Saturday, July 28, 2012

Ἀρχιμήδης +++ Archimedes of Syracuse

Archimedes of Syracuse 
(Greek: Ἀρχιμήδης; 287 BC - 212 BC)

video "Secrets of Archimedes" (52:41)

Archimedes of Syracuse was an outstanding Greek mathematician, inventor, physicist, engineer and also an astronomer. Although not much is known about his life, he is considered as one of the most eminent scientists in classical antiquity. He established strong foundations in the field of physics, particularly in statics, hydrostatics and explained the principle of the lever. In his lifetime, he made many incredible inventions such as designing innovative machines, including screw pumps and siege machines, After intensive experiments, it is concluded that the machines designed by Archimedes are capable of lifting attacking ships out of the water and even setting ships on fire using an array of mirrors. Undoubtedly, Archimedes is considered the greatest scientist and mathematician of ancient times. He applied the 'method of exhaustion' in calculating the area under the arc of a parabola with the summation of an endless series and gave a marvelously precise approximation of pi, the symbol. He also identified the spiral that bears his name, designed formulae for the volumes of surfaces of revolution and also invented a technique for expressing extremely large numbers. Archimedes was born in c. 287 BC in the seaport city of Syracuse, Sicily, which was a self-governing colony in Magna Graecia. His birth date is based on the calculations done by the Byzantine Greek historian John Tzetzes who concluded that Archimedes lived for around 75 years. In ‘The Sand Reckoner’, his father’s name is mentioned as ‘Phidias’, who was an astronomer, about whom nothing much is known. Plutarch marked in his ‘Parallel Lives’ that Archimedes was related to King Hiero II, the ruler of Syracuse. However, many aspects of Archimedes are still mysterious. For instance, whether he ever married or not or whether he had children are details that aren’t available at all. According to the information available, it is supposed that during his youth, Archimedes may have studied in Alexandria, Egypt, where Conon of Samos and Eratosthenes of Cyrene were his classmates. Archimedes had also referred to Conon of Samos as his friend and, on the other hand, two of his works viz., the Cattle Problem and the Method of Mechanical Theorems have introductions focused on Eratosthenes.

Famous Discoveries And Inventions
Archimedes' Principle
The most popular tale about Archimedes is regarding how he discovered a method for calculating the volume of objects with irregular shape. According to Vitruvius, a crown for a temple had been made for King Hiero II, who had supplied the pure gold to be used and Archimedes was asked to verify whether any silver had been used by the deceitful goldsmith. Archimedes was expected to solve the problem without damaging the crown and thus the option of melting it down into a regular shape was ruled out. One day, while taking a bath, he discerned that the level of the water in the tub increased as he got in, and comprehended that this effect could be used to determine the volume of the crown. As water is incompressible practically, so the crown after submerging would displace an amount of water equal to its own density and it would be possible to calculate the density of the crown if mass of the crown was divided by the volume of water displaced. Archimedes was so excited that he ran on the streets naked (he forgot to dress up), crying out ‘Eureka!’ meaning ’I have found it!’ The test was conducted successfully, concluding that silver had certainly been mixed with the gold.
Archimedes' Screw
Archimedes analyzed the requirements in his home city of Syracuse and tried to make inventions useful for the people at large. The Greek writer Athenaeus of Naucratis had mentioned how King Hiero II instructed Archimedes to devise a gigantic ship, the ‘Syracusia’, which could be used to travel lavishly with supplies as well as can double up as a naval warship. Thus, Syracusia is known to be the largest ship built in olden days. Athenaeus had claimed that the ship was competent of carrying 600 people and consisted of attractions such as garden decorations, a fitness center and a temple dedicated to the goddess Aphrodite, to name a few. Archimedes invented a screw to remove the bilge water to prevent the massive ship from leaking a substantial amount of water through the hull. Archimedes' screw could be described as a device with a spinning screw-shaped blade inside a cylinder. It was turned manually and could also be used to relocate water from a low-lying water body into irrigation canals. The Archimedes screw is still used to propel liquids as well as solids like grain and coal.
Claw Of Archimedes
The Claw of Archimedes is a weapon that he devised in order to guard the city of Syracuse. The claw is also referred to as "the ship shaker," and comprised of a crane-like arm from which a large metal-grasping hook was hung. When the claw was plunged onto an attacking ship, the arm would swing upwards, lifting the ship out of the water and perhaps even sinking it. Contemporary experiments have been done to examine the practicality of the weapon and, in 2005, a television documentary ‘Superweapons of the Ancient World’ constructed a form of the claw and declared that it was an effective device.
Heat Rays
Lucian, the 2nd century AD author, scripted that during the Siege of Syracuse (c. 214–212 BC) Archimedes shattered enemy ships with fire! After many years, Anthemius of Tralles wrote about burning-glasses as Archimedes' weapon. The device, also known as the ‘Archimedes heat ray’, was used to direct sunlight onto approaching ships, causing them to catch fire. Even a Greek scientist ‘Ioannis Sakkas’, conducted a test of the Archimedes heat ray in 1973. During this experiment, 70 mirrors were used, each coated with copper and about five by three feet (1.5X1 m) in size. The mirrors were faced at a plywood replica of a Roman warship, 160 feet (50m) far. When the mirrors were focused precisely, the ship burst into flames in a matter of few seconds.
The genius Archimedes was even capable of using infinitesimals in a manner similar to the modern integral calculus. Through proof by contradiction, he gave answers to problems to a great degree of exactness, while defining the boundaries within which the answer lays. This modus operandi is known as the method of exhaustion, and he employed it to find the approximate value of π. Archimedes also extended his intelligence in the measurement of circles when he gave the value of the square root of 3 as lying around 265⁄153 (approximately 1.7320261) and 1351⁄780 (approximately 1.7320512). The actual value is approximately 1.7320508, making this a very accurate calculation. In ‘The Quadrature of the Parabola’, Archimedes verified that the area encircled by a parabola and a straight line is 4⁄3 times the area of an equivalent inscribed triangle. He expressed the answer to the problem as an infinite geometric series with the common ratio 1⁄4.
Death And Legacy
When Syracuse was captured in 212 BC, during the Second Punic War under General Marcellus, a roman soldier killed Archimedes despite explicit orders to not harm him. According to the popular tale by Plutarch, Archimedes was studying a mathematical diagram and a Roman soldier ordered him to come and meet General Marcellus but Archimedes resisted, saying that he had to finish working on the matter. The soldier was furious and killed Archimedes with his sword. However, Plutarch has also mentioned another possibility to Archimedes’s death, that he may have been killed while endeavoring to surrender to a Roman soldier. According to this legend, Archimedes was carrying mathematical instruments and was murdered because the soldier had the impression that those instruments were precious items. General Marcellus was obviously enraged and the fate of the soldier can only be assumed. The last words accredited to Archimedes are, "Do not disturb my circles!" but again, there isn’t any concrete proof that Archimedes did, in fact, utter these words and they aren’t mentioned in the brief given by Plutarch.
A sphere carved within a cylinder covers the tomb of Archimedes. This is based on a remarkable invention made by Archimedes proving that the sphere has two thirds of the volume and surface area of the cylinder (including the bases of the latter). This is considered as his greatest mathematical accomplishment.

There are many legacies attached to Archimedes:
  • A crater on the Moon is called ‘Archimedes ’to revere him’ and a lunar mountain range is known as ‘the Montes Archimedes’.
  • The asteroid ‘3600 Archimedes’ is named after this ancient scientist.
  • The Fields Medal for exceptional achievement in mathematics illustrates a portrait of Archimedes, along with his proof relating to the cylinder and the sphere. The message around the head of Archimedes is a quote credited to him that reads – ‘Rise above oneself and grasp the world’.
  • Archimedes has also appeared on postage stamps issued by Spain (1963), Nicaragua (1971), East Germany (1973), San Marino (1982), Greece (1983) and Italy (1983).
  • The exclamation of ‘Eureka!’, attributed to Archimedes, became a state motto of California and relates to the discovery of gold near Sutter's Mill in 1848 that ignited the California Gold Rush. 
Such was the brilliance of this great personality that almost every scientific field can boast of having adopted something from his inventions. The lack of details available regarding his personal life only adds to the enigma of this great man and makes him a cult figure for the intellectuals.

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