Archimedes

Archimedes (287BC-212BC) was a Greek mathematician, scientist, and engineer. Born in Syracuse, Sicily, Archimedes was the son of the astronomer Pheidias. Archimedes ranks as one of the greatest mathematicians (if not the greatest ever) who ever lived. His mathematical work and inventions were so modern in spirit and technique that they were barely distinguishable from those of modern times. Among his mathematical achievements, Archimedes developed a general method (integration) for finding areas and volumes, and he used the method to find areas bounded by parabolas and spirals and to find volumes of cylinders, paraboloids, and segments of spheres. He gave a procedure for approximating π.

Archimedes was most proud of his discovery of a method for finding the volume of a sphere- he showed that the volume of a sphere is two-thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and a cylinder was engraved on his tombstone. 


In addition to mathematics, Archimedes worked extensively in the development of mechanics and hydrostatics. Archimedes actually created the discipline of hydrostatics and he used it to find the equilibrium position for various floating bodies. Almost every schoolchild knows Archimedes as the absent-minded scientist who, on realising that a floating object displaces its own weight of liquid, leaped from his bath and ran naked down the streets of Syracuse shouting, “Eureka!”, “Eureka!”- meaning, “I have found it!”

Archimedes laid down the fundamental laws of mechanics, discovered the laws of levers and calculated centres of gravity for various flat surfaces and solids. In the excitement of discovering the mathematical laws of the lever and various machines, he is said to have declared, “Give me a place to stand and I will move the Earth!”

Although Archimedes was apparently more interested in pure mathematics, he was an engineering genius. He invented super catapults that showered the Romans with rocks weighing a quarter of a ton or more, giant parabolic mirrors that set the Roman ships ablaze and fearsome mechanical devices with iron “beaks and claws” that reached over the city walls, grasped the ships, and spun them against the rocks. The Roman general Macellus called Archimedes a “geometrical Briareus (a hundred-armed mythological monster) who uses our ships like cups to ladle water from the sea”. Archimedes held the Roman fleet at bay for more than three years before a Greek traitor allowed the Roman Army into the city one evening. Contrary to Macellus’ specific orders, the 75 year-old Archimedes was killed by a Roman soldier when he cast a shadow on a mathematical problem that he was working on; the annoyed Archimedes yelled, “Don’t disturb my circles”, which made the soldier fly into a rage and cut the old man down.

Although Archimedes wrote many books, only nine works have survived to the present day. His treatise, ‘The Methods of Mechanical Theorems’, was discovered in Constantinople in 1906. In this treatise, Archimedes explains how he made his discoveries using reasoning based upon the integral calculus of modern times! Mathematicians are now becoming increasingly aware, that Archimedes actually discovered integration more than 1800 years before Newton and Leibniz had. Furthermore, it is suspected that the Antikythera mechanism, a complex differential mechanical system, that was the first ever computer discovered in a sunken ship at the bottom of the sea, off the island of Antikythera, is believed to have been invented by Archimedes to calculate solar and lunar eclipses and constructing calendars based on the relative position of stars, and may also have been used for navigation!

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