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## Archimedes*Alternate meanings: Archimedes computer, Archimedes (disambiguation).*
Archimedes of Syracuse (circa 287 BC - 212 BC), was a Greek mathematician, astronomer, physicist and engineer.
## DiscoveriesArchimedes is one of the greatest mathematicians of all time. He became a popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the First and Second Punic Wars. He is reputed to have held the Romans at bay with war engines of his design; to have been able to move a full-size ship complete with crew and cargo by pulling a single rope; to have discovered the principles of density and buoyancy while taking a bath (thereupon taking to the streets naked calling "eureka" - "I found it!"); and to have invented the irrigation device known as Archimedes' screw.
In creativity and insight, he exceeds any other mathematician prior to the European renaissance. In a civilization with an awkward number system and a language in which "a myriad" (literally ten thousand) meant "infinity", he invented a positional numeral system and used it to write numbers up to 10
In the process, he calculated the oldest known example of a geometric series with the ratio 1/4:
If the first term in this series is the area of the triangle in the illustration then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines in the illustration. Essentially, this paragraph summarizes the proof. Archimedes also gave a quite different proof of nearly the same proposition by a method using infinitesimals; that different proof is found here. He proved that the area and volume of the sphere are in the same ratio to the area and volume of a circumscribed straight cylinder, a result he was so proud of that he made it his epitaph. Archimedes is probably also the first mathematical physicist on record, and the best before Galileo and Newton. He invented the field of statics, enunciated the law of the lever, the law of equilibrium of fluids and the law of buoyancy. (He famously discovered the latter when he was asked to determine whether a crown had been made of pure gold, or gold adulterated with silver; he realized that the rise in the water level when it was immersed would be equal to the volume of the crown, and the decrease in the weight of the crown would be in proportion; he could then compare those with the values of an equal weight of pure gold.) He was the first to identify the concept of center of gravity, and he found the centers of gravity of various geometric figures, assuming uniform density in their interiors, including triangles, paraboloids, and hemispheres. Using only ancient Greek geometry, he also gave the equilibrium positions of floating sections of paraboloids as a function of their height, a feat that would be taxing to a modern physicist using calculus.
Apart from general physics he was an astronomer, and Cicero writes that in the year 212 BC when Syracuse was raided by Roman troops, the Roman consul Marcellus brought a device which mapped the sky on a sphere and another device that predicted the motions of the sun and the moon and the planets (i.e. a planetarium) to Rome. He credits Thales and Eudoxus for constructing these devices. For some time this was assumed to be a legend of doubtful nature, but the discovery of the Antikythera mechanism has changed the view of this issue, and it is indeed probable that Archimedes posessed and constructed such devices. Pappus of Alexandria writes that Archimedes had written a practical book on the construction of such spheres entitled
Archimedes' works were not very influential, even in antiquity. He and his contemporaries probably constitute the peak of Greek mathematical rigour. During the Middle Ages the mathematicians who could understand Archimedes' work were few and far between. Many of his works were lost when the library of Alexandria was destroyed and survived only in Latin or Arabic translations. As a result, his ## Writings by ArchimedesThis book spells out the law of the lever and uses it to calculate the areas and centers of gravity of various geometric figures.- On Spirals
- On the Sphere and The Cylinder
- On Conoids and Spheroids
- On Floating Bodies (2 volumes)
- The Quadrature of the Parabola
- Stomachion
- Archimedes' Cattle Problem
- The Sand Reckoner
- "The Method"
## Quotes About ArchimedesSee also: Archimedean property, Archimedean solid## External links- Wikiquote - Quotes by Archimedes
- Archimedes Home Page
- MacTutor biography of Archimedes
- The Archimedes Palimpsest web pages at the Walters Art Museum.
- Archimedes - The Golden Crown points out that in reality Archimedes may well have used a more subtle method than the one in the classic version of the story.
## References
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