Archimedes of Syracuse (287 BC -  212 BC) was an ancient Greek mathematician, physicist and engineer. Although little is known about his life, he is regarded as one of the most important scientists in classical antiquity. In addition to making important discoveries in the field of mathematics and geometry, he is credited with producing machines that were well ahead of their time. The Ancient Roman historians showed a strong interest in Archimedes and wrote several biographies relating to his life and works, while the few copies of his treatises that survived through the Middle Ages were a major influence on scientists during the Renaissance. Archimedes produced the first known summation of an infinite series with a method that is still used in the area of calculus today. Archimedes was a famous mathematician whose theorems and philosophies became world known. He gained a reputation in his own time which few other mathematicians of this period achieved. He is considered by most historians of mathematics as one of the greatest mathematicians of all time. Biography Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, which was then a colony of Magna Graecia. The date of his birth is based on an assertion by the Byzantine Greek historian John Tzetzes that he lived for seventy-five years. In The Sand Reckoner Archimedes gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote that Archimedes was related to King Hieron II, the ruler of Syracuse. A biography of Archimedes was written by his friend Heracleides but this work has been lost, leaving the details of his life obscure. It is unknown, for instance, whether he ever married or had children. Archimedes is believed to have spent part of his youth being educated in Alexandria, Egypt where he was a contemporary of Conon of Samos and Eratosthenes. Some of Archimedes' mathematical works were written in the form of letters to Eratosthenes, who was the chief librarian in Alexandria. 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 in his Parallel Lives , 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. The last words attributed to Archimedes are "Do not disturb my circles". 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. Archimedes' tomb 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 visited the tomb in Syracuse which had become overgrown with scrub. 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. The account of the siege of Syracuse given by Polybius in his Universal History was written some seventy years after the death of Archimedes, and was used 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. Discoveries and Inventions Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch. According to Plutarch, Archimedes had so low an opinion of the kind of practical invention at which he excelled and to which he owed his contemporary fame that he left no written work on such subjects. While it is true that--apart from a dubious reference to a treatise, On Sphere-Making - all of his known works were of a theoretical character, nevertheless his interest in mechanics deeply influenced his mathematical thinking. Not only did he write works on theoretical mechanics and hydrostatics, but his treatise Method Concerning Mechanical Theorems shows that he used mechanical reasoning as a heuristic device for the discovery of new mathematical theorems. He was best known for his discovery of the relation between the surface and volume of a sphere and its circumscribing cylinder, for hisformulation of a hydrostatic principle Archimedes' principle and for inventing the Archimedes screw (a device for raising water). Archimedes Principal states: an object immersed in a fluid experiences a buoyant force that is equal in magnitude to the force of gravity on the displaced fluid. He also invented things such as the hydraulic screw - for raising water from a lower to a higher level, catapult, the lever, the compound pulley and the burning mirror. In mechanics Archimedes discovered fundamental theorems concerning the center of gravity of plane figures and solids. Archimedes probably spent some time in Egypt early in his career, but he resided for most of his life in Syracuse, the principal city-state in Sicily, where he was on intimate terms with its king, Hieron II. Archimedes published his works in the form of correspondence with the principal mathematicians of his time, including the Alexandrian scholars Conon of Samos and Eratosthenes of Cyrene. He played an important role in the defense of Syracuse against the siege laid by the Romans in 213 BC by constructing war machines so effective that they long delayed the capture of the city. But Syracuse was eventually captured by the Roman general Marcus Claudius Marcellus in the autumn of 212 or spring of 211 BC, and Archimedes was killed in the sack of the city. Archimedes Screw Archimedes Screw, or Archimedean screw, or screwpump, is a machine historically used for transferring water from a low-lying body of water into irrigation ditches. It is one of several inventions and discoveries reputed to have been made by Archimedes, but as some researchers suggest, some form of this mechanism may have been used earlier by Sennacherib, King of Assyria, in the 7th century BC. Modern screw pumps, consisting of helices rotating in open inclined troughs, are effective for pumping sewage in wastewater treatment plants. The open troughs and the design of the screws permit the passage of debris without clogging. The Burning Mirror (Glass) Archimedes invented many machines which were used as engines of war. These were particularly effective in the defense of Syracuse when it was attacked by the Romans under the command of Marcellus. During the Roman siege of Syracuse, he is said to have single-handedly defended the city by constructing lenses to focus the Sun's light on Roman ships and huge cranes to turn them upside down. When the Romans finally broke the siege, Archimedes was killed by a Roman soldier after snapping at him, "Don't disturb my circles,'' a reference to a geometric figure he had outlined on the sand. While Archimedes did not invent the lever, he gave the first rigorous explanation of the principles involved, which are the transmission of force through a fulcrum and moving the effort applied through a greater distance than the object to be moved.   His Law of the Lever states: Magnitudes are in equilibrium at distances reciprocally proportional to their weights. 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." 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. 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 describes 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. According to Athenaeus, it was capable of carrying 600 people and contained garden decorations, a gymnasium and a temple dedicated to the goddess Aphrodite. Since a ship of this size would leak a considerable amount of water through the hull, the Archimedes' Screw was said to have been developed in order to remove the bilge water. Archimedes had stated in a letter to King Hieron that given the force, any given weight might be moved, and even boasted, we are told, relying on the strength of demonstration, that if there were another earth, by going into it he could remove this. Hiero being struck with amazement at this, and entreating him to make good this problem by actual experiment, and show some great weight moved by a small engine, he fixed accordingly upon a ship of burden out of the king's arsenal, which could not be drawn out of the dock without great labor and many men; and, loading her with many passengers and a full freight, sitting himself the while far off, with no great endeavor, but only holding the head of the pulley in his hand and drawing the cords by degrees, he drew the ship in a straight line, as smoothly and evenly as if she had been in the sea. The Spheres Archimedes is supposed to have made two "spheres" that Marcellus took back to Rome - one a star globe and the other a device (the details of which are uncertain) for mechanically representing the motions of the Sun, Moon, and planets. One was a solid sphere on which were engraved or painted the stars and constellations, which Marcellus placed in the Temple of Virtue. Such celestial globes predate Archimedes by several hundred years and Cicero credits the famed geometers Thales and Eudoxos with first constructing them. The second sphere, which Marcellus kept for himself, was much more ingenious and original. It was a planetarium: a mechanical model which shows the motions of the sun, moon, and planets as viewed from the earth. Cicero writes that Archimedes must have been "endowed with greater genius that one would imagine it possible for a human being to possess" to be able to build such an unprecedented device. Many other ancient writers also refer to Archimedes' planetarium in prose and in verse. Several viewed it as proof that the cosmos must have had a divine creator: for just as Archimedes' planetarium required a creator, so then must the cosmos itself have required a creator. Cicero reverses the argument to contend that since the cosmos had a divine creator, so then must Archimedes be divine to be able to imitate its motions. The Greek mathematician Pappus of Alexandria, who lived in the fourth century AD, writes that Archimedes wrote a now-lost manuscript entitled On Sphere-making. Pappus also states that it was the only manuscript that Archimedes wrote on "practical" matters. No physical trace of Archimedes' planetarium survives. Cicero refers to it as a "bronze contrivance" while Claudian describes it as "a sphere of glass." The 1752 engraving of Rowley's orrery suggests how Archimedes' planetarium might have looked. On this orrery the sun, moon and planets revolve along a flat surface driven underneath by a hidden gear works. Spherical bands surrounding the flat surface represent the celestial equator, the arctic circle, a movable horizon, and the ecliptic marked with the zodiacal signs. In 1900 a shipwreck discovered off the shore of the Greek island of Antikythera uncovered an unexpected treasure. The ship dated from the first century BC and was sailing from the Greek island of Rhodes. Amidst its cargo was a complicated gear works in a deteriorated state about the size of a cigar box. The device, now called the Antikythera mechanism, was analyzed by Derek De Solla Price of Yale University, who concluded that it was an ancient planetarium in which the positions of the heavenly bodies were indicated by dials on the face of the device. The gear works are about as complicated as those in a modern mechanical clock and represent the earliest physical evidence of an advanced metallic mechanism. Price gives evidence that this mechanism was in the Archimedean tradition and strongly suggests that Archimedes' planetarium was its forerunner. A complete presentation of Price's research can be found in Gears from the Greeks.