The tale of the scientist Archimedes, who cost an entire army. Archimedes - biography, information, personal life

Archimedes is the greatest ancient Greek mathematician, physicist, astronomer and military engineer. He surprisingly combined the qualities of a theoretical scientist and a practitioner, successfully applying his knowledge and inventions to protect his native city.

Archimedes was born in Sicily, in the wealthy city-state of Syracuse, a former Greek colony. His father, the mathematician and astronomer Phidias, was friends with the Syracusan tyrant Hieron II and may even have been his relative. The thirst for knowledge led Archimedes to Alexandria, the main scientific center of that time, where he met and became friends with many prominent scientists, such as Conon and Eratosthenes of Cyrene. After living in Alexandria for several years, Archimedes returned to Syracuse and remained there for the rest of his life.

One of the most famous statements attributed to Archimedes is: “If I had another Earth at my disposal, on which I could stand, I would move ours.” According to Plutarch's story, when Hieron II heard these words, he asked to translate such a bold idea into action and show some kind of heaviness moved by a small effort. In response, Archimedes ordered the royal three-masted cargo ship "Syracuse" to be filled with luggage, recently pulled ashore by a whole crowd of people with great difficulty, put a large team of sailors on it, and he sat at a distance and, without any tension, pulling the end of the rope passed through the composite block, He pulled the ship closer to him - so slowly and evenly, as if it was sailing on the sea.

In addition to the system of blocks, Archimedes invented a water-lifting screw, which was used in ancient times to irrigate fields and pump water from mines.

Another amazing invention of Archimedes is a small planetarium, during the movement of which one could observe the movement of the planets, as well as the phases and eclipses of the moon.

Fearing a Roman attack, Hiero II asked Archimedes to create a defensive system for Syracuse. On the advice of Archimedes, the city walls were rebuilt so that they could accommodate catapults and winches that lifted heavy stones and threw them over long distances, while the scientist himself began to develop new machines. The defense of Syracuse became a battle between the Romans and Archimedes.

One of the most terrible weapons used by the inhabitants of Syracuse were the "beaks of Archimedes." They descended on any ship that came into range, grabbed it tightly and lifted it or turned it over. No one knows how these "beaks" work, perhaps they were a huge hook lowered with a winch.

Some ancient historians of the siege of Syracuse mention focusing mirrors, with which the besieged set fire to the sails and hulls of ships that approached the city wall within an arrow's flight distance. Archimedes could have come up with such "burning" mirrors, however there is no evidence that he actually did it.

The name of Archimedes is associated not only with many legends, but also with real discoveries. He determined the value of the number i with amazing accuracy, 2000 years before the advent of integral calculus described a method for calculating the volume and surface area of curved bodies, invented a way to express very large numbers, demonstrating it by counting the number of grains of sand that exist in the Universe.

In 212 BC. e. The Romans still captured Syracuse. Bursting into the house of Archimedes, one of the soldiers saw an old man, thoughtfully drawing geometric figures on the sand. The inventor asked not to interfere with his thinking about solving the problem, which made the warrior very angry, and he, drawing his sword, killed Archimedes.

With the help of various machines invented by Archimedes, Syracuse withstood the siege of Roman ships for about three years.

Archimedes is known to have lived in Syracuse. This is Sicily.

At the same time that Hannibal was at war with Rome, the Greek Syracuse was in the unpleasant position of having to choose: they should join one of the warring parties. There was no way to remain neutral. In the city itself, there were different opinions about who to join. Better, of course, to the winner. But the situation was changing.

Syracuse, sending a detachment of 8 thousand soldiers, took part in the resistance to the Romans Leontin. The city fell. Horrors were told about his fall: everyone was killed by the Romans - warriors, civilians, everything was plundered. Titus Livius, a Roman historian, does not deny that 2,000 defectors were flogged and executed on the orders of the Roman general Marcellus.

In Syracuse, they decided that with their richer city, the Romans would have done even worse.

Roman troops launched an assault on Syracuse simultaneously from land and sea. And then they encountered Archimedes.

Archimedes was born in 287 BC. in the family of the mathematician and astronomer Phidias and was a relative of the Syracusan king Hieron II. He continued his education in Alexandria. He made interesting astronomical observations, determined the diameter of the Sun and the distances between the planets, invented the "celestial globe", which made it possible to study the movements of the planets, the phases of the moon, solar and lunar eclipses. He worked a lot in the field of mechanics, on the invention of various kinds of tools, on the solution of mathematical and physical problems.

Obviously, he saw his civic duty in protecting the fatherland from invaders.

Map of Syracuse.

Siege of Syracuse.

Marcellus stormed the wall of Ahradina from the sea with 60 quinqueremes; from some ships, slingers, archers, spearmen fired at the wall, other ships he ordered to connect two by two and, having installed siege weapons on them, bring them close to the fortifications.

Roman quinquereme.

Distant ships Archimedes struck with catapults, and to defeat neighbors he organized loopholes in the walls. When the Roman ships entered the dead zone under the very walls, an "iron paw" collapsed on them: seizing the bow of the ship with a paw, the ship was put aft or even raised above the sea, and then abandoned, the ship lost its crew, crashed, drowned.

Loopholes in the walls.

Variant of the "iron paw".

Another.

The assault from the sea was unsuccessful.

The same with sushi. The tools of Archimedes threw stones, arrows, spears, blocks on the heads of the Romans.

Marcellus abandoned his attempts to take the city by storm and proceeded to blockade.

Polybius supplements and refines Livy's story. So is Plutarch. According to him, Marcellus cried out: "Shall we not stop fighting with this geometer-Briareus, who, sitting calmly by the sea, destroys our ships and, at the same time showering us with so many arrows, surpasses the hundred-armed giants?" In the end, Archimedes inspired such horror in the Roman soldiers that they fled in panic when they saw a piece of rope or a log above the city wall.

Taking the city by storm was out of the question. The blockade also proved to be ineffective: food was regularly brought to Syracuse from Carthage. Marcellus pinned his hopes only on the "fifth clone" - the pro-Roman Syracusans.

In one place, the city wall was found to be comparatively low. But it was here that she was especially vigilantly guarded. In the besieged city, the usual three-day celebration in honor of Artemis was going on, wine was generously distributed to the people.

Late at night, a Roman detachment of a thousand soldiers entered the city. The panic began. However, Ahradina and the island of Ortigia were not going to give up.

While negotiations were going on in the Roman camp, clashes broke out in Syracuse itself. In this situation, Marcellus proceeded to storm Ahradina and landed troops on Ortigia. Now the capture is successful. He gave Ahradina to be plundered. Titus Livy: "Many disgusting examples of malice were revealed, many of greed." During this bacchanalia of violence and robbery, Archimedes died, busy drawing on the sand. Livy says that the Roman soldier did not know who he encountered, and Marcellus seemed to be upset by this death: he attended to the burial of the great scientist, and protected his relatives from violence.

Ortigia. Modern look.

Plutarch gives three stories about the death of Archimedes.

According to the first, Archimedes was busy drawing and did not pay attention to the Roman soldiers. When one of them demanded it to Marcellus, Archimedes said that he had not yet solved the problem, and the enraged warrior stabbed him to death. The second is similar to the first. And the third tells that Archimedes was going to Marcellus with his tools, when the soldiers, mistaking them for treasures, killed him for the purpose of robbery.

Zonarra tells the following: "The Romans killed many others and Archimedes." With him, Marcellus did not order to spare the scientist, did not grieve about his death, and, moreover, did not punish anyone.

Marcellus, who unleashed robberies and murders in the captured Syracuse, may have considered it necessary to express sadness about the death of Archimedes: it was unprofitable for the Romans, who needed the support of the Greeks, to present themselves in the role of murderers and rapists, exterminating the best representatives of the Hellenic thought. The comparison with Hannibal, who had Greek writers at his headquarters, was extremely unpleasant.

Cicero says that Marcellus dedicated one of the Archimedean "spheres", celestial globes, to the temple of Courage, and took the other for himself: this relic was passed down in his family from generation to generation. A sad relic - the creation of a brilliant man you killed.

Marcellus.

However, in Syracuse captured by Rome, it was apparently unsafe to mention the name of Archimedes - the uncompromising enemy of Rome. His grave was abandoned and forgotten. Only Cicero already in the 1st c. I was able to find it with great difficulty.

Archimedes Square in Syracuse.

She is. Fountain of Artemis, in whose honor the festival was held.

A statue of Archimedes with a bronze hyberbolic mirror, with the system of which he seemed to burn the Roman fleet. But that's another story.

Greetings to the constant readers and guests of the site! In the article "Archimedes: biography, discoveries, interesting facts" - about the life of the ancient Greek mathematician, physicist and engineer. Years of life 287-212 BC At the end of the article there is an interesting and informative video material about the life of a scientist.

Biography of Archimedes

The famous scientist of antiquity Archimedes was the son of the astronomer Fidius and received a good education in Alexandria, where he became acquainted with the works of Democritus,.

During the siege of Syracuse, Archimedes developed siege engines (flamethrowers), which destroyed a significant part of the enemy army. Archimedes was killed by a Roman soldier despite the orders of General Marcus Marcellus.

Edouard Vimont (1846-1930). Death of Archimedes

A legend spread by the Greeks says that the great mathematician was stabbed to death as he wrote an equation in the sand, thus wanting to counter his superiority with Roman incompetence. It is possible that his death was also revenge for the damage done by his inventions to the Roman fleet.

"Eureka!"

The most famous anecdote about Archimedes tells how he invented a method for determining the volume of an irregularly shaped object. Hieron II ordered that the golden crown be donated to the temple.

Archimedes had to determine if the jeweler had replaced some of the material with silver. He had to complete this task without damaging the crown, so he could not melt it in a simple form to calculate its density.

While bathing, the scientist noticed that the water level in the tub increases when he enters it. He understands that this effect can be used to determine the volume of the crown.

From the point of view of this experiment, water has a practically constant volume. The crown will displace the amount of water with its own volume. Dividing the mass of the corona by the volume of water displaced, its density is obtained. This density would be lower than that of gold if less expensive and lighter metals were added to it.

Archimedes, jumping out of the bath, runs naked down the street. He is so excited by his discovery and forgets to get dressed. He loudly shouts "Eureka!" ("I found"). The experience was successful and proved that silver had indeed been added to the crown.

The story of the golden crown is not present in any of the known works of Archimedes. In addition, the practical applicability of the described method is doubtful due to the need for extreme accuracy in measuring changes in water level.

The sage most likely used the principle known in the hydrostat as the law of Archimedes, and later described in his treatise on floating bodies.

According to him, a body immersed in a fluid is subjected to a force equal to the weight of the fluid displaced by it. Using this principle, the density of a golden crown can be compared with the density of gold.

heat ray

Archimedes may have used a group of mirrors acting together as a parabolic mirror to set fire to ships attacking Syracuse. Lucian, a writer of the 2nd century, writes that Archimedes destroyed the ships with fire.

Heat Ray of Archimedes

In the 6th century, Antimius of Thrallus called the weapon of Archimedes "burning glass". The device, also called "Thermim Beam Archimedes", was used to focus sunlight on ships, thus illuminating them.

This alleged weapon during the Renaissance became the subject of controversy over its actual existence. rejected it as impossible. Modern scholars attempt to recreate the described effects using only the tools available at the time of Archimedes.

There are suggestions that a large number of highly polished bronze screens acting as mirrors could be used to focus the sun's rays on a ship using the parabolic mirror principle.

Experiments of Archimedes in the modern world

In 1973, the scientist Ioannis Sakas from Greece conducted an experiment with the Archimedes heat ray at the naval base at Skaramaga. He used 70 copper-coated mirrors measuring 1.5 by 1 m. They were aimed at a plywood model ship at a distance of 50 m.

When the mirrors are focused, the mock ship ignites in a few seconds. Previously, ships were covered with resinous paint, which probably contributed to the ignition.

In October 2005, a group of students at the Massachusetts Institute of Technology conducted an experiment with 127 square mirrors measuring 30 x 30 cm, focusing on a wooden model of a ship at a distance of about 30 meters.

The flame appears on a part of the ship, in clear weather with a cloudless sky and if the ship remains stationary for about 10 minutes.

The same group is replicating the "MythBusters" television experiment using a wooden fishing boat in San Francisco. Again there is some ignition. The Mythbusters define the experience as an unfortunate one due to the long time and ideal weather conditions required for ignition.

If Syracuse is in the east, then the Roman fleet will attack in the morning for optimal focusing of the light. At the same time, conventional weapons such as flaming arrows or catapult-launched projectiles can be used much more easily to sink a ship at such a short distance.

Many scientists consider the ancient Greek scientist one of the greatest mathematicians in history, along with Gauss and Euler. Huge contribution to geometry, mechanics, he is considered one of the pioneers of mathematical analysis.

He systematically applies mathematics to the natural sciences, technical discoveries and inventions. His scientific contributions were studied and described by Eratosthenes, Conon and Dosifed.

Works of Archimedes

The mathematician calculated the surface of the parabolic segment and the volumes of various mathematical bodies.
He considered several curves and spirals, one of which bears his name: the Archimedes spiral.
Defined semi-regular multistats called Archimedes.
Presented a proof of the infinity of an array of natural numbers (also known as the axiom of Archimedes).

Biography

Archimedes (Ἀρχιμήδης; 287 BC - 212 BC) was an ancient Greek mathematician, physicist and engineer from Syracuse. He made many discoveries in geometry. He laid the foundations of mechanics, hydrostatics, was the author of a number of important inventions.

Information about the life of Archimedes left us Polybius , Titus Livy, Cicero, Plutarch, Vitruvius and others. Almost all of them lived many years later than the events described, and it is difficult to assess the reliability of this information.

Archimedes was born in Syracuse, a Greek colony on the island of Sicily. Archimedes' father may have been the mathematician and astronomer Phidias. According to Plutarch, Archimedes was closely related to Hieron II, tyrant of Syracuse. For training, Archimedes went to Alexandria of Egypt - the scientific and cultural center of that time.

Alexandria

In Alexandria, Archimedes met and became friends with famous scientists: the astronomer Conon, the versatile scientist Eratosthenes, with whom he then corresponded until the end of his life. At that time, Alexandria was famous for its library, which contained more than 700 thousand manuscripts.

Apparently this is where Archimedes got to know the work Democritus, Eudoxus and other remarkable Greek geometers, whom he mentioned in his writings.

After completing his studies, Archimedes returned to Sicily. In Syracuse, he was surrounded by attention and did not need funds. Due to the prescription of years, the life of Archimedes is closely intertwined with the legends about him.

legends

Already during the life of Archimedes, legends were created around his name, the reason for which were his amazing inventions, which produced a stunning effect on his contemporaries. There is a story about how Archimedes was able to determine whether the crown of King Hieron was made of pure gold, or a jeweler mixed a significant amount of silver into it. The specific gravity of gold was known, but the difficulty was to accurately determine the volume of the crown: after all, it had an irregular shape! Archimedes thought about this problem all the time. Once he was taking a bath and noticed that as much water was flowing out of it, what was the volume of his body immersed in the bath, and then a brilliant idea came to his mind: by immersing the crown in water, you can determine its volume by measuring the volume of water displaced by it . According to legend, Archimedes jumped naked into the street shouting "Eureka!" (ancient Greek εὕρηκα), that is, “Found!”. At that moment, the basic law of hydrostatics, the law of Archimedes, was discovered.

Another legend tells that the heavy multi-deck ship Syracusia, built by Hieron as a gift to the Egyptian king Ptolemy, could not be launched. Archimedes built a system of blocks (polyspast), with the help of which he was able to do this work with one movement of his hand. According to legend, Archimedes said at the same time: “If I had another Earth at my disposal, on which I could stand, I would move ours” (in another version: “Give me a fulcrum, and I will turn the world upside down”).

Siege of Syracuse

The engineering genius of Archimedes manifested itself with particular force during the siege of Syracuse by the Romans in 212 BC. e. during the Second Punic War. At this point, Archimedes was already 75 years old. A detailed description of the siege of Syracuse by the Roman general Marcellus and the participation of Archimedes in the defense is contained in the writings of Plutarch and Titus Livy.

The powerful throwing machines built by Archimedes threw heavy stones at the Roman troops. Thinking that they would be safe at the very walls of the city, the Romans rushed there, but at that time light short-range throwing machines threw a hail of cannonballs at them. Powerful cranes grabbed the ships with iron hooks, lifted them up, and then threw them down, so that the ships turned over and sank. In recent years, several experiments have been carried out in order to verify the veracity of the description of this "superweapon of antiquity." The constructed structure has shown its full performance.

The Romans were forced to abandon the idea of taking the city by storm and proceeded to the siege. The famous historian of antiquity Polybius wrote: “Such is the miraculous power of one person, one talent, skillfully directed to some business ... the Romans could quickly take over the city if someone removed one elder from among the Syracusans.”

According to one legend, during the siege, the Roman fleet was burned by the defenders of the city, who, using mirrors and shields polished to a shine, focused the sun's rays on them on the orders of Archimedes. There is an opinion that the ships were set on fire by accurately thrown incendiary shells, and the focused beams served only as an aiming mark for the ballistas. However, in an experiment by the Greek scientist Ioannis Sakkas (1973), a plywood model of a Roman ship was set on fire from a distance of 50 m using 70 copper mirrors. However, the authenticity of the legend is doubtful; neither Plutarch nor other ancient historians mention mirrors when describing the defensive inventions of Archimedes; for the first time this episode was discovered in the treatise of Anthemius of Tralles (VI century), one of the architects of Hagia Sophia in Constantinople (the treatise was devoted to convex and concave mirrors). In the 12th century, the legend gained popularity after the publication of an extensive chronicle of world history by John Zonara.

In the autumn of 212 B.C. e. due to the betrayal of Syracuse, they were taken by the Romans. At the same time, Archimedes was killed.

Death of Archimedes

The story of the death of Archimedes at the hands of the Romans exists in several versions:

The story of John Zetz (Chiliad, book II): in the midst of the battle, the 75-year-old Archimedes sat on the threshold of his house, reflecting in depth on the drawings he had made right on the road sand. At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman with a cry: “Do not touch my drawings!” The soldier stopped and cold-bloodedly cut the old man down with his sword.
Plutarch's story: “A soldier approached Archimedes and announced that Marcellus was calling him. But Archimedes insistently asked him to wait one minute, so that the task he was engaged in would not remain unsolved. The soldier, who did not care about his proof, got angry and pierced him with his sword. Plutarch claims that the consul Marcellus was angry at the death of Archimedes, whom he supposedly ordered not to be touched.
Archimedes himself went to Marcellus to bring him his instruments for measuring the magnitude of the Sun. On the way, his burden caught the attention of the Roman soldiers. They decided that the scientist was carrying gold or jewelry in a casket, and, without thinking twice, cut his throat.
The story of Diodorus Siculus: “Making a sketch of a mechanical diagram, he bent over it. And when the Roman soldier came up and began to drag him as a prisoner, he, completely absorbed in his diagram, not seeing who was in front of him, said: “Get out of my diagram!” Then, when the man continued to drag him, he turned and recognized in the Roman, exclaimed: “Quickly, someone, give me one of my cars!” The Roman, frightened, killed the weak old man, one whose achievements were a miracle. As soon as Marcellus found out about this, he was very upset and, together with noble citizens and Romans, arranged a magnificent funeral among the graves of his ancestors. As for the killer, he seems to have been beheaded."
“Roman history from the founding of the city” by Titus Livius (Book XXV, 31): “It is reported that when, with the strong turmoil that the panic that spread in the taken city could cause, the soldiers fled, plundering, many disgusting examples of malice and greed; by the way, one warrior killed Archimedes, busy drawing geometric figures on the sand, not knowing who he was. Marcellus, they say, was upset by this, attended to the burial of the murdered, even sought out the relatives of Archimedes, and his name and memory of him brought respect and safety to the latter.

Cicero, who was quaestor in Sicily in 75 BC. e., writes in the "Tusculan conversations" (book V) that he was in 75 BC. e., 137 years after these events, it was possible to discover the dilapidated tomb of Archimedes; on it, as bequeathed by Archimedes, there was an image of a ball inscribed in a cylinder.

Scientific activity

Maths

According to Plutarch, Archimedes was simply obsessed with mathematics. He forgot about food, did not care about himself at all.

The works of Archimedes related to almost all areas of mathematics of that time: he owns remarkable research in geometry, arithmetic, and algebra. So, he found all the semi-regular polyhedra that now bear his name, significantly developed the theory of conic sections, gave a geometric method for solving cubic equations of the form x^2 (a \pm x) = b, the roots of which he found using the intersection of a parabola and a hyperbola . Archimedes also carried out a complete study of these equations, that is, he found under what conditions they will have real positive different roots and under what conditions the roots will coincide.

However, the main mathematical achievements of Archimedes relate to problems that are now classified as the field of mathematical analysis. The Greeks before Archimedes were able to determine the area of polygons and a circle, the volume of a prism and a cylinder, a pyramid and a cone. But only Archimedes found a much more general method for calculating areas or volumes; for this he perfected and masterfully applied the method of exhaustion of Eudoxus of Cnidus. In his Epistle to Eratosthenes on the Method (sometimes called the Method of Mechanical Theorems), he used infinitesimals to calculate volumes. The ideas of Archimedes subsequently formed the basis of integral calculus.

Archimedes was able to establish that the volumes of a cone and a ball inscribed in a cylinder, and the cylinder itself, are related as 1:2:3.

He considered the determination of the surface and volume of a ball to be his best achievement - a task that no one before him could solve. Archimedes asked to knock out a ball inscribed in a cylinder on his grave.

In his essay Quadrature of a Parabola, Archimedes proved that the area of a segment of a parabola cut off from it by a straight line is 4/3 of the area of a triangle inscribed in this segment (see figure). To prove it, Archimedes calculated the sum of an infinite series:

Each term of the series is the total area of the triangles inscribed in the part of the parabola segment not covered by the previous members of the series.

In addition to the above, Archimedes calculated the surface area for the segment of the ball and the coil of the "Archimedes' spiral" discovered by him, determined the volumes of the segments of the ball, ellipsoid, paraboloid and two-sheeted hyperboloid of revolution.

The next problem is related to the geometry of curves. Let some curved line be given. How to define a tangent at any of its points? Or, if we put this problem into the language of physics, let us know the path of some body at each moment of time. How to determine its speed at any point? At school they teach how to draw a tangent to a circle. The ancient Greeks were also able to find tangents to the ellipse, hyperbola and parabola. The first general method for solving this problem was also found by Archimedes. This method subsequently formed the basis of differential calculus.

Of great importance for the development of mathematics was the ratio of circumference to diameter calculated by Archimedes.

Mechanics

Archimedes became famous for many mechanical designs. The lever was known even before Archimedes, but only Archimedes outlined his complete theory and successfully applied it in practice. Plutarch reports that Archimedes built many block-lever mechanisms in the port of Syracuse to facilitate the lifting and transportation of heavy loads. The screw (auger) invented by him for scooping out water is still used in Egypt.

Archimedes is also the first theoretician of mechanics. He begins his book On the Equilibrium of Plane Figures with a proof of the law of the lever. This proof is based on the axiom that equal bodies on equal arms must necessarily balance. Similarly, the book "On the Float of Bodies" begins with a proof of the law of Archimedes. These proofs of Archimedes represent the first thought experiments in the history of mechanics.

Astronomy

Archimedes built a planetarium or "celestial sphere", during the movement of which one could observe the movement of five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, the disappearance of both bodies behind the horizon line. Engaged in the problem of determining the distances to the planets; presumably, his calculations were based on a system of the world with a center in the Earth, but the planets Mercury, Venus and Mars, revolving around the Sun and, together with it, around the Earth. In his essay "Psammit" conveyed information about the heliocentric system of the world of Aristarchus of Samos.

Compositions

The following have been preserved to this day:

Parabola quadrature / τετραγωνισμὸς παραβολῆς - the area of the parabola segment is determined.
On the ball and cylinder / περὶ σφαίρας καὶ κυλίνδρου - it is proved that the volume of the ball is 2/3 of the volume of the cylinder circumscribed around it, and the surface area of the ball is equal to the area of the lateral surface of this cylinder.
About spirals / περὶ ἑλίκων - the properties of Archimedes' spiral are derived.
About conoids and spheroids / περὶ κωνοειδέων καὶ σφαιροειδέων - volumes of segments of paraboloids, hyperboloids and ellipsoids of revolution are determined.
On the balance of plane figures / περὶ ἰσορροπιῶν - the law of balance of the lever is derived; it is proved that the center of gravity of a flat triangle is at the point of intersection of its medians; are the centers of gravity of the parallelogram, trapezoid and parabolic segment.
Epistle to Eratosthenes about the method / πρὸς Ἐρατοσθένην ἔφοδος - discovered in 1906, partially duplicates the work “On the Sphere and Cylinder” in terms of subject matter, but here the mechanical method of proving mathematical theorems is used.
About floating bodies / περὶ τῶν ὀχουμένων - the law of floating bodies is deduced; the problem of the equilibrium of the section of a paraboloid simulating a ship's hull is considered.
Measurement of a circle / κύκλου μέτρησις - only an excerpt from this work has come down to us. It is in it that Archimedes calculates an approximation for the number \pi.
Psummit / ψαμμίτης - a way of writing very large numbers is introduced.
Stomachion / στομάχιον - a description of a popular game is given.
The problem of Archimedes about bulls / πρόβλημα βοικόν - a problem is set, reduced to the Pell equation.
A number of works by Archimedes have survived only in Arabic translation:

Treatise on the construction of a bodily figure near the ball with fourteen bases;
Book of Lemmas;
A book about building a circle divided into seven equal parts;
A book about touching circles.

A native and citizen of Syracuse. Educated in Alexandria, the greatest cultural center of the ancient world.

Archimedes owns a number of important mathematical discoveries. The highest achievements of the scientist in the field of physics are the scientific substantiation of the action of the lever and the discovery of the law according to which any body immersed in a liquid is subjected to an upward buoyancy force equal to the weight of the liquid displaced by it.

During the 2nd Punic War, Syracuse, who had defected to Carthage, was subjected to a Roman siege. Archimedes became famous for his active participation in the defense of the city. He created many war machines that delayed the capture of Syracuse for a long time. The possibility of the existence of some of these mechanisms is still in doubt among a number of scientists. So, Archimedes seems to have managed to focus the sunlight with the help of a giant mirror and direct the resulting beam at enemy ships.

During the capture of Syracuse, the scientist was killed by Roman soldiers.

Archimedes was an ancient Greek scientist, physicist, mathematician and engineer from Syracuse who lived from 287-212 BC. In addition to many discoveries made in the field of mathematics, especially in geometry, he also became the founder of mechanics, hydrostatics, and the author of a number of other significant inventions. He owns many significant discoveries in the field of mathematics and physics. For example, the ratio of the length and diameter of the circle, the scientific rationale for the action of the lever, and others.

Some treatises of Archimedes have survived to the present, which speak of the genius of the scientist. Among them are "On the ball and the cylinder", "On floating bodies", "On spirals", "On the equilibrium of plane figures" and others. Many discoveries were made in the field of astronomy. So, for example, Archimedes built the first planetarium, with the help of which it was possible to observe the movement of several planets, the rising of the Sun and the Moon, the phases of the eclipse of the Moon, etc. In one of his writings, he mentions the heliocentric system of the world. In memory of Archimedes, a crater and an asteroid are named after him.

Greek mechanic, physicist, mathematician, engineer. Born and spent most of his life in Syracuse. Studied in Alexandria. He was an adviser to King Hieron II of Sicily. According to legend, with the help of a system of mirrors reflecting the sun's rays, he burned the Roman fleet that laid siege to Alexandria. Considered the inventor of the catapult. He established the rule of the lever, in connection with which the saying is attributed to him: "Give me a fulcrum, and I will move the Earth."

Archimedes brilliantly combined the talents of an engineer-inventor and a theoretical scientist. In addition to military vehicles, he designed a planetarium and a propeller for lifting water, which is still in use. He wrote treatises: "On spirals", "On a ball and a cylinder", "On conoids and spheroids", "On levers", "On floating bodies", etc. He calculated the volume of the sphere and the value of the number "pi". Calculate the number of grains of sand in the volume of the globe.

One day King Hieron II asked Archimedes to determine if jewelers had mixed silver with gold when they made his crown. To do this, it was necessary to find out not only the weight, but also the volume of the product. Archimedes solved the difficult problem gracefully: he lowered the crown into the water and determined the volume of the displaced liquid. They say that the thought of this came to him when he was taking a bath. Joyful, he ran out into the street in what he was with a cry: "Eureka!" .

Many legends are associated with the name of Archimedes, the authenticity of which can hardly be confirmed. Of course, he could not burn enemy ships with the help of mirrors. But the story of the royal crown is quite plausible.

It is said that Hieron suggested that he lift the greater part with a small force. The scientist invented a mechanism by which he pulled a heavily loaded trireme ashore. One of the historians of science suggested that Archimedes used his screw in connection with a system of gears. True, most likely this story was invented in order to more vividly represent the engineering genius of Archimedes. Greek sailors, apparently, were able to pull even large ships ashore with the help of levers and blocks, but was Archimedes alone able to cope with such a task? Hardly.

Rumors about the planetarium he created are considered more reliable. In the center was the Earth, the Sun, the Moon and several planets revolved around it, set in motion by some mechanism. This building was enthusiastically mentioned by Cicero, without leaving a detailed description. It is assumed that in the Middle Ages, similar ones were created on the model of the Archimedean planetarium.

Outstanding discoveries of Archimedes

The ancient Greek scientist Archimedes was an inventor, mathematician, designer, engineer, physicist, astronomer, and mechanic. He founded such a direction as mathematical physics. The researcher also developed methods for finding volumes, surfaces and areas of various bodies and figures, anticipating the integral calculus. He is the author of many inventions. The name of the scientist is associated with the emergence of the laws of the lever, the introduction of the term center of gravity and research in the field of hydrostatics. When the Romans attacked Syracuse, it was Archimedes who organized the engineering defense of the city.

In times of high technology and scientific discoveries, we are accustomed to perceive achievements as something ordinary, forgetting that the foundations of existing knowledge were laid by ancient scientists. They were the pioneers. And Archimedes of Syracuse was generally a genius. After all, he confirmed most of his ideas in practice. Our contemporaries successfully use them in their work, although they do not even know who their author was. The biography of Archimedes has come down to our days only from legends and memories. We invite you to familiarize yourself with it.

Childhood and studies

Archimedes, whose brief biography will be presented below, was born in the city of Syracuse around 287 BC. e. His childhood fell on the period when King Pyrrhus waged wars with the Carthaginians and Romans, trying to create a new Greek state. Hieron, a relative of Archimedes, who later became the ruler of Syracuse, especially distinguished himself in this war. Phidias was Hieron's close associate. This allowed him to give Archimedes a good education. But the young man lacked theoretical knowledge, and he went to Alexandria, which was at that time a scientific center. Here, the Ptolemies, the rulers of Egypt, gathered the best Greek scientists and thinkers of that time. Also in Alexandria was the largest library in the world, where Archimedes studied mathematics and the works of Eudoxus, Democritus, etc. for a long time. In those years, the future researcher became friends with the astronomer Konon, the geographer and mathematician Eratosthenes. He then carried on frequent correspondence with them.

Sources: allbiograf.ru, citaty.su, www.sdamna5.ru, biopeoples.ru, fb.ru

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