CONTRIBUTIONS TO MATHEMATICS
- Discovered the method to determine the area and volumes of circles, spheres and cones.
- Discovered the actual value of PI.
- Archimedes‘s investigation on Method of Exhaustion led way to current form of Integral Calculus which is now updated. Though it is outdated it is believed that he invented the method of Integral Calculus 2000 years before Newton and Leibniz.
- Archimedes performed countless experiments on screws, levers, and pulleys.
- Archimedes invented the water screw, a machine for raising water to bring it to fields.
- His work with levers and pulleys led to the inventions of compound pulley systems and cranes.
- His compound pulleys are highlighted in a story that reports that Archimedes moved a fully-loaded ship single-handedly while seated at a distance.
- His crane was reportedly used in warfare during the Roman siege of his home, Syracuse.
- Wartime inventions attributed to Archimedes include rock-throwing catapults, grappling hooks, and lenses or mirrors that could allegedly reflect thesun's rays and cause ships to catch on fire.
- Another invention was a miniature planetarium, a sphere whose motion imitated that of the earth, sun, moon, and the five planets that were then known to exist.
A FAMOUS STORY
There are many stories about how Archimedes made his discoveries. A famous one tells how he uncovered an attempt to cheat King Hieron.
The king ordered a golden crown and gave the crown's maker the exact amount of gold needed. The maker delivered a crown of the required weight, but Hieron suspected that some silver had been used instead of gold. He asked Archimedes to think about the matter. One day Archimedes was considering it while he was getting into a bathtub. He noticed that the amount of water overflowing the tub was proportional (related consistently) to the amount of his body that was being immersed (covered by water). This gave him an idea for solving the problem of the crown. He was so thrilled that he ran naked through the streets shouting, "Eureka!" (Greek for "I have discovered it!").
There are several ways Archimedes may have determined the amount of silver in the crown. One likely method relies on an idea that is now called Archimedes's principle. It states that a body immersed in a fluid is buoyed up (pushed up) by a force that is equal to the weight of fluid that is displaced (pushed out of place) by the body. Using this method, he would have first taken two equal weights of gold and silver and compared their weights when immersed in water. Next he would have compared the weight of the crown and an equal weight of pure silver in water in the same way. The difference between these two comparisons would indicate that the crown was not pure gold.