Who was Archimedes?
Archimedes was a Greek mathematician and inventor who was born in 287 BC in Syracuse, a Greek city-state in Italy. He spent most of his life in Syracuse and collaborated with multiple fellow mathematicians, including Conon of Samos and Eratosthenes of Cyrene, to make new discoveries.
Simulations and Inventions
Archimedes made several renowned contributions to science and math. He created two spheres—one was a star globe, and the other was a mechanical representation of the movements of the sun, moon, and planets. His Archimedes screw pump, a device used to raise water for irrigation pumps using a rotating helix screw, is still used in developing countries today.
Mathematic Formulas
Two of Archimedes’ acclaimed mathematical accomplishments include the discoveries of formulas for calculating the surface area and volume of a sphere. Archimedes determined that the surface area of a sphere with radius r can be calculated as four times the area of its biggest circle, also known as SA = 4
r². He also deduced that the volume of any sphere is 2/3 that of a cylinder in which it is inscribed, resulting in the formula for volume of a sphere: V = 
r³. This discovery was important enough to Archimedes that he left instructions for his tomb to show a drawing of a sphere inscribed inside a cylinder upon his death.
The "Eureka" Legend
One famous story about Archimedes involves his quest to calculate the proportion of gold and silver contained in an ornate wreath as per the orders of King Hieron II. According to legend, Archimedes discovered suddenly that he could observe the relative densities of gold and silver by weighing the wreath in water; as he was in his bathtub when he came upon this realization, he supposedly ran through Syracuse naked shouting “Eureka!” This tale is likely untrue, but it is an amusing way of remembering another of Archimedes’ accomplishments.
Legacy
Archimedes died in either 212 or 211 BC in Syracuse, but his inventions and equations remain full of life—as does the striking image of him sprinting through Syracuse, bursting with excitement about his latest discovery.
Discussion Questions
- Why might Archimedes’ work with both mathematics and machines have made each area of study more useful to him?
- What does Archimedes’ interest in the sphere-and-cylinder relationship suggest about what he valued in mathematics?
- Why should readers distinguish the famous “Eureka” story from Archimedes’ documented mathematical accomplishments?
- How does the Archimedes screw illustrate the way an ancient idea can remain useful long after its inventor’s lifetime?