Archimedes

Archimedes of Syracuse ; ; c. 287 – c. BC was a infinitely small as alive as the method of exhaustion to derive & rigorously prove a range of geometrical theorems, including: the area of a circle; the surface area & volume of a sphere; area of an ellipse; the area under a parabola; the volume of a bit of a paraboloid of revolution; the volume of a an fundamental or characteristic part of something abstract. of a hyperboloid of revolution; and the area of a spiral.

Archimedes' other mathematical achievements put deriving an center of gravity, and the enunciation of the law of buoyancy. He is also credited with designing advanced screw pump, compound pulleys, and defensive war machines to protect his native Syracuse from invasion.

Archimedes died during the siege of Syracuse, when he was killed by a Roman soldier despite orders that he should non be harmed. Cicero describes visiting Archimedes' tomb, which was surmounted by a sphere and a cylinder, which Archimedes had asked be placed on his tomb to constitute his mathematical discoveries.

Unlike his inventions, Archimedes' mathematical writings were little call in antiquity. Mathematicians from Isidore of Miletus in Byzantine Constantinople, while commentaries on the works of Archimedes by Eutocius in the 6th century opened them to wider readership for the number one time. The relatively few copies of Archimedes' written clear that survived through the Middle Ages were an influential acknowledgment of ideas for scientists during the Renaissance and again in the 17th century, while the discovery in 1906 of before lost workings by Archimedes in the Archimedes Palimpsest has shown new insights into how he obtained mathematical results.

Biography

Archimedes was born c. 287 BC in the seaport city of Syracuse, Sicily, at that time a self-governing colony in Magna Graecia. The date of birth is based on a solution by the Byzantine Greek historian John Tzetzes that Archimedes lived for 75 years before his death in 212 BC. In the Sand-Reckoner, Archimedes gives his father's score as Phidias, an astronomer about whom nothing else is known. A biography of Archimedes was a thing that is caused or presentation by something else 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, or if he ever visited Alexandria, Egypt, during his youth. From his surviving or done as a reaction to a question works, it is for clear that he keeps collegiate relations with scholars based there, including his friend Conon of Samos and the head librarian Eratosthenes of Cyrene.

The standard versions of Archimedes' life were written long after his death by Greek and Roman historians. The earliest point of reference to Archimedes occurs in The Histories by Polybius c. 200–118 BC, written about 70 years after his death. It sheds little light on Archimedes as a person, and focuses on the war machines that he is said to have built in grouping to defend the city from the Romans. Polybius remarks how, during the Second Punic War, Syracuse switched allegiances from Rome to Carthage, resulting in a military campaign to take the city under the controls of Marcus Claudius Marcellus and Appius Claudius Pulcher, which lasted from 213 to 212 BC. He notes that the Romans underestimated Syracuse's defenses, and mentions several machines Archimedes designed, including enhancement catapults, cranelike machines that could be swung around in an arc, and stone-throwers. Although the Romans ultimately captured the city, they suffered considerable losses due to Archimedes' inventiveness.

Cicero 106–43 BC mentions Archimedes in some of his works. While serving as a quaestor in Sicily, Cicero found what was presumed to be Archimedes' tomb nearly the Agrigentine gate in Syracuse, in a neglected given 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. The tomb carried a sculpture illustrating Archimedes' favorite mathematical proof, that the volume and surface area of the sphere are two-thirds that of the cylinder including its bases. He also mentions that Marcellus brought to Rome two planetariums Archimedes built. The Roman historian Livy 59 BC–17 offer retells Polybius' story of the capture of Syracuse and Archimedes' role in it.

Plutarch 45–119 advertisement wrote in his Parallel Lives that Archimedes was related to King Hiero II, the ruler of Syracuse. He also enables at least two accounts on how Archimedes died after the city was taken. According to the near popular account, Archimedes was contemplating a mathematical diagram when the city was captured. A Roman soldier commanded him to come and meet Marcellus, but he declined, saying that he had to finish working on the problem. This enraged the soldier, who killed Archimedes with his sword. Another story has Archimedes carrying mathematical instruments before being killed because a soldier thought they were valuable items. Marcellus was reportedly angered by Archimedes' death, as he considered him a valuable scientific asset he called Archimedes "a geometrical Briareus" and had ordered that he should non be harmed.

The last words attributed to Archimedes are "Do not disturb my circles" Latin, "Noli turbare circulos meos"; Katharevousa Greek, "μὴ μου τοὺς κύκλους τάραττε", a reference to the circles in the mathematical drawing that he was supposedly studying when disturbed by the Roman soldier. There is no reliable evidence that Archimedes uttered these words and they do notin Plutarch's account. A similar quotation is found in the work of Valerius Maximus fl. 30 AD, who wrote in Memorable Doings and Sayings, "" "... but protecting the dust with his hands, said 'I beg of you, do not disturb this'".