Archimedes - SpeedyLook encyclopedia

Biographical elements

The life of Archimedes is known little, it is not known for example if he were married or had children. Information relating to it comes mainly from Polybe (202 av. J-C - 126 av. J-C), Plutarque (46 - 125), Tite-Live (59 av. J-C - 17 a. J-C) or even in the case of the anecdote of the bath-tub, of Vitruve, a famous Roman architect. These writings are thus, except for Polybe, very posterior with the life of Archimedes.

Concerning mathematics, there is trace of a certain number of publications, work and correspondences. He on the other hand considered to be useless to consign in writing his work of engineer which is known for us only by thirds.

Archimedes would have been born with Syracuse in 287 av. J. - C. His/her father would be an astronomer Phidias, wire of Acupater, which would have begun its instruction. It was contemporary in Eratosthène. It is supposed that it completes its studies with very famous the school of Alexandria. At least, one is sure that he knew professors of them since one found letters which he would have exchanged with them.

Of the family of Hiéron II, king de Syracuse, (here the term of family is to be taken with the very broad direction somebody of the house of Hiéron ), it enters to its service in the capacity as engineer and takes part in the defense of the city at the time of the Second Punic War. He dies in 212 av. J. - C. at the time of the catch of the city by the Romain Marcellus.

Contributions in geometry

Archimedes is a mathematician, mainly geometrician, of great scale. It was interested in numeration, seeking, for example to write the number of all the grains of sand of the universe. The major part of its work relate to the geometry with:

the study of the Circle where it determines a method of approximation of π using polygons regular and proposes the approximations $\ frac {22} {7}$ and $\ frac {223} {71}$
the study of the Conique S in particular the Parabole of which it presents two very original squarings. It prolongs the work of Eudoxe de Cnide on the Méthode of exhaustion
the study of the surfaces and volumes which make of him a precursor in the calculation which is not called yet integral. He worked in particular on the volume of the sphere and the cylinder and asked so that these figures be engraved on its tomb. “The report/ratio of volumes of a sphere and a cylinder, if the sphere is tangent with the cylinder by the side face and the two bases, is equal to 2/3. ”
the study of the spiral which bears its name of which it also gave a squaring.

Contributions in mechanics

Archimedes is regarded as the father of the Mécanique statics. In its treaty, Of the balance of the plane figures , it is interested in the principle of the lever and research of Center of gravity.

One allots also the to him Archimedes' principle on the bodies plunged in a liquid ( Of the floating bodies ).

He also worked on optics ( reflecting the ).

He into practice puts his theoretical knowledge in a great number of inventions. One owes him, for example,

of the tensile testing machines where it shows that using pulleys, of hoists and levers, the man can raise much more than his weight
of the machines of war (principle of the loophole, catapults, mechanical arms used in the naval action).

Among the machines of very important wars one must underline the apparatus to measure the distances (Odomètre) that the Romans borrowed from Archimedes. Indeed so that the army is effective, it must be rested and the days of walk must thus be identical. The machine of Archimedes must be realized with pointed and nonsquare teeth of wheel. One put to reconstitute it very a long time because this error was made.

the Endless screw and the Archimedes' screw, of which it pays, seems it, the principle of Egypt and from which it is used for to go up water. One allots also the invention to him of the screw and the nut.
the principle of the toothed wheel thanks to which it builds a planet gear represented the Universe known at the time.

Archimedes the scientist

We have a palimpsest known under the name of manuscript of Archimedes. At the time of the study of this one, one realized that Archimedes had the notion of the infinitesimal calculus, thing very modern and completely necessary to progress in sciences. One is reminded that for the former Greeks, God perfect because is finished.

Caption

The genius of Archimedes in mechanics and mathematics makes of him an exceptional character of ancient Greece and justifies creation about it legendary facts. Its admirors among whom Cicéron which discovered its tomb, Plutarque which reported its life, Léonard de Vinci, and later Auguste Count perpetuated, enriched the tales and legends by Archimedes.

Following the example all large scientists, the collective memory associated a sentence, a fable transforming the discoverer into mythical hero: with Newton the apple is associated, with Pasteur small the Joseph Meister, with Albert Einstein the formula E = mc ². For Archimedes, it will be the sentence Eureka! (in Greek: I found!) pronounced while running naked through the streets of the city whereas it had just found the explanation of the thorough same name. Archimedes finally had just found the solution with its problem: indeed, it was current at that time that the kings in lack of money found their gold jewels and discover that the present which had been made to them were actually only plated lead gold or a mixture of gold-silver! The king had charged Archimedes with finding a means to thwart this fraud. It is in its bath-tub, whereas he sought for a long time, that he found the solution, from where his joy! He could measure the volume of the crown by immersion in water then to weigh it in order to compare his density with that of the solid gold.

The head office of Syracuse and mirrors of Archimedes

At the time of the attack of Syracuse, then Greek colony, by the Roman fleet , the legend wants that it developed giant mirrors to reflect and concentrate the rays of the Sun in the veils of the Roman ships and thus to ignite them. That seems scientifically not very probable bus of the sufficiently large mirrors were technically inconceivable, the silver mirror not existing yet. Only polished bronze mirrors could be used.

An experiment undertaken by students of the Massachusetts Institute off Technology (MIT) in October 2005 seemed to show that this assumption was realistic. Professor David Wallace and his students indeed managed to ignite a reconstitution of Roman boat 30 away meters in ten minutes. However, this experiment had been undertaken out of water, on seasoned wood, a motionless target and using ordinary mirrors and not of bronze mirrors like those of the time of Archimedes.

The experiment was renewed during the television program Mythbusters on Discovery Channel in January 2006; professor Wallace and the team of students of the MIT were invited to take part in this new attempt. However, this reconstitution was recreated under conditions much more realistic and gave very different results.

First of all, the team of Mythbusters chooses for target a true boat whose hull was consequently mouthful of moisture. That Ci will remain completely motionless during all the experiment. Then, the participants used bronze mirrors polished, the only available ones at the time of Archimedes. After several tests using various mirrors, the participants were unable to pare fire with the ship 30 away meters, simply succeeding in making smoke the hull without it taking fire and provided that the boat remains strictly motionless. An attempt carried out on the veils of the ship does not lead quite simply to any result, the white veils returning the heat of the rays luminous and leaving constantly the hearth because of the wind.

Lastly, a new attempt with 20 meters using ordinary mirrors and on an always motionless ship managed to painfully ignite the hull after a few minutes.

The many difficulties encountered during the experiment show according to any probability that the legend of the mirrors of Archimedes is unrealistic. Several factors tend to prove that:

Syracuse faces the sea by the East, which would have forced Archimedes to use the rays of the sun of the morning, less powerful than those of midday.
the mirrors can function only when the sun is visible, which makes this “weapon” not very reliable because entirely at the thank you of the state of the sky.
the Roman ships were probably moving, which strongly complicates the task to find the hearth. To be effective, the mirrors should have functioned very quickly, which was not the case during the reconstitution.
the veils could not have been taken for target, because their clear color returns the luminous rays best and heat as well as the hull does not concentrate; moreover, the veils are constantly moving because of the wind and consequently, leave the hearth unceasingly.
Historiquement, it is mentioned use of mirrors at the time of the seat of Syracuse only 800 years after the facts, which makes the anecdote rather doubtful. Several older authors reporting this episode mention neither the mirrors, nor even the fire of the Roman ships. The historian Tite-Live (XXIV-34) described the big role of Archimedes as engineer in the defense of his city (installation of the ramparts, construction of loopholes, construction of small scorpions and various machines of war), but it does not say a word of these famous mirrors. In the same way, he tells the catch of Syracuse, organized during the night not by fear of the sun, but to benefit from the general relaxation at the time three days of festivities (liberally sprinkled) in the honor of the goddess Diane. (XXV-23)
the use of mirrors would mobilize a great number of people for not very convincing results. 300 mirrors were thus used for the reconstitution during the emission, and at the end of the emission, a rather weak wind reversed of it a great number, of which several were broken by the fall.

The organizers and the participants in the emission concluded from it that the mirrors of Archimedes used during the head office of Syracuse were only one myth.

The death of Archimedes

In -212, after several years of seat, the Romans would then have waited a cloudy day to seize Syracuse and to plunder it. The Marcellus general wished nevertheless to save the scientist. Unfortunately, according to Plutarque, a Roman Soldat crossed Archimedes whereas this one traced geometrical figures on the ground, nonconscious of the catch of the city by the enemy. Disturbed in its concentration by the soldier, Archimedes would have launched to him “does not disturb my circles!” (" Μη μου τους κύκλους τάραττε! "). The soldier upset not to see obtempérer old man the 75 year old, would then have killed it out of a blow of sword. In homage to its genius, Marcellus made him great funeral and made draw up a tomb decorated with sculptures representing work of the missing.

Treaties

Archimedes wrote several treaties, of which twelve reached us. It is supposed that three or four were lost.

Of the balance of the plane figures , delivers I.
the Squaring of the parabola .
Of the balance of the plane figures , delivers II.
Of the sphere and the cylinder , books I and II.
Of the spirals .
On the conoïdes and the spheroids .
Of the floating bodies , books I and II.
Of the measurement of the circle .
the arénaire .
reflecting the
Of the method .

Quotations

( I found! ), pronounced according to the legend when Archimedes discovered its famous principle.
Give to me a fulcrum and a lever and I will raise the Earth.
Do not disturb my circles! , pronounced in front of a Roman soldier who decentralized it shortly after the catch of Syracuse. Out of rage, the soldier killed it.

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