**ca. 287-212 B.C.**

**Greek mathematician**

Archimedes is considered to be the greatest mathematician of the ancient world. He played a major role in the development „ of mathematics after Euclid, making significant contributions to geometry and physics. Archimedes is also remembered for several ingenious inventions.

Life of Archimedes. Archimedes was born about 287 B.C. in the Greek colony of Syracuse on the island of Sicily. The son of an astronomer, Archimedes studied in Alexandria in Egypt, an important center of Hellenistic* culture. According to historians, Archimedes designed one of his most famous inventions while in Alexandria—a mechanical device for raising water from the Nile River into canals for the irrigation of nearby farm fields. Known as Archimedes’ screw, the device consisted of a screw-shaped spiral enclosed in a cylinder. When the bottom of the device was placed in water and the cylinder rotated, water traveled up the spiral and flowed out the top. Modern versions of Archimedes’ screw are still in use in some parts of Egypt.

After completing his studies in Alexandria, Archimedes returned to Syracuse, where he continued his work in mathematics and science. In about 214 B.C., the Romans attacked Syracuse and began a siege that lasted more than two years. During that time, Archimedes helped defend the city by inventing several war machines and weapons. One of these was a catapult, a device for hurling stones, arrows, and other objects. Another was supposedly a system of mirrors that could concentrate the rays of the sun and set Roman ships on fire. Even so, the Romans defeated Syracuse in 212 B.C.

* Hellenistic referring to the Greek-influenced culture of the Mediterranean world during the three centuries after Alexander the Great, who died in 323 B.C.

**Archimedes was one of the greatest mathematicians in history. He died during the Roman conquest of his home city of Syracuse in 212 B.C. According to a famous story, Archimedes was immersed in a mathematical problem during a battle and was killed by a Roman soldier. This copy of a Roman mosaic from the A.D. 100s depicts this story.**

According to legend, Archimedes was working on a mathematical problem and drawing figures in the sand when the Romans entered the city. Absorbed in his work, Archimedes ignored the questions of a Roman soldier, who became angry and killed him. The Romans knew of his reputation and allowed him to be buried with honors. Archimedes had designed his own tomb—a sphere inside a cylinder, to commemorate the mathematical discovery that the sphere occupies two-thirds of the space of the cylinder.

Archimedes' Achievements. Archimedes was famous in his own time primarily for his clever inventions. In addition to the Archimedes’ screw and various weapons, he also invented a compound pulley*. According to a story recounted by Plutarch, King Hieron of Syracuse overheard Archimedes’ boast: “Give me a point of support and I shall move the world.” When Hieron asked for a demonstration, Archimedes attached a pulley to a ship loaded with men and cargo. Then, by gently pulling on the ropes attached to the pulley, he moved the ship toward him as easily as if it were running along the surface of the water.

Although best known for his inventions, Archimedes’ contributions to mathematics and physics are perhaps more significant. In geometry, Archimedes calculated an approximate number for pi (tc), the value that represents the ratio of the circumference of a circle to its diameter. Archimedes also explored the properties of complex curved figures and determined how to calculate their areas and volumes.

Archimedes wrote many works on mathematics and science, discussing his various principles and providing proof of their accuracy. Only nine of these works have survived. One of those, On Floating Bodies, is the first known work in the field of hydrostatics, a branch of physics dealing with the properties and characteristics of fluids. On Floating Bodies discusses the physical law of nature that has come to be known as Archimedes’ principle. According to Archimedes’ principle, an object immersed in a fluid is buoyed, or kept afloat, by a force equal to the weight of the fluid displaced by the object. This important scientific principle explains how and why objects float.

A story is told of how Archimedes came to discover this principle. King Hieron had ordered a new crown of solid gold, but he suspected that the craftsman had cheated him by mixing silver with the gold. Hieron asked Archimedes to determine if the crown contained solid gold. At first, Archimedes could not think of a way to do this. The answer came to him suddenly one day as he was bathing. He noticed the water level of his bath changed as he sat down in the water. Archimedes realized that the amount of water displaced by an object depends on its weight and volume. By measuring the amounts of water displaced by equal quantities of silver and gold, he would be able to determine whether or not the crown was made of solid gold. As the story continues, Archimedes was so excited by his discovery that he jumped out of his bath and ran naked through the streets shouting “Eureka,” which means “I have found it” in Greek.

* compound pulley mechanical device with a series of wheels and rope that is used to transmit force from one object to another

Remember. Consult the Index at the end of volume 4 to find more Information on many topics.

Like many scientific discoveries from the ancient world, the importance of Archimedes’ principle and his other discoveries was not evident until many years later. After the rediscovery of his works during the Renaissance*, Archimedes’ ideas profoundly influenced the development of both mathematics and physics. (See also Mathematics, Greek; Science; Technology.)

* Renaissance period of the rebirth of interest in classical art, literature, and learning that occurred in Europe from the late 1300s through the 1500s