# Obituary: Density and Syracuse Archimedes

Applying math to real life

September 3, 2010

Obituary for Archimedes of Syracuse

Archimedes was born in Syracuse, Italy in 287 B.C. His father was Pheidias, who happened to be an astronomer. He studied at Alexandria, Egypt. He was also close friends with the King of Syracuse. He died in 212 B.C. Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid, excelling especially at computing areas and volumes using the method of exhaustion. He was especially proud of his discovery for finding the volume of a sphere, showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder was engraved on his tombstone. In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle. Archimedes was also an outstanding engineer, formulating Archimedes' principle of buoyancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is supposed to have run naked through the streets of Syracuse shouting "Eureka!" (I have found it). Archimedes is also purported to have invented the Archimedean screw. Some of Archimedes's geometric proofs were actually motivated by mechanical arguments which led him to the correct answer. During the Roman siege of Syracuse, he is said to have single-handedly defended the city by constructing lenses to focus the Sun's light on Roman ships and huge cranes to turn them upside down. When the Romans finally broke the siege, Archimedes was killed by a Roman soldier after snapping at him "Don't disturb my circles," a reference to a geometric figure he had outlined on the sand.

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