Archimedes: Mathematics, Mechanics, and the Defence of Syracuse
The ancient world produced no mind more astonishing than Archimedes of Syracuse. Born around 287 BCE in the Greek colony of Syracuse on Sicily, he spent most of his life there, maintaining scholarly correspondence with the Library of Alexandria and producing a body of work in mathematics and mechanics that was not surpassed until the seventeenth century. His mathematical achievements were breathtaking in scope and rigour. Using a method of exhaustion anticipating integral calculus, he calculated the area of a circle, the surface area and volume of a sphere, and the area under a parabola. He approximated pi as lying between 223/71 and 22/7, a result accurate to within 0.04 percent. His work The Sand Reckoner invented a notation system for expressing astronomically large numbers and used it to estimate the number of grains of sand that could fill the universe, demonstrating in passing that Aristarchus had proposed a heliocentric model of the solar system. The Method, rediscovered in a Constantinople palimpsest only in 1906, reveals a heuristic technique using mechanical reasoning to derive results he would then prove rigorously — a proto-integration method two thousand years before Leibniz and Newton. His mechanics were equally transformative. The principle of the lever, the concept of centre of gravity, and the hydrostatic principle now bearing his name (a body immersed in fluid is buoyed up by a force equal to the weight of the fluid displaced) were all his formulations. The story of Eureka, running naked through Syracuse after detecting gold fraud in a crown by measuring water displacement, may be apocryphal but captures his methods. The Archimedean screw, a helical device for raising water, remains in use today. His compound pulleys allegedly allowed a single man to drag a fully laden ship across the harbour. The most dramatic test of his engineering genius came during the Roman siege of Syracuse (214–212 BCE). Serving his friend and kinsman King Hiero II, Archimedes designed a battery of war machines that paralysed the Roman assault for two years: giant cranes that lifted enemy ships out of the water and capsized them, catapults calibrated to varying ranges, and possibly mirrors focusing sunlight to ignite Roman sails. The Roman general Marcellus, awed and frustrated, reportedly called him 'that geometrical Briareus.' When Syracuse finally fell in 212 BCE, Marcellus gave explicit orders that Archimedes was to be spared. According to several ancient sources, a Roman soldier found him drawing geometric figures in the sand and killed him when he refused to leave before finishing his proof. Marcellus is said to have wept and arranged an honourable burial.
- Year: 250 BCE
- Category: Scientific
