A Contribution of Archimedes in Physics and Math

When the name Archimedes is mentioned two totally different things come to mind. One might think of Archimedes of Syracuse who is considered to be one of greatest physicist and mathematician of the ancient world. On the other hand, someone might think of that little owl who is Merlin’s sidekick in Disney’s animated version of The Sword in the Stone. This report will focus on the life of the human Archimedes and not on the cartoon.

Archimedes lived from 287-212BC and details concerning his personal life are unclear due to the fact that the only biography on Archimedes (written by his friend Heracleides) have been lost for centuries. Therefore some of the accounts of Archimedes’ life and his achievements are not verifiable, while some incidents concerning his accomplishments are concerned legends (Abbot 13).

Archimedes is believed to have been born in Syracuse, Sicily then a Greek colony. His father Phidias, was an astronomer and his family was of noble fame, perhaps even related to King Hieron II (Abbot 13).

After his stay in Syracuse, Archimedes moved to Alexandria to study under Conon in order to learn more about math and physics. Unlike most other mathematicians and physicists, Archimedes did not remain in Alexandria for the rest of his life, he returned back to his home after his hiatus in Alexandria. Back in Sicily, Archimedes devoted the rest of his life to the serious study of physics of mathematics and physics (Abbot 13).

The best known result of Archimedes’ work in Syracuse is the Archimedes Principle which states that a body immersed in water will displace a volume of fluid which weighs as much as the body would in air (Abbot 14) or a body immersed in fluid is acted upon by a vertical force equal to the weight of fluid displaced, and a body floating in the fluid displaces its own weight of fluid (Street 42). Immersed means either completely or partially submerged. For example, if we fully immersed a 3N brick into a bucket of water then the brick will weigh about 1N in the water but will displace 2N of water for a total of 3N. In other words, if you were to walk into a pool of water that was filled all the way to the top, then your normal weight would equal your weight under water plus the weight of the water that was displaced from the pool. No matter how far down you go or what shape you make your body into. Also, a completely submerged object will always displace a volume of liquid equal to its own volume (Hewitt 278). Archimedes is said to have discovered this principle when causing water to overflow from a bathtub. He was so exhilarated by his discovery that he ran around the town naked and crying out "Eureka!" which means "I’ve got it!" . Archimedes put his new principle to the test when the problem of weather or not King Hieron’s new crown was pure gold came about. To solve the mystery without damaging the crown in any way was a mystery. But, Archimedes realized that if the crown had been mixed with silver , which is less dense then gold, the crown would have a greater volume and therefore displace more water then if its was pure gold. As the legends goes, the crown was found to be a gold-silver mixture and the goldsmith who constructed the crown was immediately executed (Abbott 14).

Archimedes also made several other accomplishments in the fields of statics and hydrostatics. In statics, Archimedes is given credit for working out the unyielding proofs behind the law of the lever. Archimedes was not the first person to use the lever but, he was the first person too mathematically demonstrate that the ratio of the effort used to raise the load is equal to the inverse ratio of the distances of the effort and load from the fulcrum of the lever. Archimedes said that if he had a place to stand, he could use a lever to move the world.

When he heard of this claim King Hieron challenged Archimedes to prove that he could easily move a heavy object from one place to another. According to legend, a large number of men lifted a ship out of the harbor and onto dry land. Then Archimedes developed a system of compound pulleys and levers to move the ship across the land as if it were gliding across the water (Abbott 14).

Archimedes’ other inventions include a design for a model planetarium that is able to show the sun and planets in orbit. Archimedes is also given credit for inventing the Archimedes screw although he may have just borrowed the idea from the Egyptians while he was in Egypt. The Archimedes screw is basically a drill that brought water up from the river by spiral chambers when the handle is turned. As far as mathematics, Archimedes did intensive studies on the value of p. He also came up with methods to solve cubic equations and to determine square roots by approximation. Archimedes is probably most renown for naming the Archimedean solids and his work in early calculus (Abbott 14-15).

Archimedes died at the age of 75 after being killed by a Roman solider despite the fact that he was ordered to be taken alive during the Roman’s siege of Syracuse which lasted for nearly three years. Reportedly, the siege took so long because Archimedes was able to keep the Roman ships at bay with weapons that set fire to ships and sunk them (Abbott 13-14).

Despite his reputation has a great physicists and mathematician his work was not widely known during ancient times. However, his work was advanced and preserved by Byzantium and Islam where it eventually spread into Europe by the twelfth century. Archimedes’ work is now become a stalemate in many physics and mathematics books. Archimedes’ methods of finding proofs and his methods of experimentation and observation became the method of modern science introduced by Simon Stevinus, Johann Kepler, Galileo and Evangelista Torricelli. Archimedes work with levers and pulleys has proven to be invaluable today in our methods of constructing large structures and moving heavy objects (Abbott 15)