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(Syracuse, current Italy, h. 287 BC - ID, 212 BC) Greek mathematician. The great progress of mathematics and Astronomy of Hellenism are debtors, largely, of previous scientific advances and of the legacy of Eastern knowledge, but also of new opportunities that provided the Hellenistic world. Euclid, who bequeathed to posterity a prolific work of synthesis of knowledge of its time which fortunately was preserved almost full and became an almost indispensable reference to the contemporary age is located in the beginning of the Hellenistic period.

Archimedes

Archimedes in his representation

traditional: abstracted and meditative

Archimedes

But the most famous and prestigious mathematician Archimedes. His writings, which have been kept in a dozen, are eloquent proof of the multifaceted nature of their scientific knowledge. Son of the astronomer Phidias, who probably introduced him to mathematics, learned from his father the elements of the discipline in which he was destined to overcome all the ancient mathematicians, to the point of appearing as prodigious, "divine", even for the founders of modern science.

His studies were perfected in that great center of Hellenistic culture which was the Alexandria of the Ptolemies, where Archimedes was, around the year 243 BC, pupil of the astronomer and mathematician Conon of Samos, which always had respect and admiration.

There, after learning the not inconsiderable mathematical culture of school (recently that had died the great Euclid), strengthened relations of friendship with other great mathematicians, among whom was Eratosthenes, which always maintained correspondence, even after his return to Sicily. Eratosthenes Archimedes dedicated his

*method*, in which exposed his brilliant application of mechanics to geometry, in which «weighed"imaginary areas and unknown volumes to determine its value. He then returned to Syracuse, where he dedicated himself fully to the scientific work. Apparently, later returned to Egypt for some time as "engineer" of Ptolemy, and designed its first great invention, the "cochlea", a kind of machine that was used to raise water and water in this way areas that did not flood of the Nile there. But his mature scientist activity unfolded completely in Syracuse, where enjoyed the favor of the tyrant Hieron II. There he alternated mechanical inventions with studies of theoretical mechanics with high math, always printed in them his characteristic spirit, wonderful fusion of intuitive boldness and methodical rigor.

His mechanical inventions are many, and more people even attributed the legend (among these last must reject the ustorios mirrors, huge mirrors that would have set on fire the Roman fleet besieging Syracuse); but are historical, as well as the "cochlea", numerous machines of war Defense military of the city, as well as a "sphere", large and ingenious planetary mechanical that, after the taking of Syracuse, was taken to Rome as booty of war, and there saw him still Cicero and Ovid.

Archimedes in his representation

traditional: abstracted and meditative

The biography of Archimedes is more populated by tasty anecdotes that facts such as the previously related. In lathe to the ancient writers, and finally the Arabs; wove the plot of a legendary figure first fellow and the Romans, then already Plutarco attributed a "superhuman intelligence" to this great mathematician and engineer.

The most reported these anecdotes recounts Vitruvio and refers to the method used to check whether there was fraud in the making of a Gold Crown charge by Hiero II, tyrant of Syracuse and guard of Archimedes, and perhaps even relative. It is said that the tyrant, suspecting that the jeweler had deceived him with silver on the inside of the ring, asked Archimedes that it determined the metals that was made without breaking it.

Archimedes meditated long on the difficult problem, until one day, finding in one of the bathrooms, it warned that water overflowing the tub as he was entering it. This observation inspired you the idea that enabled him to solve the question posed to him by the tyrant: If you dipped the Crown into a container filled to the brim and measuring the water is overflowing, any body know its volume; It could then compare the volume of the Crown with the volume of an object of gold of the same weight and check if they were the same. It is said that, driven by the joy, Archimedes ran naked through the streets of Syracuse toward his house shouting 'Eureka! I.e. "I found Eureka!"! I found it!».

The idea of Archimedes is reflected in one of the initial proposals of his work

*on floating bodies*, pioneer of hydrostatics, which would be carefully studied by the founders of modern science, including Galileo. Corresponds to the famous principle of Archimedes (whole body immersed in a fluid experiences an upthrust equals the weight of the volume of water that dislodges), and as there described, making use of it is possible to calculate the law of an alloy, which enabled him to discover that Goldsmith had committed fraud.According to another famous anecdote, collected among others by Plutarch, Archimedes was so excited by the power getting to get their machines, able to lift heavy weights with relatively little effort, which secured the tyrant who, if they gave you a support point, would move the Earth; It is believed that, urged by the King to put into practice its assertion, he managed to effortlessly apparent, through a complicated system of pulleys, set in motion a three-masted with its cargo ship.

Similar mental concentration and abstraction in the meditation shows the episode of her death. Reportedly, the war Mills whose paternity attributed the tradition allowed Syracuse withstand the Roman siege, three years before falling in the hands of the troops of Marcelo. While they ransacked Syracuse soldiers of Marcelo, who finally had gotten troops the city, the old mathematician was meditating, forgotten everything in their problems of geometry.

Surprised by a soldier that asked him who he was, Archimedes did not answer him, or, according to another version, replied irritably that he not molestara you or damaged him drawings that had drawn in the sand. and the soldier, irate, killed him. Marcelo was much saddened to know him and commanded that they should you a monument, taking his figure of the Treaty

*on the sphere and cylinder*. Cicero recognized by this figure, many years later, his forgotten Tomb.This passion of Archimedes by erudition, that caused her death, it was also that, in life, is said to you he made you forget to eat and that soliera entertain yourself by tracing geometric patterns in the ashes of the home or even, to anoint it in oils covering your skin. This image contrasts with the inventor of war machines that speak Polybius and Tito Livio; However, as Plutarch says, his interest in this machinery was only in the fact that raised its design as mere intellectual entertainment.

The Archimedes static become a rigorous doctrinal body is comparable to the one done by Euclid for the same purpose with respect to the geometry. This effort is reflected in particular in two of his books; in the first of them,

*flat balances*, explained the law of the lever, deducing it from a small number of postulates, and determined the center of gravity of parallelograms, triangles, trapezoids and a segment of a parabola.In the work

*on the sphere and the cylinder*used the method known as exhaustion, preceding integral calculus, to determine the surface of a sphere and to establish the relationship between a sphere and the cylinder contained therein. The latter result was be your favorite theorem, which was engraved on his tomb, fact which Cicero was able to recover the figure of Archimedes when it had already been forgotten by his express desire.