the year 1586 Galileo Galilei invented a hydrostatic balance for weighing metals in air and water after apparently being inspired by the work of Archimedes.[44] Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... A dissection puzzle, also called a transformation puzzle is a tiling puzzle where a solver is given a set of pieces that can be assembled in different ways to produce two or more distinct geometric shapes. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... For other uses, see Euclid (disambiguation). ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... On Sphere-Making is the title of a lost work by Archimedes, mentioned by Pappus of Alexandria. ... For the game magazine, see Polyhedron (magazine). ... Theon (c. ... For the property of metals, see refraction (metallurgy). ... The Byzantine Empire is the term conventionally used to describe the Roman Empire during the Middle Ages, centered at its capital in Constantinople. ... Isidore of Miletus was the architect who together with Anthemius of Tralles designed Hagia Sophia in modern day Istanbul The Emperor Justinian I decided to rebuild the 4th century basilica in Constantinople which was destroyed during the Nika riots of 532. ... (836 in Harran, Mesopotamia – February 18, 901 in Baghdad) was an Arab astronomer and mathematician, who was known as Thebit in Latin. ... Gerard of Cremona (Italian: Gerardo da Cremona; Latin: Gerardus Cremonensis; c. ... This article is about the European Renaissance of the 14th-17th centuries. ... For other uses, see Basel (disambiguation). ... Galileo redirects here. ...


The foremost document containing the work of Archimedes is the Archimedes Palimpsest. A palimpsest is a document written on vellum that has been re-used by scraping off the ink of an older text and writing new text in its place. This was often done during the Middle Ages since animal skin parchments were expensive. In 1906, the Danish professor Johan Ludvig Heiberg realized that a goatskin parchment of prayers written in the 13th century AD also carried an older work written in the 10th century AD, which he identified as previously unknown copies of works by Archimedes. The parchment spent hundreds of years in a monastery library in Constantinople before being sold to a private collector in the 1920s. On October 29, 1998 it was sold at auction to an anonymous buyer for $2 million at Christie's in London. The palimpsest holds seven treatises, including the only surviving copy of On Floating Bodies in the original Greek. It is the only known source of the Method of Mechanical Theorems, referred to by Suidas and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts. The palimpsest is now stored at the Walters Art Museum in Baltimore, Maryland, where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten text.[45] The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... A palimpsest is a manuscript page, scroll, or book that has been written on, scraped off, and used again. ... Vellum (from the Old French Vélin, for calfskin[1]) is a sort of parchment, a material for the pages of a book or codex, characterized by its thin, smooth, durable properties. ... For the Danish poet, see Johan Ludvig Heiberg (poet). ... This article is about the city before the Fall of Constantinople (1453). ... is the 302nd day of the year (303rd in leap years) in the Gregorian calendar. ... Year 1998 (MCMXCVIII) was a common year starting on Thursday (link will display full 1998 Gregorian calendar). ... The Christies auction house in South Kensington, London Christies American branch in Rockefeller Center, New York Christies is a fine art auction house, the largest and by some accounts the oldest in the world. ... This article is about the capital of England and the United Kingdom. ... The Walters Art Museum, located in Baltimore, Marylands Mount Vernon neighborhood, is a small privately-formed art collection open to the public. ... Flag Seal Nickname: Monument City, Charm City, Mob Town, B-more Motto: Get In On It (formerly The City That Reads and The Greatest City in America; BELIEVE is not the official motto but rather a specific campaign) Location Location of Baltimore in Maryland Coordinates , Government Country State County United... Official language(s) None (English, de facto) Capital Annapolis Largest city Baltimore Largest metro area Baltimore-Washington Metropolitan Area Area  Ranked 42nd  - Total 12,407 sq mi (32,133 km²)  - Width 101 miles (145 km)  - Length 249 miles (400 km)  - % water 21  - Latitude 37° 53′ N to 39° 43′ N... For other uses, see Ultraviolet (disambiguation). ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... For other uses, see Light (disambiguation). ...


The treatises in the Archimedes Palimpsest are: On the Equilibrium of Planes, On Spirals, The Measurement of the Circle, On the Sphere and the Cylinder, On Floating Bodies, The Method of Mechanical Theorems and Stomachion.


Legacy

The Fields Medal carries a portrait of Archimedes.

There is a crater on the Moon named Archimedes (29.7° N, 4.0° W) in his honor, and a lunar mountain range, the Montes Archimedes (25.3° N, 4.6° W).[46] The asteroid 3600 Archimedes is named after him.[47] Image File history File links Metadata Size of this preview: 624 × 600 pixelsFull resolution (800 × 769 pixel, file size: 115 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... Image File history File links Metadata Size of this preview: 624 × 600 pixelsFull resolution (800 × 769 pixel, file size: 115 KB, MIME type: image/jpeg) File historyClick on a date/time to view the file as it appeared at that time. ... The obverse of the Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. ... Tycho crater on Earths moon. ... This article is about Earths moon. ... Archimedes is a large lunar impact crater on the eastern edges of the Mare Imbrium. ... Montes Archimedes is a mountain range on the Moon. ... For other uses, see Asteroid (disambiguation). ... 3600 Archimedes is a small main belt asteroid. ...


The Fields Medal for outstanding achievement in mathematics carries a portrait of Archimedes, along with his proof concerning the sphere and the cylinder. The inscription around the head of Archimedes is a quote attributed to him which reads in Latin: "Transire suum pectus mundoque potiri" (Rise above oneself and grasp the world).[48] The obverse of the Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians not over 40 years of age at each International Congress of the International Mathematical Union, a meeting that takes place every four years. ...


Archimedes has appeared on postage stamps issued by East Germany (1973), Greece (1983), Italy (1983), Nicaragua (1971), San Marino (1982) and Spain (1963).[49] This article is about the state which existed from 1949 to 1990. ...


The exclamation of Eureka! attributed to Archimedes is the state motto of California. In this instance the word refers to the discovery of gold near Sutter's Mill in 1848 which sparked the California gold rush.[50] Eureka (Eureka!, or Heureka; Greek (later ); IPA: (modern Greek), (ancient Greek, both former and later forms), Anglicised as ) is a famous exclamation attributed to Archimedes. ... This article is about the U.S. state. ... Sutters Mill in 1850. ... The California Gold Rush (1848–1855) began shortly after January 24, 1848 (when gold was discovered at Sutters Mill in Coloma). ...


See also

This article or section contains information that has not been verified and thus might not be reliable. ... An Archimedes number, named after the ancient Greek scientist Archimedes, to determine the motion of fluids due to density differences, is a dimensionless number in the form where: g = gravitational acceleration (9. ... The Archimedes Paradox states that an object can float in water that has less volume than the object itself, if its average density is less than that of water. ... In mathematics (particularly abstract algebra), the Archimedean property is a property held by some ordered algebraic structures, and in particular by the ordered field of real numbers. ... In geometry an Archimedean solid or semi-regular solid is a semi-regular convex polyhedron composed of two or more types of regular polygon meeting in identical vertices. ... The ancient Greek mathematician, physicist, and engineer Archimedes of Syracuse was the first mathematician to make explicit use of infinitesimals. ... This article presents and explains several methods which can be used to calculate square roots. ... For other uses, see Zhang Heng (disambiguation). ...

Notes and references

Notes

a. ^ In the preface to On Spirals addressed to Dositheus of Pelusium, Archimedes says that "many years have elapsed since Conon's death." Conon of Samos lived c. 280–220 BC, suggesting that Archimedes may have been an older man when writing some of his works. Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ...


b. ^ The treatises by Archimedes known to exist only through references in the works of other authors are: On Sphere-Making and a work on polyhedra mentioned by Pappus of Alexandria; Catoptrica, a work on optics mentioned by Theon of Alexandria; Principles, addressed to Zeuxippus and explaining the number system used in The Sand Reckoner; On Balances and Levers; On Centers of Gravity; On the Calendar. Of the surviving works by Archimedes, T. L. Heath offers the following suggestion as to the order in which they were written: On the Equilibrium of Planes I, The Quadrature of the Parabola, On the Equilibrium of Planes II, On the Sphere and the Cylinder I, II, On Spirals, On Conoids and Spheroids, On Floating Bodies I, II, On the Measurement of a Circle, The Sand Reckoner. On Sphere-Making is the title of a lost work by Archimedes, mentioned by Pappus of Alexandria. ... Theon (c. ... The Sand Reckoner (Greek: Ψαμμίτης, Psammites) is a work by Archimedes in which he set out to determine an upper bound for the number of grains of sand that fit into the universe. ... Sir Thomas Little Heath (October 5, 1861 - March 16, 1940) was a mathematician, classical scholar, historian of ancient Greek mathematics, and translator. ...


c. ^ Boyer, Carl Benjamin A History of Mathematics (1991) ISBN 0471543977 "Arabic scholars inform us that the familiar area formula for a triangle in terms of its three sides, usually known as Heron's formula—k=sqrt(s(s-a)(s-b)(s-c)), where s is the semiperimeter—was known to Archimedes several centuries before Heron lived. Arabic scholars also attribute to Archimedes the 'theorem on the broken chord' [...] Archimedes is reported by the Arabs to have given several proofs of the theorem." Carl Benjamin Boyer (November 3, 1906 - April 26, 1976) was a historian of mathematics. ... A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ...


References

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  4. ^ Archimedes - The Palimpsest. Walters Art Museum. Retrieved on 2007-10-14.
  5. ^ Sandifer, Ed. Review of Archimedes: What Did He Do Besides Cry Eureka?. Mathematical Association of America. Retrieved on 2007-07-23.
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  9. ^ a b Rorres, Chris. Death of Archimedes: Sources. Courant Institute of Mathematical Sciences. Retrieved on 2007-01-02.
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  11. ^ Rorres, Chris. Siege of Syracuse. Courant Institute of Mathematical Sciences. Retrieved on 2007-07-23.
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  13. ^ HyperPhysics. Buoyancy. Georgia State University. Retrieved on 2007-07-23.
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  15. ^ Quoted by Pappus of Alexandria in Synagoge, Book VIII
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  17. ^ Casson, Lionel (1971). Ships and Seamanship in the Ancient World. Princeton University Press. ISBN 0691035369. 
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  20. ^ Watch an animation of an Archimedes' screw. Wikimedia Commons. Retrieved on 2007-07-23.
  21. ^ Rorres, Chris. Archimedes' Claw - Illustrations and Animations - a range of possible designs for the claw. Courant Institute of Mathematical Sciences. Retrieved on 2007-07-23.
  22. ^ Carroll, Bradley W. Archimedes' Claw - watch an animation. Weber State University. Retrieved on 2007-08-12.
  23. ^ Ancient Greek Scientists: Hero of Alexandria. Technology Museum of Thessaloniki. Retrieved on 2007-09-14.
  24. ^ Cicero. De re publica 1.xiv §21. thelatinlibrary.com. Retrieved on 2007-07-23.
  25. ^ Cicero. De re publica Complete e-text in English from Gutenberg.org. Project Gutenberg. Retrieved on 2007-09-18.
  26. ^ Rorres, Chris. Spheres and Planetaria. Courant Institute of Mathematical Sciences. Retrieved on 2007-07-23.
  27. ^ Ancient Moon 'computer' revisited. BBC News (November 29, 2006). Retrieved on 2007-07-23.
  28. ^ Hippias, C.2.
  29. ^ John Wesley. A Compendium of Natural Philosophy (1810) Chapter XII, Burning Glasses. Online text at Wesley Center for Applied Theology. Retrieved on 2007-09-14.
  30. ^ Bonsor, Kevin. How Wildfires Work. HowStuffWorks. Retrieved on 2007-07-23.
  31. ^ Archimedes Death Ray: Testing with MythBusters. MIT. Retrieved on 2007-07-23.
  32. ^ Archimedes' Weapon. Time Magazine (November 26, 1973). Retrieved on 2007-08-12.
  33. ^ Plutarch. Extract from Parallel Lives. fullbooks.com. Retrieved on 2007-08-07.
  34. ^ Quoted in T. L. Heath, Works of Archimedes, Dover Publications, ISBN 0-486-42084-1.
  35. ^ Carroll, Bradley W. The Sand Reckoner. Weber State University. Retrieved on 2007-07-23.
  36. ^ Heath,T.L.. The Works of Archimedes (1897). The unabridged work in PDF form (19 MB). Archive.org. Retrieved on 2007-10-14.
  37. ^ Kolata, Gina (December 14, 2003). In Archimedes' Puzzle, a New Eureka Moment. New York Times. Retrieved on 2007-07-23.
  38. ^ Rorres, Chris. Archimedes' Stomachion. Courant Institute of Mathematical Sciences. Retrieved on 2007-09-14.
  39. ^ Calkins, Keith G. Archimedes' Problema Bovinum. Andrews University. Retrieved on 2007-09-14.
  40. ^ English translation of The Sand Reckoner. University of Waterloo. Retrieved on 2007-07-23.
  41. ^ Archimedes' Book of Lemmas. cut-the-knot. Retrieved on 2007-08-07.
  42. ^ Wilson, James W. Problem Solving with Heron's Formula. University of Georgia. Retrieved on 2007-09-14.
  43. ^ Editions of Archimedes' Work. Brown University Library. Retrieved on 2007-07-23.
  44. ^ Van Helden, Al. The Galileo Project: Hydrostatic Balance. Rice University. Retrieved on 2007-09-14.
  45. ^ X-rays reveal Archimedes' secrets. BBC News (August 2, 2006). Retrieved on 2007-07-23.
  46. ^ Friedlander, Jay and Williams, Dave. Oblique view of Archimedes crater on the Moon. NASA. Retrieved on 2007-09-13.
  47. ^ Planetary Data System. NASA. Retrieved on 2007-09-13.
  48. ^ Fields Medal. International Mathematical Union. Retrieved on 2007-07-23.
  49. ^ Rorres, Chris. Stamps of Archimedes. Courant Institute of Mathematical Sciences. Retrieved on 2007-08-25.
  50. ^ California Symbols. California State Capitol Museum. Retrieved on 2007-09-14.

St Marys College Bute Medical School St Leonards College[5][6] Affiliations 1994 Group Website http://www. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 219th day of the year (220th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 219th day of the year (220th in leap years) in the Gregorian calendar. ... Mapúa Institute of Technology (MIT, MapúaTech or simply Mapúa) is a private, non-sectarian, Filipino tertiary institute located in Intramuros, Manila. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... 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Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ... Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive and distribute cultural works. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 2nd day of the year in the Gregorian calendar. ... The Courant Institute of Mathematical Sciences (CIMS) is a division of New York University (NYU) and serves as a center for research and advanced training in computer science and mathematics. ... 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HyperPhysics is an educational resource on Physics topics. ... Georgia State University (GSU) is an urban research university in the heart of downtown Atlanta, Georgia, USA. Founded in 1913, it serves over 28,000[1] students, and is one of the University System of Georgias four research universities. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Weber State University is a public university located in the city of Ogden in Weber County, Utah, USA. There is also a Davis County satellite campus located in Layton. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Pappus of Alexandria is one of the most important mathematicians of ancient Greek time, known for his work Synagoge or Collection (c. ... The Society of Women Engineers (SWE) is a professional organization founded in 1950, by Beatrice Alice Hicks, to support and promote the activities and presence of women in the often male-dominated field of engineering. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... The Wikimedia Commons (also called Wikicommons) is a repository of free content images, sound and other multimedia files. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 224th day of the year (225th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 257th day of the year (258th in leap years) in the Gregorian calendar. ... For other uses, see Cicero (disambiguation). ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... For other uses, see Cicero (disambiguation). ... Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive and distribute cultural works. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 261st day of the year (262nd in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... is the 333rd day of the year (334th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... For other persons named John Wesley, see John Wesley (disambiguation). ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 257th day of the year (258th in leap years) in the Gregorian calendar. ... HowStuffWorks is a website created by Marshall Brain but now owned by the Convex Group. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... (Clockwise from upper left) Time magazine covers from May 7, 1945; July 25, 1969; December 31, 1999; September 14, 2001; and April 21, 2003. ... is the 330th day of the year (331st in leap years) in the Gregorian calendar. ... 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Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 287th day of the year (288th in leap years) in the Gregorian calendar. ... is the 348th day of the year (349th in leap years) in the Gregorian calendar. ... Year 2003 (MMIII) was a common year starting on Wednesday of the Gregorian calendar. ... The New York Times is an internationally known daily newspaper published in New York City and distributed in the United States and many other nations worldwide. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... 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Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... cut-the-knot is an educational website maintained by Alexander Bogomolny and devoted to popular exposition of a great variety of topics in mathematics. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 219th day of the year (220th in leap years) in the Gregorian calendar. ... The University of Georgia (UGA) is the largest institution of higher learning in the U.S. state of Georgia. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 257th day of the year (258th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Lovett Hall William Marsh Rice University (commonly called Rice University and opened in 1912 as The William Marsh Rice Institute for the Advancement of Letters, Science and Art) is a private, comprehensive research university located in Houston, Texas, USA, near the Museum District and adjacent to the Texas Medical Center. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 257th day of the year (258th in leap years) in the Gregorian calendar. ... is the 214th day of the year (215th in leap years) in the Gregorian calendar. ... Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... The National Aeronautics and Space Administration (NASA) (IPA [ˈnæsÉ™]) is an agency of the United States government, responsible for the nations public space program. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 256th day of the year (257th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 256th day of the year (257th in leap years) in the Gregorian calendar. ... The International Mathematical Union is an international non-governmental organization devoted to international cooperation in the field of mathematics. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 204th day of the year (205th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 237th day of the year (238th in leap years) in the Gregorian calendar. ... Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ... is the 257th day of the year (258th in leap years) in the Gregorian calendar. ...

Further reading

  • Boyer, Carl Benjamin (1991). A History of Mathematics. New York: Wiley. ISBN 0-471-54397-7. 
  • Dijksterhuis, E.J. (1987). Archimedes. 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.
  • Gow, Mary (2005). Archimedes: Mathematical Genius of the Ancient World. Enslow Publishers, Inc. ISBN 0-7660-2502-0. 
  • Hasan, Heather (2005). Archimedes: The Father of Mathematics. Rosen Central. ISBN 978-1404207745. 
  • Heath, T.L. (1897). Works of Archimedes. Dover Publications. ISBN 0-486-42084-1.  Complete works of Archimedes in English.
  • Netz, Reviel and Noel, William (2007). The Archimedes Codex. Orion Publishing Group. ISBN 0-297-64547-1. 
  • Simms, Dennis L. (1995). Archimedes the Engineer. Continuum International Publishing Group Ltd. ISBN 0-720-12284-8. 
  • Stein, Sherman (1999). Archimedes: What Did He Do Besides Cry Eureka?. Mathematical Association of America. ISBN 0-88385-718-9. 

Carl Benjamin Boyer (November 3, 1906 - April 26, 1976) was a historian of mathematics. ... Eduard Jan Dijksterhuis (1892-1965), Historian of Science from the Netherlands. ... Thomas Little Heath (October 5, 1861 - March 16, 1940) was a mathematician, classical scholar, historian of ancient Greek mathematics, and translator. ...

External links

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Archimedes
Persondata
NAME Archimedes
ALTERNATIVE NAMES
SHORT DESCRIPTION ancient Greek mathematician, physicist and engineer
DATE OF BIRTH circa 287 BC
PLACE OF BIRTH Syracuse, Sicily, Magna Graecia
DATE OF DEATH circa 212 BC
PLACE OF DEATH Syracuse, Sicily, Magna Graecia

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Greek mathematics, as that term is used in this article, is the mathematics written in Greek, developed from the 6th century BC to the 5th century AD around the Eastern shores of the Mediterranean. ... Anaxagoras Anaxagoras (Greek: Αναξαγόρας, c. ... Anthemius of Tralles (c. ... Archytas Archytas (428 BC - 347 BC) was a Greek philosopher, mathematician, astronomer, statesman, strategist and commander-in-chief. ... Aristaeus the Elder (370 BCE-300 BCE) Aristaeus the Elder was a Greek mathematician who worked on conic sections. ... For other uses of this name, including the grammarian Aristarchus of Samothrace, see Aristarchus Statue of Aristarchus at Aristotle University in Thessalonica, Greece Aristarchus (Greek: Ἀρίσταρχος; 310 BC - ca. ... Apollonius of Perga [Pergaeus] (ca. ... Autolycus of Pitane (c. ... For other people of the same name, see Boethius (disambiguation). ... Bryson of Heraclea (ca. ... Calippus of Syracuse Callippus (or Calippus) (ca. ... Chrysippus of Soli (279-207 BC) was Cleanthess pupil and eventual successor to the head of the stoic philosophy (232-204 BC). ... Cleomedes was a Greek astronomer who is known chiefly for his book On the Circular Motions of the Celestial Bodies. ... Conon of Samos (circa 280 BC - circa: 220 BC) was a Greek mathematician and astronomer. ... ‎ Democritus (Greek: ) was a pre-Socratic Greek materialist philosopher (born at Abdera in Thrace ca. ... Dicaearchus (also Dicearchos, Dicearchus or Dikæarchus, Greek Δικαιαρχος; circa 350 BC – circa 285 BC) was a Greek philosopher, cartographer, geographer, mathematician and author. ... Diocles was a Greek mathematician and geometer, who probably flourished sometime around the end of the second century and the beginning of the first century BC. He was probably the first to prove the focal property of a parabola. ... Title page of the 1621 edition of Diophantus Arithmetica, translated into Latin by Claude Gaspard Bachet de Méziriac. ... Dinostratus (b. ... Dionysodorus of Caunus (ca. ... Domninus of Larissa (ca. ... This article is about the Greek scholar of the third century BC. For the ancient Athenian statesman of the fifth century BC, see Eratosthenes (statesman). ... For other uses, see Euclid (disambiguation). ... Another article concerns Eudoxus of Cyzicus. ... Eutocius of Ascalon (ca. ... Geminus of Rhodes was a Greek astronomer and mathematician. ... Hero (or Heron) of Alexandria (Greek: Ήρων ο Αλεξανδρεύς) (c. ... For the Athenian tyrant, see Hipparchus (son of Pisistratus). ... Hippasus of Metapontum, born circa 500 B.C. in Magna Graecia, was a Greek philosopher. ... Hippias can also refer to a son of Pisistratus and a tyrant of Athens. ... Hippocrates of Chios was an ancient Greek mathematician (geometer) and astronomer, who lived c. ... Hypatia could refer to: Hypatia of Alexandria (?370–415), a neo-Platonic philosopher, mathematician, and teacher. ... Hypsicles (ca. ... 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This article is about Proclus Diadochus, the Neoplatonist philosopher. ... This article is about the geographer, mathematician and astronomer Ptolemy. ... Pythagoras of Samos (Greek: ; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism. ... Serenus of Antinouplis (ca. ... Simplicius, a native of Cilicia, a disciple of Ammonius and of Damascius, was one of the last of the Neoplatonists. ... Sporus of Nicaea was a Greek mathematician and astronomer, born: circa 240, probably Nicaea (Greek Nikaia), ancient district Bithynia, (modern-day Iznik) in province Bursa, in modern day Turkey, died: circa 300. ... For the Defense and Security Company, see Thales Group. ... Theaetetus (ca. ... Theano was one of the few women in ancient mathematics. ... This article is about Theodorus the mathematician from Cyrene. ... Theodosius of Bithynia (ca. ... Theon (c. ... Theon of Smyrna (ca. ... Thymaridas of Paros (ca. ... Xenocrates of Chalcedon (396 - 314 BC) was a Greek philosopher and scholarch or rector of the Academy from 339 to 314 BC. Removing to Athens in early youth, he became the pupil of the Socratic Aeschines, but presently joined himself to Plato, whom he attended to Sicily in 361. ... Zeno of Elea (IPA:zÉ›noÊŠ, É›lɛɑː)(circa 490 BC? – circa 430 BC?) was a pre-Socratic Greek philosopher of southern Italy and a member of the Eleatic School founded by Parmenides. ... Zeno of Sidon, Epicurean philosopher of the 1st century BC and contemporary of Cicero. ... Zenodorus (ca. ... Almagest is the Latin form of the Arabic name (al-kitabu-l-mijisti, i. ... The Archimedes Palimpsest is a palimpsest on parchment in the form of a codex which originally was a copy of an otherwise unknown work of the ancient mathematician, physicist, and engineer Archimedes of Syracuse and other authors. ... Arithmetica, an ancient text on mathematics written by classical period Greek mathematician Diophantus in the second century AD is a collection of 130 algebra problems giving numerical solutions of determinate equations (those with a unique solution), and indeterminate equations. ... Apollonius of Perga [Pergaeus] (ca. ... The frontispiece of Sir Henry Billingsleys first English version of Euclids Elements, 1570 Euclids Elements (Greek: ) is a mathematical and geometric treatise consisting of 13 books written by the Greek mathematician Euclid in Alexandria circa 300 BC. It comprises a collection of definitions, postulates (axioms), propositions (theorems... Aristarchuss 3rd century BC calculations on the relative sizes of the Earth, Sun and Moon, from a 10th century CE Greek copy On the Sizes and Distances [of the Sun and Moon] is the only extant work written by Aristarchus of Samos, an ancient Greek astronomer who lived circa... On Sizes and Distances [of the Sun and Moon] (Peri megethoon kai apostèmátoon) is a text by the ancient Greek astronomer Hipparchus. ... For other uses, see Academy (disambiguation). ... Inscription regarding Tiberius Claudius Balbilus of Rome (d. ... Babylonian clay tablet YBC 7289 with annotations. ... This article or section is in need of attention from an expert on the subject. ... In the history of mathematics, Islamic mathematics or Arabic mathematics refers to the mathematics developed by the Islamic civilization between 622 and 1600. ... This article is under construction. ... The term ancient Greece refers to the periods of Greek history in Classical Antiquity, lasting ca. ... Look up Aegean Sea in Wiktionary, the free dictionary. ... The Helespont/Dardanelles, a long narrow strait dividing the Balkans (Europe) along the Gallipoli peninsula from Asia Anatolia (Asia Minor). ... Ancient Macedons regions and towns Macedon or Macedonia (Greek ) was the name of an ancient kingdom in the northern-most part of ancient Greece, bordered by the kingdom of Epirus to the west and the region of Thrace to the east. ... For modern day Sparta, see Sparti (municipality). ... This article is about the capital of Greece. ... Corinth, or Korinth (Greek: Κόρινθος, Kórinthos; see also List of traditional Greek place names) is a Greek city-state, on the Isthmus of Corinth, the narrow stretch of land that joins the Peloponnesus to the mainland of Greece. ... Thebes (Demotic Greek: Θήβα — Thíva; Katharevousa: — Thêbai or Thívai) is a city in Greece, situated to the north of the Cithaeron range, which divides Boeotia from Attica, and on the southern edge of the Boeotian plain. ... For the clipper ship, see Thermopylae (clipper). ... It has been suggested that this article or section be merged into Antakya. ... This article is about the city in Egypt. ... View of the reconstructed Temple of Trajan at Pergamon Sketched reconstruction of ancient Pergamon Pergamon or Pergamum (Greek: Πέργαμος, modern day Bergama in Turkey, ) was an ancient Greek city, in Mysia, north-western Anatolia, 16 miles from the Aegean Sea, located on a promontory on the north side of the river... The lower half of the benches and the remnants of the scene building of the theater of Miletus (August 2005) Miletus (Carian: Anactoria Hittite: Milawata or Millawanda, Greek: Μίλητος transliterated Miletos, Turkish: Milet) was an ancient city on the western coast of Anatolia (in what is now Aydin Province, Turkey), near... For other uses, see Delphi (disambiguation). ... Olympia among the principal Greek sanctuaries Olympia (Greek: Olympía or Olýmpia, older transliterations, Olimpia, Olimbia), a sanctuary of ancient Greece in Elis, is known for having been the site of the Olympic Games in classical times, comparable in importance to the Pythian Games held in Delphi. ... For other uses of Troy or Ilion, see Troy (disambiguation) and Ilion (disambiguation). ... The art of ancient Greece has exercised an enormous influence on the culture of many countries from ancient times until the present, particularly in the areas of sculpture and architecture. ... Kylix, the most common drinking vessel in ancient Greece, c. ... TRENT IS SOOOOOOOOO HOT!!!!!!!!!!!!!!!!!!!!!!! Ancient Greek law is a branch of comparative jurisprudence relating to the laws and legal institutions of Ancient Greece. ... This article or section is in need of attention from an expert on the subject. ... To the ancient Greeks, Paideia (παιδεία) was the process of educating man into his true form, the real and genuine human nature. ... Pederastic courtship scene Athenian black-figure amphora, 5th c. ... Bilingual amphora by the Andokides Painter, ca. ... Courtesan and her client, Attican Pelike with red figures by Polygnotus, c. ... Funerary stele: the slave represented as a shorter person, beside the mistress, Munich Glyptothek Slavery was an essential component of the development of Ancient Greece throughout its history. ... Ancient Greek technology is a set of artifacts and customs that lasted for more than one thousand years. ... Ruins of the training grounds at Olympia The Ancient Olympic Games, originally referred to as simply the Olympic Games (Greek: ; Olympiakoi Agones) were a series of athletic competitions held between various city-states of Ancient Greece. ... Greek philosophy focused on the role of reason and inquiry. ... Pythagoras of Samos (Greek: ; between 580 and 572 BC–between 500 and 490 BC) was an Ionian (Greek) philosopher[1] and founder of the religious movement called Pythagoreanism. ... Heraclitus of Ephesus (Ancient Greek - Herákleitos ho Ephésios (Herakleitos the Ephesian)) (about 535 - 475 BC), known as The Obscure (Ancient Greek - ho Skoteinós), was a pre-Socratic Greek philosopher, a native of Ephesus on the coast of Asia Minor. ... Parmenides of Elea (Greek: , early 5th century BC) was an ancient Greek philosopher born in Elea, a Hellenic city on the southern coast of Italy. ... Protagoras (in Greek Πρωταγόρας) was born around 481 BC in Abdera, Thrace in Ancient Greece. ... Empedocles (Greek: , ca. ... ‎ Democritus (Greek: ) was a pre-Socratic Greek materialist philosopher (born at Abdera in Thrace ca. ... This page is about the Classical Greek philosopher. ... For other uses, see Plato (disambiguation). ... For other uses, see Aristotle (disambiguation). ... Zeno of Citium Zeno of Citium (The Stoic) (sometime called Zeno Apathea) (333 BC-264 BC) was a Hellenistic philosopher from Citium, Cyprus. ... Epicure redirects here. ... Ancient Greek literature refers to literature written in the Greek language until the 4th century AD. // Wikisource has original text related to this article: an essay on the transition to written literature in Greece This period of Greek literature stretches from Homer until the 4th century BC and the rise... For other uses, see Homer (disambiguation). ... Roman bronze bust, the so-called Pseudo-Seneca, now identified by some as possibly Hesiod Hesiod (Hesiodos, ) was an early Greek poet and rhapsode, who presumably lived around 700 BC. Hesiod and Homer, with whom Hesiod is often paired, have been considered the earliest Greek poets whose work has survived... For the PINDAR military bunker in London, please see the PINDAR section of Military citadels under London Pindar (or Pindarus, Greek: ) (probably born 522 BC in Cynoscephalae, a village in Boeotia; died 443 BC in Argos), was a Greek lyric poet. ... For other uses, see Sappho (disambiguation). ... This article is about the ancient Greek playwright. ... This article is about the Greek tragedian. ... A statue of Euripides. ... This article is about the 5-4th century BC dramatist. ... Bust of Menander Menander (342–291 BC) (Greek ), Greek dramatist, the chief representative of the New Comedy, was born in Athens. ... Herodotus of Halicarnassus (Greek: HÄ“rodotos Halikarnāsseus) was a Greek historian from Ionia who lived in the 5th century BC (ca. ... Bust of Thucydides residing in the Royal Ontario Museum, Toronto. ... Xenophon, Greek historian Xenophon (In Greek , ca. ... Mestrius Plutarchus (Greek: Πλούταρχος; 46 - 127), better known in English as Plutarch, was a Greek historian, biographer, essayist, and Middle Platonist. ... Lucian. ... Polybius (c. ... Aesop, as conceived by Diego Velázquez Aesop, as depicted in the Nuremberg Chronicle by Hartmann Schedel in 1493. ... The restored Stoa of Attalus, Athens Architecture, defined as building executed to an aesthetically considered design, was extinct in Greece from the end of the Mycenaean period (about 1200 BC) to the 7th century BC, when urban life and prosperity recovered to a point where public building could be undertaken. ... For other uses, see Parthenon (disambiguation). ... The site of the Temple of Artemis at Ephesus in Turkey. ... The Acropolis of Athens is the best known acropolis (high city, The Sacred Rock) in the world. ... Remains of the agora built in Athens in the Roman period (east of the classical agora). ... [Image:http://www. ... A 1908 illustration of the temple as it might have looked in the 5th century BCE Ruins of the Temple of Zeus at Olympia, Greece Metope showing Hercules and the Cretan Bull The Temple of Zeus at Olympia, Greece was built between 470 BCE and completed by 456 BCE to... “The Colossus of Rhodes” redirects here. ... Temple of Hephaestus, an Doric Greek temple in Athens with the original entrance facing east, 449 BC (western face depicted) Temple of Hephaestus, Athens: eastern face The Temple of Hephaestus in central ancient Athens, Greece, is the best-preserved ancient Greek temple in the world, but is far less well... General location of Samothrace The Samothrace Temple Complex, known as the Sanctuary of the Great Gods is one of the principal Pan-Hellenic religious sanctuaries, located on the island of Samothrace within the larger Thrace. ... Insert non-formatted text here This is a timeline of ancient Greece. ... Aegean civilization is a general term for the Bronze Age civilizations of Greece and the Aegean. ... The Minoan civilization was a bronze age civilization which arose on Crete, an island in the Aegean Sea. ... This article is about the Greek archaeological site. ... The Greek Dark Ages (ca. ... Parthenon This article is on the term Classical Greece itself. ... The Hellenistic period of Greek history was the period between the death of Alexander the Great in 323 BC and the annexation of the Greek peninsula and islands by Rome in 146 BC. Although the establishment of Roman rule did not break the continuity of Hellenistic society and culture, which... Roman Greece is the period of Greek history following the Roman victory over the Corinthians at the Battle of Corinth in 146 BC until the reestablishment of the city of Byzantium and the naming of the city by Emperor Constantine I as the capital of the Roman Empire (as Nova... This an alphabetical list of ancient Greeks. ... For the film of the same name, see Alexander the Great (1956 film). ... // Lycurgus Lycurgus (Greek: , Lukoûrgos; 700 BC?–630 BC) was the legendary lawgiver of Sparta, who established the military-oriented reformation of Spartan society in accordance with the Oracle of Apollo at Delphi. ... For the Shakespeare play, see Pericles, Prince of Tyre. ... Alcibiades Cleiniou Scambonides (Greek: ; English /ælsɪbaɪədi:z/; 450 BC–404 BC), also transliterated as Alkibiades, was a prominent Athenian statesman, orator, and general. ... Demosthenes (384–322 BC, Greek: Δημοσθένης, DÄ“mosthénÄ“s) was a prominent Greek statesman and orator of ancient Athens. ... Themistocles (Greek: ; c. ... For other uses, see Hippocrates (disambiguation). ... The Charioteer of Delphi, Delphi Archaeological Museum. ... The great kouros of Samos, the largest surviving kouros in Greece (Samos Archaeological Museum) The Ancient Greek word kouros meant a male youth, and is used by Homer to refer to young soldiers. ... The Lady of Auxerre, an example of a kore Kore (Greek - maiden), plural korai, is the name given to a type of ancient Greek sculpture of the archaic period, the female equivalent of a kouros. ... The Kritios boy belongs to the Late Archaic period and is considered the precursor to the later classical sculptures of athletes. ... The Doryphoros of Polykleitos The Doryphoros (Greek δορυφόρος, lit. ... Statue of Zeus The Greek sculptor Phidias created the 12-m (40-ft) tall Statue of Zeus in about 435 bc. ... Townley Discobolus, London, British Museum, with incorrectly restored head defying the balance of the figure The Discobolus of Myron (discus thrower Greek Δισκοβόλος του Μύρωνα) is a famous Roman marble copy of a lost Greek bronze original, completed during the zenith of the classical period between 460-450 BC. Myrons Discobolus was... -1... The statue of Laocoön and His Sons, also called the Laocoön Group, is a monumental marble sculpture, now in the Vatican Museums, Rome. ... Phidias Showing the Frieze of the Parthenon to his Friends by Sir Lawrence Alma-Tadema Phidias (or Pheidias) (in ancient Greek, ) (c. ... Death of Sarpedon, painted by Euphronios Euphronios was a Greek painter and potter of red-figure vases, active in Athens between 520 and 470 BC, the time of the Persian Wars. ... Polykleitos (or Polycletus, Polyklitos, Polycleitus, Polyclitus) the Elder was a Greek sculptor of the 5th century BC and the early 4th century BC. Next to famous Phidias, Myron and Kresilas he is the most important sculptor of the Classical antiquity. ... Minotaur, from a fountain in Athens, reflecting Myrons lost group of Theseus and the Minotaur (National Archeological Museum, Athens) Myron of Eleutherae (Greek Μύρων) working 480-444 BCE, was an Athenian sculptor from the mid-fifth century BCE.[1] He was born in Eleutherae on the borders of Boeotia and... Cavalry from the Parthenon Frieze, West II, British Museum. ... Praxiteles of Athens, the son of Cephisodotus, was the greatest of the Attic sculptors of the 4th century BC, who has left an imperishable mark on the history of art. ... Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... Magna Graecia around 280 b. ... Syracuse (Italian Siracusa, Sicilian Sarausa, Greek , Latin Syracusae) is an Italian city on the eastern coast of Sicily and the capital of the province of Syracuse. ... Magna Graecia around 280 b. ...


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