**Archimedes** was born in Syracuse, Sicily in 287 BC, and was educated in Alexandria, Egypt. It was devoted to mathematics, more especially to geometry. Very young still began to distinguish itself for its scientific works. Returning to Syracuse, he devoted himself to the study of geometry and mechanics, managing to discover principles and make applications that immortalized him.

## Discoveries

Although Archimedes is most famous for the principle of Hydrostatics that bears his name, his investigations into the square of the circle, which is the discovery of the relationship between the circumference and its diameter, are perhaps most notable. In Hydrostatics, the "**Archimedes Principle**"It can and should be considered an important discovery that has made a great advance in the study of the physical sciences and has produced happy results. It has applications in the natural sciences, in pharmacy and even in the frequent activities of daily living. We can enunciate this Principle in two parts:

a) Every body submerged in a liquid, displaces a certain amount of that liquid, whose volume is exactly equal to the volume of the submerged body.

b) The body submerged in the liquid "loses" from its weight an amount equal to the weight of the volume of liquid equal to the submerged volume of the body.

Archimedes invented the balance that bears his name and was the first to determine the laws of balance in the balance. The activities of his father, the astronomer Phidias, undoubtedly influenced the vocation and scientific background of Archimedes who, from a young age, was in Alexandria, where he became friends with several Alexandrian masters.

## Heureca!

Back in Syracuse, he devoted his entire life to scientific research. One of the best known stories about Archimedes is that of the "Hieron Golden Crown", told as follows:

*Among the great number of discoveries made by Archimedes, it is necessary to note the following: When Hieron reigned in Syracuse, he proposed to offer, in a certain temple, a golden crown to the immortal gods. He combined the making of the work with an artisan through a good sum of money and delivery of the amount of gold by weight. ”The artisan delivered the crown on the date agreed with the King, who found it perfectly executed, appearing to contain all the gold that had been delivered to him. The artisan had removed part of the gold, replacing it with an equivalent weight in silver, and the king, indignant at this deceit and not having the means to prove to the artisan his deception, charged Archimedes to take care of the matter and that with his intelligence. One day when Archimedes, concerned about this matter, happened to stumble into a bath house, he realized that as he entered the bathtub, water overflowed. The reason for his discovery made him discover the reason he was looking for and, without waiting, for the joy it brought him, he left the bath still naked and running to his house, shouting: Heureka! Heureka !, that is, "found! Found!".*

On the basis of this discovery, he then took two masses of equal weight to the crown: one of gold and one of silver. He then plunged the silver mass into a vase, which produced an amount of water equal to the volume of that mass; He then took out the mass and refilled the vessel with the same amount of water that he had poured and was careful to measure so that he could know the amount of water that corresponded to the silver mass he had introduced into the vessel.

After this experiment, he also plunged the gold mass into the water-filled vessel and, having removed it, measured the overflowing water again, finding that the gold mass had not displaced as much water as silver and that the difference was less was equal to the difference between the volumes of the gold mass and the silver mass by equal weight. Finally, he filled the vase again, plunging the crown this time, which displaced more water than it had displaced the mass of gold of equal weight but less than the mass of silver. Calculating, then, from these experiments, how much more water the crown had dislodged than the one that displaced the gold mass, he knew how much silver was mixed with gold, thus clearly showing fraud. of the craftsman ".

## The death of Archimedes

Archimedes' death is narrated in different ways. According to Plutarch, Archimedes' death came after the Roman army conquered the most important parts of the besieged city:

*"And when they had taken the same morning, Marcelo marched to the Hexapils, congratulating him on all the chiefs who were at his command; but he himself says that seeing and recording from above the grandeur and beauty of such a city, he shed many tears. pitying what was going to happen… the soldiers who had asked to grant them the right to the looting… and to be set on fire and destroyed. ”None of this consented to Marcelo, and only by force and disgust condescended to take advantage of the goods. and of the slaves… expressly ordering that no death, violence, or enslavement of any of the Syracusans be done… But what mainly afflicted Marcelo was what happened to Archimedes: he was casually handed over to the examination of a certain mathematical figure, and fixed on it his spirit and his sight, did not perceive the invasion of the Romans, nor the conquest of the city. ”A soldier suddenly came to him, commanding him to do so. to go to Marcelo's house; but he did not want to go before solving the problem and reaching the demonstration; with which, irritated, the soldier drew his sword and killed him ... Marcelo felt sorry for him and ordered the assassin soldier to withdraw from his presence as abominable, and sending for the wise man's relatives, treated them with the greatest appreciation and distinction".*

In Archimedes' production the researcher is revealed exclusively. His writings are true scientific memoirs, original works, in which all that was produced on the subject are known beforehand, and their own new elements are presented. Archimedes' main works were on:

1. The *sphere and the cylinder* - One of the most beautiful writings of Archimedes. Among its results, the lateral area of the cone and the cylinder.

2. The*s conoids and the spheroids* - Refers to the solids we today call revolution ellipsoid, revolution paraboloid and revolution hyperboloid.

3. The*s spirals* - It is a monographic study of a flat curve, today called the Archimedes spiral, which is obtained by a simple combination of rotation and translation movements. Among the results is a process for rectifying the circumference.

4. The* circle measure* - Contains only 3 propositions and is one of the works that best reveals Aristotle's mathematical mind. In technical ostentation, exact and approximate mathematics, arithmetic, and geometry are admirably combined to propel and steer the classic problem of square squaring in a new direction.

5. *Parable Square* - This writing offers the first example of quadrature, that is, of determining an equivalent polygon, of a flat myring figure: the segment of the parable.

6. *The Arenary* - Archimedes conducts a study, in which he interleaves his own numbering system, which allows him to calculate and, above all, express huge quantities, and a series of astronomical considerations of great historical importance, as they allude to the heliocentric system of antiquity, due to Aristarchus. from Samos.

7. The* balance of plans* - It's the first scientific treatise on static. The lever, the centers of gravity of some polygons, among other results.

8. *Of floating bodies* (Book I and II). - The scientific basis of hydrostatics.

9. *From the method concerning mechanical theorems* Archimedes comes remarkably close to our current concepts of integral calculus.

10. *The Stomachion* - It's a geometric game, kind of *puzzle*, formed by a series of polygonal pieces that complete a rectangle.

11. *The oxen problem* - A problem regarding number theory.

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