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Archimedes (Greek: Template:Polytonic; c. 287 BC – c. 212 BC) was a Greek mathematician, physicist, engineer, astronomer, and philosopher.

Many consider Archimedes one of the greatest, if not the greatest, mathematicians in antiquity. Carl Friedrich Gauss, himself frequently called the most influential mathematician of all time, modestly claimed that Archimedes was one of the three epoch-making mathematicians (the others being Isaac Newton and Ferdinand Eisenstein). Apart from his fundamental theoretical contributions to maths, Archimedes also shaped the fields of physics and practical engineering, and has been called "The greatest scientist ever".

He was a relative of the Hiero monarchy, which was the ruling family of Syracuse, a seaport kingdom. King Hiero II, who was said to be Archimedes's uncle, commissioned him to design and build a new class of ships for his navy, which were crucial for the preservation of the ruling class in Syracuse. Hiero had promised large caches of grain to the Romans in the north in return for peace. Faced with war when unable to present the promised amount, Hiero commissioned Archimedes to develop a large luxury/supply/war barge in order to serve the changing requirements of his navy. It is said that the Archimedes screw was an invention of happenstance, as he needed a tool to remove bilge water. The ship, named Syracusia, after its nation, was huge, and its construction caused stupor in the Greek world.

He is credited with many inventions and discoveries, some of which are still in use today, like his Archimedes screw. He designed the compound pulley, a system of pulleys used to lift heavy loads such as ships. Although Archimedes did not invent the lever, he gave the first rigorous explanation of the principles involved, which are the transmission of force through a fulcrum and moving the effort applied through a greater distance than the object to be moved. His Law of the Lever states: Magnitudes are in equilibrium at distances reciprocally proportional to their weights. His work on levers caused him to remark famously: "Give me a place to stand on, and I will move the Earth." He designed several war machines for his patron King Hiero II and produced work in geometry, which included finding the surface areas and volumes of solids accurately. He also laid down the laws of flotation and described Archimedes's principle, which states that a body immersed in a fluid experiences a buoyant force equal to the weight of the displaced fluid.

Biography

He was born circa 287 BC in the Grecian seaport colony of Syracuse, Magna Graecia. In his work The Sand Reckoner he gives his father's name as Phidias, an astronomer about whom nothing is known. Plutarch wrote that Archimedes was also related to King Hieron II of Syracuse. Heracleides, a friend of Archimedes, apparently wrote a biography of Archimedes, but this work has become lost. Thus many details of his life remain incomplete.

A Roman soldier during the sack of Syracuse during the Second Punic War, despite orders from the Roman general Marcellus that he was not to be harmed. The Greeks said that he was killed while performing a geometric construction in the sand; engrossed in his diagram and impatient with being interrupted, he is said to have muttered his famous last words before being slain by an enraged Roman soldier: Μη μου τους κύκλους τάραττε ("Don't disturb my circles"). The phrase is often given in Latin as "Noli turbare circulos meos" but there is no direct evidence that Archimedes ever uttered these words. This story was sometimes told to contrast the Greek high-mindedness with Roman ham-handedness; however, it should be noted that Archimedes designed the siege engines that Cicero had the tomb cleaned up, and was able to see the carving and read some of the verses that had been added as an inscription.

Discoveries and inventions

Archimedes became a very popular figure as a result of his involvement in the defense of Syracuse against the Roman siege in the Second Punic War. He is reputed to have held the Romans at bay with war machines of his own design, to have been able to move a full-size ship complete with crew and cargo by pulling a single rope, and to have discovered the principles of density and buoyancy, also known as Archimedes's principle, while taking a bath. The story goes that a new crown in the shape of a laurel wreath had been made for King Hiero, and Archimedes was asked to determine whether it was of solid gold, or whether other metals had been added by a dishonest goldsmith. Archimedes had to solve the problem without damaging the crown, so he could not melt it down in order to measure its volume. While taking a bath, he noticed that the level of the water rose as he got in. He realised that this effect could be used to determine the volume of the crown, and therefore its density after weighing it. The density of the crown would be lower if cheaper and lighter metals had been added. He then took to the streets naked, being so elated with his discovery that he forgot to dress, crying "Eureka!" ("I have found it!"). He has also been credited with the possible invention of the odometer during the First Punic War. One of his inventions used for military defense of Syracuse against the invading Romans was the claw of Archimedes.

It is said that he prevented one Roman attack on Syracuse by using a large array of mirrors (line is 4/3 the area of a triangle with equal base and height. (See the illustration below. The "base" is any secant line, not necessarily orthogonal to the parabola's axis; "the same base" means the same "horizontal" component of the length of the base; "horizontal" means orthogonal to the axis. "Height" means the length of the segment parallel to the axis from the vertex to the base. The vertex must be so placed that BI)|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 [[

Writings by Archimedes

fuck anyone who reads this fgyuyjyjj

• On the Equilibrium of Planes (2 volumes)

This scroll explains the law of the lever and uses it to calculate the areas and centers of gravity of various geometric figures.

• On Spirals

In this scroll, Archimedes defines what is now called Archimedes's spiral. This is the first mechanical curve (i.e., traced by a moving point) ever considered by a Greek mathematician.

• On the Sphere and The Cylinder

In this scroll Archimedes obtains the result he was most proud of: the relation between the area of a sphere to that of a circumscribed straight cylinder is the same as that of the volume of the sphere to the volume of the cylinder (exactly 2/3).

• On Conoids and Spheroids

In this scroll Archimedes calculates the areas and volumes of sections of cones, spheres, and paraboloids.

• On Floating Bodies (2 volumes)

In the first part of this scroll, Archimedes spells out the law of equilibrium of fluids, and proves that water will adopt a spherical form around a center of gravity. This was probably an attempt at explaining the observation made by Greek astronomers that the Earth is round. Note that his fluids are not self-gravitating: he assumes the existence of a point towards which all things fall and derives the spherical shape. One is led to wonder what he would have done had he struck upon the idea of universal gravitation.

In the second part, a veritable tour-de-force, he calculates the equilibrium positions of sections of paraboloids. This was probably an idealization of the shapes of ships' hulls. Some of his sections float with the base under water and the summit above water, which is reminiscent of the way icebergs float, although Archimedes probably was not thinking of this application.

• The Quadrature of the Parabola

In this scroll, Archimedes calculates the area of a segment of a parabola (the figure delimited by a parabola and a secant line not necessarily perpendicular to the axis). The final answer is obtained by triangulating the area and summing the geometric series with ratio 1/4.

• Stomachion

This is a Greek puzzle similar to a Tangram. In this scroll, Archimedes calculates the areas of the various pieces. This may be the first reference we have to this game. Recent discoveries indicate that Archimedes was attempting to determine how many ways the strips of paper could be assembled into the shape of a square. This is possibly the first use of combinatorics to solve a problem.

• Archimedes' cattle problem

Archimedes wrote a letter to the scholars in the Library of Alexandria, who apparently had downplayed the importance of Archimedes's works. In these letters, he dares them to count the numbers of cattle in the Herd of the Sun by solving a number of simultaneous Diophantine equations, some of them quadratic (in the more complicated version). This problem is one of the famous problems solved with the aid of a computer. The solution is a very large number, approximately 7.760271×10

• The Sand Reckoner

In this scroll, Archimedes counts the number of grains of sand fitting inside the universe. This book mentions Aristarchus of Samos' theory of the solar system (concluding that "this is impossible"), contemporary ideas about the size of the Earth and the distance between various celestial bodies. From the introductory letter we also learn that Archimedes's father was an astronomer.

• "The Method"

In this work, which was unknown in the Middle Ages, but the importance of which was realised after its discovery, Archimedes pioneers the use of infinitesimals, showing how breaking up a figure in an infinite number of infinitely small parts could be used to determine its area or volume. Archimedes probably considered these methods not mathematically precise, and he used these methods to find at least some of the areas or volumes he sought, and then used the more traditional method of exhaustion to prove them. Some details can be found at how Archimedes used infinitesimals.

Notes

1. "Archimedes (287-212 B.C.), Greatest Scientist Ever" [[Jürgen Schmidhuber|by J. Schmidhuber]]". {{cite web}}: URL–wikilink conflict (help); Unknown parameter |accessmonthday= ignored (help); Unknown parameter |accessyear= ignored (|access-date= suggested) (help)
2. Athenaeus, Deipnosophistae, v, 207b.
3. Eminent scientists, Published by scholastic India pvt. Ltd.
4. J. J. O'Connor, E. F. Robertson. "Archimedes of Syracuse". University of St Andrews. Retrieved 2007-01-02.
5. "Tomb of Archimedes: Sources". Courant Institute of Mathematical Sciences. Retrieved 2007-01-02.
6. "Archimedes on Spheres and Cylinders". MathPages. Retrieved 2007-01-02.

References

• E. J. Dijksterhuis, Archimedes, 1987, Princeton University Press, Princeton, ISBN 0-691-08421-1. Republished translation of the 1938 study of Archimedes and his works by an historian of science
• Fred S. Kliner Christin J. Mamiya, "Gardener's Art Through the Ages" twelfth ed. Vol II 2005, Thompson Wadsworth- Los Angeles

External links

• Archimedes's Book of Lemmas at cut-the-knot
• Archimedes and the Rhombicuboctahedron by Antonio Gutierrez from Geometry Step by Step from the Land of the Incas.
• Archimedes Home Page
• O'Connor, John J.; Robertson, Edmund F., "Archimedes", MacTutor History of Mathematics Archive, University of St Andrews
• The Archimedes Palimpsest web pages at the Walters Art Museum.
• NOVA program on Archimedes Palimpsest
• The Archimedes Palimpsest project at The Walters Art Museum in Baltimore, Maryland
• 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.
• Archimedes's Quadrature Of The Parabola Translated by Thomas Heath.
• Archimedes's On The Measurement Of The Circle Translated by Thomas Heath.
• The Works Of Archimedes by Thomas Heath.
• Works by Archimedes at Project Gutenberg
• Archimedes and his Burning Mirrors, Reality or Fantasy?
• Biography of Archimedes
• Squaring the circle History Topic at MacTutor

• Archimedes
• 287 BC births
• 212 BC deaths
• Natives of Syracuse
• Ancient Greek engineers
• Ancient Greek inventors
• Ancient Greek mathematicians
• Ancient Greek physicists
• Dynamicists
• Hellenistic philosophers
• Sicilian Greeks
• Sicilian mathematicians
• Sicilian scientists
• Murdered scientists
• Geometers
• Greek murder victims
• People with craters of the Moon named after them