Karl Friedrich Gauss considered Archimedes the greatest mathematician ever, with only sir isaac newton as his equal. Archimedes’ estimation for the numerical value of pi survived as the best approximation available into the Middle Ages. However, Archimedes was most renowned for his practical applications of mathematical and physical theories. Two of his innovations, Archimedes’ principle and the Archimedes screw, involved the displacement of water, and he was considered the founder of hydrostatics.
Though little is known about Archimedes’ personal life, his own writings revealed the identity of his father, the astronomer Phidias. Archimedes was born in Syracuse on the island of Sicily in about 287 b.c. Evidence suggests that he traveled to Alexandria, where he studied mathematics under the successors of Euclid. He returned to Sicily, which was under the rule of King Hieron II, supposedly a relative or at least a friend (Archimedes dedicated The Sand-Reckoner to Hieron’s son, Gelon).
In this late text, Archimedes contrived a notation system for very large numbers, and in another text, Measurement of the Circle, he estimated the value of pi as 22/7, a relatively accurate figure. However, his applications of mathematical concepts proved even more profound than his abstract realizations. In De archi-tectura, Vitruvius told the dubious story of Archimedes’ solution to a problem posed by Hieron—how to test whether a gift crown was indeed pure gold, as claimed the giver, or alloyed with less precious metals, as Hieron suspected. As Archimedes pondered the problem in the bathtub, he noticed that the farther he immersed his body into the tub, the more water spilled over the edge. He hypothesized that the density of the displaced water equaled the density of his submerged body. In his excitement, he rushed through the streets naked shouting in Greek, "Heurgka!" While testing the authenticity of the crown, he noticed that a block of pure gold equal in weight to the crown displaced less water than the crown, thus casting doubt on its veracity.
This test, which hinged on relative density and buoyancy, became known as Archimedes’ principle. Archimedes described this principle, along with his understanding of buoyancy (or the upward force exerted on solids by liquids), in On Floating Bodies, a text that established him as the founder of hydrostatics. Of even greater practical value was his invention of what became known as the Archimedes screw, a device that could draw water along an ascending helix.
Archimedes was apparently most proud of his formulation of the volume of a sphere as two-thirds that of the cylinder in which it is inscribed, as discussed in one of his most famous works, On the Sphere and the Cylinder. When Cicero was the Quaestor of Sicily in 75 b.c., he tracked down Archimedes’ grave and verified that it was indeed inscribed with a sphere and cylinder as well as the formula for their intersection.
Hieron called upon Archimedes to invent weapons to stay the Roman invasion of Sicily in 215 b.c., led by Marcellus. Experts doubt that Archimedes invented the weapon of mirrors that ignited distant ships with focused sunlight, though he did invent various catapults. Marcel-lus ultimately captured Sicily in 212 b.c., and though the general himself admired Achimedes’ work, his soldiers put the mathematician to death, supposedly while he was making calculations in the sand.
