Archimedes

 Archimedes

                                                                       

Born: - 287 BC

Died: - 212 BC

Books: - Floating Bodies, Spirals, The Sand Reckoner, Measurement of the  Circle,

Main Contribution:- Found that the value of pi lies between 22/7 and 223/71 , Archimedes' principle , Archimedes screw (a device for raising water) etc.

Archimedes was a native of Syracuse, Sicily where he was born in 287 BC. His father Phidias was an astronomer. There is no more information available about his family background. He studied at Euclid's school (probably after Euclid's death), but his work far surpassed the works of Euclid.

 Archimedes is universally acknowledged to be the greatest of ancient mathematicians. He had gained the reputation in his own time which few other mathematicians of this period achieved. Some math historians consider Archimedes to be one of history's greatest mathematicians, along with possibly Newton, Gauss, and Euler. He is therefore called – the wise man, the master, and the great geometer.  Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch.

His achievements are particularly impressive given the lack of good mathematical notation in his day. His proofs are noted not only for brilliance but for their "awesome" clarity. Archimedes made advances in number theory, algebra, and analysis, but is most renowned for his many theorems of plane and solid geometry.  His excellent approximation to √3 indicates that he'd partially anticipated the method of continued fractions. He found a method to trisect an arbitrary angle.  His original achievements in physics include the principles of leverage, the first law of hydrostatics, and inventions like the compound pulley, the hydraulic screw, and war machines. He had invented more machines which were used as engines of war that were particularly effective in the defence of Syracuse when it was attacked by the Romans.

                  Archimedes Screw

His books include Floating Bodies, Spirals, The Sand Reckoner, Measurement of the Circle, and Sphere and Cylinder.  Archimedes proved that the volume of a sphere is two-thirds the volume of a circumscribing cylinder. He requested that a representation of such a sphere and cylinder be inscribed on his tomb. Archimedes discovered formulae for the volume and surface area of a sphere, and may even have been first to notice and prove the simple relationship between a circle's circumference and area. For these reasons, π is often called Archimedes' constant. His approximation 223/71 < π < 22/7 was the best of his day.

His fascination with geometry is beautifully described by Plutarch:-

Of times Archimedes' servants got him against his will to the baths, to wash and anoint him, and yet being there, he would ever be drawing out of the geometrical figures, even in the very embers of the chimney. And while they were anointing of him with oils and sweet savours, with his fingers he drew lines upon his naked body, so far was he taken from himself, and brought into ecstasy or trance, with the delight he had in the study of geometry.

His most famous theorem which gives the weight of a body immersed in liquid called Archimedes principle 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. 

Legend has it that Archimedes discovered his famous theory of buoyancy - Archimedes Principle - while taking a bath. He was so excited that he ran naked through the streets of Syracuse shouting "Eureka, eureka (I have found it)!” He used this principle to unearth the truth of the Golden crown of the king Hieron II of Syracuse.

His famous quote is -"Give me a place to stand and rest my lever on, and I can move the Earth."

The mathematical genius of such repute was beheaded mercilessly by the Roman soldier in 212 BC while Archimedes was busy solving a sum on sand.  He was buried at Syracuse, where he was born, grew up, worked and died. On his grave there is an inscription of pi, his most famous discovery. His followers also placed on his tombstone the figure of a sphere inscribed inside a cylinder and the 2:3 ratios of the volumes between them, the solution to the problem he considered his greatest achievement.