Archimedes of Syracuse (from the Greek Arkhimêdês), born in Syracuse in 287 BC. AD and died in Syracuse in 212 BC. J.-C.), is a great Greek scientist from Sicily (Major Greece) of Antiquity, physicist, mathematician and engineer.
The life of Archimedes is little known, we do not know for example if he was married or had children. The information concerning him comes mainly from Polybius (202 BC. J. Chr. - 126 BC. J. Chr.), Plutarch (46 - 125), Livy (59 - 17) or even for the case of anecdote of the bathtub, by Vitruvius, a famous Roman architect. These writings are therefore, except for Polybius, much later than the life of Archimedes.
Concerning mathematics, we have traces of a certain number of publications, works and correspondence. On the other hand, he deemed it unnecessary to record in writing his engineering work, which is only known to us by third parties.
Archimedes was born in Syracuse in 287 BC. His father would be [1] the astronomer Phidias who would have started his education. It is assumed that he completed his studies at the very famous school of Alexandria. At least, we are sure that he knew some of their teachers since we have found letters that he would have exchanged with them[2].
From the family of Hieron II, king of Syracuse, (here the term family is to be taken in the very broad sense of someone from the house of Hieron), he entered his service as an engineer and participated in the defense of the city during the Second Punic War. He died in 212 BC. AD when the city was taken by the Roman Marcellus.
Archimedes, the surveyor
Archimedes is a mathematician, mainly geometer, of great stature. He was interested in numeration, seeking, for example, to write the number of all the grains of sand in the universe[3]. Most of his work concerns geometry with
* the study of the circle where he determines a method of approximation of π using regular polygons and proposes the approximations \frac22 7 and \frac223 71
* the study of conics in particular the parabola of which he presents two very original quadratures. It extends the work of Eudoxe on the method of exhaustion
* the study of areas and volumes which make him a precursor in the calculation which is not yet called integral. He worked in particular on the volume of the sphere and the cylinder and requested that these figures be engraved on his tomb. “The ratio of the volumes of a sphere and a cylinder, if the sphere is tangent to the cylinder by the side face and the two bases, is equal to 2/3. »
* the study of the spiral which bears his name, of which he also gave a quadrature.
Archimedes, the mechanic
Archimedes is considered the father of static mechanics. In his treatise, On the Balance of Plane Figures, he is interested in the principle of the lever and the search for the center of gravity.
He is also credited with Archimedes' principle on bodies immersed in a liquid (Floating bodies).
He also worked on optics (Catoptrics).
He puts his theoretical knowledge into practice in a large number of inventions. We owe him, for example,
* traction machines where he demonstrates that with the help of pulleys, hoists and levers, man can lift much more than his weight
* war machines (principle of the loophole, catapults, mechanical arms used in naval combat).
Among the very important war machines, we must highlight the device for measuring distances (odometer) that the Romans borrowed[4] from Archimedes. Indeed, for the army to be effective, it must be rested and the days of march must therefore be identical. Archimedes' machine should be made with pointed, not square, cog teeth. It took us a very long time to reconstruct it because we made this mistake.
* the endless screw and the screw of Archimedes, of which he brings back, it seems, the principle of Egypt and which he uses to bring up water. He is also credited with the invention of the screw and the nut.
* the cogwheel principle by which he built a planetary represented the known Universe at the time.
Archimedes the scientist
We have a palimpsest known as the Archimedes manuscript. When studying it, we realized that Archimedes had the notion of infinitesimal calculus, something very modern and absolutely necessary to progress in science. It is recalled that for the ancient Greeks, God is perfect because finite.
Archimedes and the legend
Archimedes' genius in mechanics and mathematics makes him an exceptional character of ancient Greece and justifies the creation of legendary facts about him. His admirers, including Cicero who discovered his tomb, Plutarch who recounted his life, Leonardo da Vinci, and later Auguste Comte perpetuated and enriched the tales and legends of Archimedes.
Like all great scientists, collective memory has associated a phrase, a fable transforming the discoverer into a mythical hero:Newton is associated with the apple, Pasteur with little Joseph Meister, Albert Einstein with the formula E =mc². For Archimedes, it will be the phrase Eureka! (in Greek:I found!) pronounced while running naked through the streets of the city when he had just found the explanation for the push of the same name. Archimedes had finally found the solution to his problem:Indeed, it was common at that time for kings in need of money to melt their jewelry in gold and discover that the presents that had been made to them were in fact only gold. gold-plated lead or a mixture of gold-silver! The king had instructed Archimedes to find a way to thwart this fraud[5]. It was in his bathtub, when he had been looking for a long time, that he found the solution, hence his joy! He was able to measure the volume of the crown by immersion in water and then weigh it in order to compare its density to that of solid gold.
The Siege of Syracuse and the Mirrors of Archimedes[edit]
Using the Sun to Defend Syracuse
Using the Sun to Defend Syracuse
During the attack on Syracuse, then a Greek colony, by the Roman fleet, legend has it that he developed giant mirrors to reflect and concentrate the rays of the sun in the sails of Roman ships and thus ignite them. This seems scientifically unlikely because sufficiently large mirrors were technically inconceivable, the silver mirror not yet existing. Only polished bronze mirrors could be used.
An experiment conducted by MIT students in October 2005 seemed to demonstrate that this assumption was realistic. Professor David Wallace and his students indeed managed to ignite a reconstruction of a Roman boat 30 meters away in ten minutes. However, this experiment was conducted out of water, on dry wood, on a stationary target and using ordinary mirrors and not bronze mirrors like those of Archimedes' time.
The experiment was repeated during the Mythbusters television show on the Discovery Channel in January 2006; Professor Wallace and the team of MIT students were invited to take part in this new attempt. However, this reconstruction was recreated under much more realistic conditions and gave very different results.
First, the Mythbusters team chose to target a real boat, whose hull was therefore full of moisture. Then, the participants used polished bronze mirrors, the only ones available at the time of Archimedes. After several attempts using different mirrors, the participants were unable to set fire to the ship from 30 meters away, only managing to smoke the hull without catching fire. An attempt on the sails of the ship simply did not lead to any results, the white sails reflecting the heat of the light rays and constantly flying out of focus due to the wind.
Finally, a new attempt at 20 meters using ordinary mirrors and on a still stationary ship managed to painfully ignite the hull after a few minutes.
The many difficulties encountered during the experiment show in all likelihood that the legend of Archimedes' mirrors is unrealistic. Several factors tend to prove this:
* Syracuse faces the sea from the East, which would have forced Archimedes to use the rays of the morning sun, which are less powerful than those of noon.
* Mirrors can only work when the sun is visible, which makes this "weapon" unreliable because it is entirely at the mercy of the state of the sky.
* The Roman ships were probably in motion, which greatly complicates the task to find the home. To be effective, the mirrors would have had to operate very quickly, which they did not during the reenactment.
* The sails could not have been targeted, as their light color Reflects light rays better and does not concentrate heat as well as the shell; moreover, the sails are constantly in motion due to the wind and therefore constantly fly out of focus.
* Historically, there is no mention of the use of mirrors during the siege of Syracuse only 800 years after the facts, which makes the anecdote quite dubious[6]. Several older authors recounting this episode do not mention the mirrors or even the burning of Roman ships. The historian Livy (XXIV-34) describes the important role of Archimedes as an engineer in the defense of his city (development of the ramparts, construction of loopholes, construction of small scorpions and various war machines), but he does not say not a word of those famous mirrors. Similarly, he recounts the capture of Syracuse, organized during the night not for fear of the sun, but to take advantage of the general relaxation during three days of festivities (generously sprinkled) in honor of the goddess Diana. (XXV-23)
* The use of mirrors would mobilize a large number of people for inconclusive results. 300 mirrors were thus used for the reconstruction during the broadcast, and at the end of the broadcast, a fairly light wind knocked over a large number of them, several of which were broken by the fall.
The show's organizers and participants concluded that the Archimedean mirrors used during the Siege of Syracuse were a myth.
The death of Archimedes
In -212, after several years of siege, the Romans would have waited for a cloudy day to seize Syracuse and loot it. General Marcellus nevertheless wished to spare the scholar. Unfortunately, according to Plutarch[7], a Roman soldier came across Archimedes while he was tracing geometric figures on the ground, unaware of the enemy's capture of the city. Disturbed in his concentration by the soldier, Archimedes would have shouted to him “Don’t disturb my circles! ("Μη μου τους κύκλους τάραττε!"). The soldier, upset at not seeing the 75-year-old man comply, would then have killed him with a sword. In homage to his genius, Marcellus gave him a grand funeral and erected a tomb decorated with sculptures representing the work of the deceased.
Treaties
Archimedes wrote several treatises, twelve of which have come down to us. It is assumed that three or four were lost.
* On the equilibrium of plane figures, book I.
* The Quadrature of the parabola.
* On the equilibrium of plane figures, book II.
* On the sphere and the cylinder, Books I and II.
* On spirals.
* On conoids and spheroids .
* Of floating bodies, books I and II.
* Of the measurement of the circle.
* The arena.
* The catoptic
* Of the method.
Quotes
* “Eureka! (I found it!), pronounced according to the legend when Archimedes discovered his famous principle.
* "Give me a fulcrum and a lever and I will lift the Earth." "
* "Don't disturb my circles! », spoken in front of a Roman soldier who distracted him shortly after the capture of Syracuse. In rage, the soldier killed him.