Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes


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Mathematics: Rhyme and Reason

On this occasion 70 mirrors were used, each with a copper coating and a size of around five by three feet 1. When the mirrors were focused accurately, the ship burst into flames within a few seconds.

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The plywood ship had a coating of tar paint, which may have aided combustion. Flames broke out on a patch of the ship, but only after the sky had been cloudless and the ship had remained stationary for around ten minutes.

It was concluded that the device was a feasible weapon under these conditions. The MIT group repeated the experiment for the television show MythBusters , using a wooden fishing boat in San Francisco as the target. Again some charring occurred, along with a small amount of flame.

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When MythBusters broadcast the result of the San Francisco experiment in January , the claim was placed in the category of "busted" or failed because of the length of time and the ideal weather conditions required for combustion to occur. It was also pointed out that since Syracuse faces the sea towards the east, the Roman fleet would have had to attack during the morning for optimal gathering of light by the mirrors.


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MythBusters also pointed out that conventional weaponry, such as flaming arrows or bolts from a catapult, would have been a far easier way of setting a ship on fire at short distances. In December , MythBusters again looked at the heat ray story in a special edition entitled "President's Challenge".

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The show concluded that a more likely effect of the mirrors would have been blinding, dazzling , or distracting the crew of the ship. While Archimedes did not invent the lever , he gave an explanation of the principle involved in his work On the Equilibrium of Planes.

Earlier descriptions of the lever are found in the Peripatetic school of the followers of Aristotle , and are sometimes attributed to Archytas. The odometer was described as a cart with a gear mechanism that dropped a ball into a container after each mile traveled. After the capture of Syracuse c. Cicero mentions similar mechanisms designed by Thales of Miletus and Eudoxus of Cnidus. The dialogue says that Marcellus kept one of the devices as his only personal loot from Syracuse, and donated the other to the Temple of Virtue in Rome.

Mathematics: Rhyme and Reason

Marcellus' mechanism was demonstrated, according to Cicero, by Gaius Sulpicius Gallus to Lucius Furius Philus , who described it thus:. This is a description of a planetarium or orrery. Pappus of Alexandria stated that Archimedes had written a manuscript now lost on the construction of these mechanisms entitled On Sphere-Making. Modern research in this area has been focused on the Antikythera mechanism , another device built c. While he is often regarded as a designer of mechanical devices, Archimedes also made contributions to the field of mathematics.

Plutarch wrote: "He placed his whole affection and ambition in those purer speculations where there can be no reference to the vulgar needs of life. Through proof by contradiction reductio ad absurdum , he could give answers to problems to an arbitrary degree of accuracy, while specifying the limits within which the answer lay.

In Measurement of a Circle he did this by drawing a larger regular hexagon outside a circle and a smaller regular hexagon inside the circle, and progressively doubling the number of sides of each regular polygon, calculating the length of a side of each polygon at each step.


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  • As the number of sides increases, it becomes a more accurate approximation of a circle. In On the Sphere and Cylinder , Archimedes postulates that any magnitude when added to itself enough times will exceed any given magnitude. This is the Archimedean property of real numbers. The actual value is approximately 1.

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    He introduced this result without offering any explanation of how he had obtained it. This aspect of the work of Archimedes caused John Wallis to remark that he was: "as it were of set purpose to have covered up the traces of his investigation as if he had grudged posterity the secret of his method of inquiry while he wished to extort from them assent to his results. If the first term in this series is the area of the triangle, then the second is the sum of the areas of two triangles whose bases are the two smaller secant lines , and so on. In The Sand Reckoner , Archimedes set out to calculate the number of grains of sand that the universe could contain.

    In doing so, he challenged the notion that the number of grains of sand was too large to be counted. He wrote: "There are some, King Gelo Gelo II, son of Hiero II , who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited. The works of Archimedes were written in Doric Greek , the dialect of ancient Syracuse. Pappus of Alexandria mentions On Sphere-Making and another work on polyhedra , while Theon of Alexandria quotes a remark about refraction from the now-lost Catoptrica.

    The writings of Archimedes were first collected by the Byzantine Greek architect Isidore of Miletus c. Any body wholly or partially immersed in a fluid experiences an upthrust equal to, but opposite in sense to, the weight of the fluid displaced. Archimedes' Book of Lemmas or Liber Assumptorum is a treatise with fifteen propositions on the nature of circles. The earliest known copy of the text is in Arabic. The scholars T. Heath and Marshall Clagett argued that it cannot have been written by Archimedes in its current form, since it quotes Archimedes, suggesting modification by another author.

    The Lemmas may be based on an earlier work by Archimedes that is now lost. It has also been claimed that Heron's formula for calculating the area of a triangle from the length of its sides was known to Archimedes. The foremost document containing the work of Archimedes is the Archimedes Palimpsest. In , the Danish professor Johan Ludvig Heiberg visited Constantinople and examined a page goatskin parchment of prayers written in the 13th century AD. He discovered that it was a palimpsest , a document with text that had been written over an erased older work.

    Palimpsests were created by scraping the ink from existing works and reusing them, which was a common practice in the Middle Ages as vellum was expensive. The older works in the palimpsest were identified by scholars as 10th century AD copies of previously unknown treatises by Archimedes. It is the only known source of The Method of Mechanical Theorems , referred to by Suidas and thought to have been lost forever. Stomachion was also discovered in the palimpsest, with a more complete analysis of the puzzle than had been found in previous texts.

    The palimpsest is now stored at the Walters Art Museum in Baltimore , Maryland , where it has been subjected to a range of modern tests including the use of ultraviolet and x-ray light to read the overwritten text. Of the surviving works by Archimedes, T. Arabic scholars also attribute to Archimedes the 'theorem on the broken chord ' Archimedes is reported by the Arabs to have given several proofs of the theorem.

    From Wikipedia, the free encyclopedia. For other uses, see Archimedes disambiguation. Greek mathematician, physicist, engineer, inventor, and astronomer. Archimedes Thoughtful by Domenico Fetti Syracuse, Sicily Magna Graecia. Archimedes' principle Archimedes' screw hydrostatics levers infinitesimals Neuseis constructions [1]. Mathematics Physics Engineering Astronomy Invention. Main article: Archimedes' principle.

    Play media. Main article: Archimedes' screw. Hanc sphaeram Gallus cum moveret, fiebat ut soli luna totidem conversionibus in aere illo quot diebus in ipso caelo succederet, ex quo et in caelo sphaera solis fieret eadem illa defectio, et incideret luna tum in eam metam quae esset umbra terrae, cum sol e regione. When Gallus moved the globe, it happened that the Moon followed the Sun by as many turns on that bronze contrivance as in the sky itself, from which also in the sky the Sun's globe became to have that same eclipse, and the Moon came then to that position which was its shadow on the Earth, when the Sun was in line.

    Main article: Archimedes Palimpsest. Historia Mathematica. But in both instances the issue is Archimedes' inappropriate use of a "solid neusis," that is, of a construction involving the sections of solids, in the solution of a plane problem. Yet Pappus' own resolution of the difficulty [IV, 54] is by his own classification a "solid" method, as it makes use of conic sections.

    Collins Dictionary. Retrieved 25 September BBC History. Retrieved Henshaw 10 September JHU Press.

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    Archimedes is on most lists of the greatest mathematicians of all time and is considered the greatest mathematician of antiquity. A Contextual History of Mathematics. Shortly after Euclid, compiler of the definitive textbook, came Archimedes of Syracuse ca.

    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes
    Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes Mathematical Circles Squared: A Third Collection of Mathematical Stories and Anecdotes

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