Archimedes

Archimedes of Syracuse (ca. 287-ca. 212 BC)

Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch.

Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid (Greek geometer who wrote the Elements, the world's most definitive text on geometry.), excelling especially at computing areas and volumes using the METHOD OF EXHAUSTION(a integral-like limiting process to compute the area and volume of 2-D lamina and 3-D solids.).

2-D Lamina¡¦s:

3-D Solids

He was especially proud of his discovery for finding the volume of a sphere, showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder as engraved on his tombstone.

In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle, for instance, he was able to constrain the value of (pi ) between 3 10/71 and 3+1/7.

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Archimedes was also an outstanding engineer, formulating Archimedes' principle of buayancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is supposed to have run naked through the streets of Syracuse shouting ``Eureka!'' (I have found it). Archimedes is also purported to have invented the Archimedean screw.

Some of Archimedes's geometric proofs were actually motivated by mechanical arguments which led him to the correct answer.

Archimedes of Syracuse (ca. 287-ca. 212 BC)

Greek mathematician who flourished in Sicily. He is generally considered to be the greatest mathematician of ancient times. Most of the facts about his life come from a biography about the Roman soldier Marcellus written by the Roman biographer Plutarch.

Archimedes performed numerous geometric proofs using the rigid geometric formalism outlined by Euclid (Greek geometer who wrote the Elements, the world's most definitive text on geometry.), excelling especially at computing areas and volumes using the METHOD OF EXHAUSTION(a integral-like limiting process to compute the area and volume of 2-D lamina and 3-D solids.).

2-D Lamina¡¦s:

3-D Solids

He was especially proud of his discovery for finding the volume of a sphere, showing that it is two thirds the volume of the smallest cylinder that can contain it. At his request, the figure of a sphere and cylinder as engraved on his tombstone.

In fact, it is often said that Archimedes would have invented calculus if the Greeks had only possessed a more tractable mathematical notation. By inscribing and circumscribing polygons on a circle, for instance, he was able to constrain the value of (pi ) between 3 10/71 and 3+1/7.

ƒà

Archimedes was also an outstanding engineer, formulating Archimedes' principle of buayancy and the law of the lever. Legend has it that Archimedes discovered his principle of buoyancy, which states that the buoyancy force is equal to the weight of the liquid displaced, while taking a bath, upon which he is supposed to have run naked through the streets of Syracuse shouting ``Eureka!'' (I have found it). Archimedes is also purported to have invented the Archimedean screw.

Some of Archimedes's geometric proofs were actually motivated by mechanical arguments which led him to the correct answer.

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Archimedes (287BC-212BC) was truly one of the greatest mathematical minds of all time. The discoveries and inventions of Archimedes formed the basis of many of the fundamental concepts of modern physics and mathematics.

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## Archimedes

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Archimedes S. Romano Archimedes was a native of Syracuse, Sicily. Some authors have said that he visited Egypt and invented a device there now known as Archimedes' screw. This screw is a pump, still used in many parts of the world. When Archimedes was a young man, he studied with the descendants of Euclid in Alexandria. He was familiar with the mathematics used there, and he knew personally the mathematicians working there and he sent his results to Alexandria with personal messages.

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...to the Second Punic War with the defense of Syracuse. He even made amazing engineering tools and machines that benefitted the community, like the Archimedes screw, which helped irrigation among other things. The Archimedes’ principle, which is said to of helped King Hiero ll, showed the different densities between objects using the buoyancy of the water. The findings in mathematics from Archimedes like The Quadrature of the Parabola and the Measurement of a Circle have greatly benefitted mathematics and are still helping now. Archimedes wrote a lot of different works, including his most famous Archimedes Palimpsest, which contained many more important writing like On Floating Bodies. With his amazing inventions, intricate ideas on science, intelligent theorems and principles in mathematics, and his life in general, Archimedes has greatly affected society in many ways

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The discovery that Archimedes is perhaps most famous for is the Archimedes Principle. King Hiero II gave a goldsmith a certain amount of gold and asked that he make a crown from it. Once the crown was finished, the king suspected that the goldsmith had substituted some of the gold in the crown for silver. Archimedes was asked find out the truth without melting the crown to calculate its density (“Archimedes’ Principle”). When he later took a bath, Archimedes saw the water run over the edges of the tub. As he watched the water spill over, he suddenly found his answer. “Eureka!” he shouted, jumping out of the tub and running down the street without his clothes (qtd. in Gow 50). Archimedes to Hawking by Clifford A. Pickover explains it this way: “Because gold has a greater density than silver, a gold cube would be smaller than a silver cube of equal weight, causing less water to spill out of the bucket.” Archimedes could do the same thing with the crown as he did in the bath to find out the densit...

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Archimedes is regarded as one of the greatest scientists of all time, and most of his inventions, theories, and discoveries are used even to this day. Archimedes was born sometime in the year 287 BC, in Syracuse Sicily (Mac).

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Historically speaking, ancient inventors of Greek origin, mathematicians such as Archimedes of Syracuse, and Antiphon the Sophist, were the first to discover the basic elements that translated into what we now understand and have formed into the mathematical branch called calculus. Archimedes used infinite sequences of triangular areas to calculate the area of a parabolic segment, as an example of summation of an infinite series. He also used the Method of Exhaustion, invented by Antiphon, to approximate the area of a circle, as an example of early integration.

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