Archimedes

c. 287-212 B.C.

Greek Mathematician and Engineer

Heralded as one of the foremost mathematical geniuses of all time, Archimedes made major contributions to the fields of geometry and mechanics, and laid the groundwork for the much later development of logarithms and calculus. Some of his most famous work included the relationships between the volumes and surface areas of spheres, cones, and cylinders thatshare the same dimensions of base and height. His work influenced scientists for years to come, including Galileo Galilei (1564-1642) and Isaac Newton (1642-1727).

Born around 287 B.C., Archimedes was the son of the astronomer Phidias and was possibly related to Sicily's King Hieron II. Archimedes temporarily left his childhood home in the Sicilian port of Syracuse to take up studies in Alexandria, the cultural hub of Greece, at the school established by Euclid (c. 300 B.C.) a few decades earlier.

The young man quickly became enthralled by mathematics and maintained his enthusiasm for the field throughout his life. Over the years, he produced many mathematical treatises, including On the Equilibrium of Planes, On the Sphere and Cylinder and On Floating Bodies. In the first, he considered the mechanics of levers and the importance of the center of gravity in balancing equal weights.

In On the Sphere and Cylinder, Archimedes built on the previous work of Euclid to reach conclusions about spheres, cones, and cylinders. As described in The Scientific 100 (Simmons 1996): "He showed that if these figures have the same base and height-imagine a cone inscribed in a hemisphere which itself is inscribed within a cylinder-the ratio of their volumes will be 1:2:3. In addition, the surface of the sphere is equivalent to two-thirds of the surface of the cylinder which encloses it." Archimedes was immensely pleased with this discovery, even requesting that his family have a sphere and cylinder engraved on his tombstone.

Archimedes used On Floating Bodies to recount his theory regarding water displacement and help found the science of hydrostatics. In this book, he demonstrated that when an object of any shape and weight is floated in water, its vertical, buoyant force is equal to the weight of the water it displaces. One legend of Archimedes holds that he first understood this connection between the weight of a floating object and the resulting increase in water level while watching bath water rise as he sunk his body into a tub. He was said to have been so excited by this insight that he jumped from the tub and ran stark naked through the streets proclaiming his discovery.

Although mathematical theory was his passion, Archimedes often put his ideas to practical use. For example, he used his theory of water displacement to confirm King Hieron's suspicion that a golden wreath (some say it was a crown) was not actually pure gold. He likewise utilized his insights on levers and constructed a device to launch a particularly large ship. One of his inventions was the Archimedean screw, which helped raise water from underground.

Archimedes also helped defend Syracuse from the invading armies of Roman general Marcellus by creating mechanical devices to heave stones and beams at the attacking troops, and to damage enemy ships. Archimedes efforts to protect his homeland were not sufficient, however, and after eight months, Marcellus's armies were victorious. Archimedes, then 75 years old, died at the hands of the Roman soldiers. Some reports state that his preoccupation with mathematics played a role in his demise. As the story goes, Archimedes was too wrapped up in thought to pay attention to the demands of a soldier, who killed him for his insubordination.

As Archimedes wished, his grave was marked with the geometrical figures of a cylinder and sphere.