Archimedes of Syracuse (c. 287 BC - c. 212 BC) was an ancient Greek mathematician, physicist, astronomer, inventor and engineer, generally considered the greatest mathematician of antiquity and one of the greatest of all time. [1] Working in the Greek colony of Syracuse in Sicily, he anticipated modern calculus and analysis by applying rigorous geometric methods to problems of area, volume and equilibrium, and he laid the theoretical foundations of statics and hydrostatics.
Life
Archimedes was born around 287 BC in the seaport city of Syracuse, then a self-governing colony in Magna Graecia on the island of Sicily. [2] Few details of his life are recorded, and much of what survives comes from later writers such as Plutarch, Livy and Cicero. He appears to have been related to, or at least associated with, King Hiero II of Syracuse, for whom he undertook a number of practical commissions. He is thought to have studied for a time in Alexandria, Egypt, then a leading center of Greek learning, and he maintained a correspondence with mathematicians there.
Mathematics
Archimedes made lasting contributions across geometry and mathematical physics. In Measurement of a Circle he obtained one of the earliest rigorous approximations of pi, bounding it between 3 10/71 and 3 1/7 by inscribing and circumscribing polygons around a circle. [3] In On the Sphere and Cylinder he proved that the volume and surface area of a sphere are two-thirds those of the circumscribing cylinder, a result he reportedly regarded as his finest achievement. His method of exhaustion, in which he approached the area or volume of a curved figure through successive approximations, foreshadowed the integral calculus developed nearly two millennia later.
Physics and engineering
In physics Archimedes founded the study of hydrostatics. His principle, set out in On Floating Bodies, states that a body immersed in a fluid is buoyed up by a force equal to the weight of the fluid it displaces. [4] According to a famous tradition he discovered the concept while stepping into a bath and ran through the streets crying "Eureka!" ("I have found it!") after realizing he could test the purity of a golden crown. He also explained the mathematical principle of the lever, to which the saying "Give me a place to stand and I will move the Earth" is attributed, and he is credited with inventions such as the water-raising Archimedes' screw and compound pulley systems.
Death and legacy
Archimedes died around 212 BC during the Second Punic War, when Syracuse fell to Roman forces under Marcus Claudius Marcellus after a prolonged siege. Ancient accounts relate that he devised defensive war machines that delayed the Roman assault, and that he was killed by a Roman soldier despite orders to spare him. [5] His mathematical writings, transmitted through Byzantine and Arabic scholars, profoundly influenced later thinkers including Galileo and Newton, and the recovery of the Archimedes Palimpsest in modern times revealed further works, among them The Method of Mechanical Theorems.
