Biography

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

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

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 Hiero II, the tyrant of Syracuse. To study, 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 collected more than 700 thousand manuscripts.

Apparently this is where Archimedes got acquainted with the works Democritus, Eudoxus and other remarkable Greek geometers, which 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. Because of how long ago the life of Archimedes was, it was closely intertwined with the legends about him.

Legends

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

Another legend says that the heavy multi-deck ship Syracuse, built by Hieron as a gift to the Egyptian king Ptolemy, could not be launched. Archimedes built a system of blocks (pulley hoist), 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 to stand on, 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 moment, Archimedes was already 75 years old. Detailed description the siege of Syracuse by the Roman commander Marcellus and the participation of Archimedes in the defense is contained in the writings of Plutarch and Titus Livy.

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 pelted them with a hail of cannonballs. Powerful cranes grabbed ships with iron hooks, lifted them up, and then threw them down, so that the ships turned over and sank. IN last years Several experiments were conducted to test the veracity of the description of this “superweapon of antiquity.” The constructed structure showed its full functionality.

The Romans were forced to abandon the idea of ​​taking the city by storm and switched to a siege. The famous ancient historian Polybius wrote: “Such is the miraculous power of one person, one talent, skillfully directed towards any task... the Romans could quickly take possession of the city if someone had removed one old man 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 on them Sun rays by order of Archimedes. There is an opinion that the ships were set on fire by well-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), it was possible to set fire to a plywood model of a Roman ship from a distance of 50 m using 70 copper mirrors. However, the authenticity of the legend is questionable; neither Plutarch nor other ancient historians mention mirrors when describing the defensive inventions of Archimedes; this episode was first discovered in the treatise of Anthemius of Trallia (VI century), one of the architects of Hagia Sophia in Constantinople (the treatise was dedicated to convex and concave mirrors). In the 12th century, the legend gained popularity after John Zonar published an extensive chronicle of world history.

In the autumn of 212 BC. e. As a result of treason, Syracuse was taken by the Romans. At the same time, Archimedes was killed.

Death of Archimedes

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

The story of John Tzetz (Chiliad, book II): in the midst of the battle, 75-year-old Archimedes sat on the threshold of his house, pondering in depth over the drawings he made right on the sand of the road. At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman shouting: “Don’t touch my drawings!” The soldier stopped and coldly killed the old man 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 problem he was working on would not remain unsolved. The soldier, who did not care about his proof, became angry and pierced him with his sword.” Plutarch claims that the consul Marcellus was angry at the death of Archimedes, whom he allegedly ordered not to be touched.
Archimedes himself went to Marcellus to take him his instruments for measuring the magnitude of the Sun. On the way, his burden attracted the attention of Roman soldiers. They decided that the scientist was carrying gold or jewelry in the casket, and, without thinking twice, cut his throat.
The story of Diodorus Siculus: “While sketching 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 away from my diagram!” Then, as the man continued to drag him, he turned and recognized The Roman, looking at him, exclaimed: “Quickly, someone, give me one of my cars!” The Roman, frightened, killed the weak old man, the one whose achievements were a miracle. As soon as Marcellus learned of this, he was greatly distressed and, together with the noble citizens and the Romans, arranged a magnificent funeral among the graves of his ancestors. As for the killer, he appears to have been beheaded.”
“Roman History from the Founding of the City” by Titus Livius (Book XXV, 31): “It is reported that when, in the great turmoil that the panic that had spread throughout the captured city could have caused, the soldiers fled, plundering, many disgusting examples of malice and greed; by the way, one warrior killed Archimedes, who was busy drawing in the sand geometric shapes without knowing who he is. Marcellus, they say, was upset by this, took care of the burial of the murdered man, even found 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 “Tusculan Conversations” (Book V) that in 75 BC. e., 137 years after these events, it was possible to discover the dilapidated tomb of Archimedes; on it, as Archimedes bequeathed, there was an image of a ball inscribed in a cylinder.

Scientific activity

Mathematics

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

Archimedes' works related to almost all areas of mathematics of that time: he did remarkable research on geometry, arithmetic, and algebra. Thus, he found all the semiregular polyhedra that now bear his name, significantly developed the doctrine of conic sections, and 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 would have real positive different roots and under what conditions the roots would coincide.

However, the main mathematical achievements of Archimedes concern problems that are now classified as mathematical analysis. The Greeks before Archimedes were able to determine the area of ​​polygons and a circle, the volume of a prism and cylinder, pyramid and cone. But only Archimedes found much more general method calculations of areas or volumes; For this purpose, he improved 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. Archimedes' ideas later formed the basis of integral calculus.

Archimedes was able to establish that the volumes of a cone and a sphere inscribed in a cylinder and the cylinder itself are in a ratio of 1:2:3.

He considered his best achievement to be determining the surface and volume of a sphere - a problem that no one had been able to solve before him. 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 ​​the triangle inscribed in this segment (see figure). To prove this, 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 terms of the series.

In addition to the above, Archimedes calculated the surface area for a segment of a ball and a turn of the “Archimedes spiral” he discovered, and determined the volumes of segments of a ball, an ellipsoid, a paraboloid and a two-sheet hyperboloid of revolution.

The next problem concerns the geometry of curves. Let some curved line be given. How to determine a tangent at any point? Or, if we put this problem into the language of physics, let us know the path of a certain 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 an ellipse, hyperbola and parabola. The first general method for solving this problem was found by Archimedes. This method subsequently formed the basis of differential calculus.

The ratio of the circumference of a circle to its diameter, calculated by Archimedes, was of great importance for the development of mathematics.

Mechanics

Archimedes became famous for many mechanical designs. The lever was known before Archimedes, but only Archimedes outlined its 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 Archimedes screw (auger) he invented for scooping up water is still used in Egypt.

Archimedes is also the first theorist of mechanics. He begins his book "On Balance" flat figures» with proof of the law of leverage. This proof is based on the axiom that equal bodies on equal shoulders must necessarily balance. In the same way, the book “On the Floating of Bodies” begins with a proof of Archimedes’ law. 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 the five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, the disappearance of both bodies beyond the horizon. He worked on the problem of determining distances to planets; Presumably, his calculations were based on a world system centered on the Earth, but with the planets Mercury, Venus and Mars revolving around the Sun and with it around the Earth. In his work, “Psammit” conveyed information about the heliocentric system of the world of Aristarchus of Samos.

Essays

The following have survived to this day:

Quadrature of a parabola / τετραγωνισμὸς παραβολῆς - the area of ​​a parabola segment is determined.
About the ball and the cylinder / περὶ σφαίρας καὶ κυλίνδρου - it is proved that the volume of the ball is equal to 2/3 of the volume of the cylinder described 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 the Archimedes spiral are derived.
About conoids and spheroids / περὶ κωνοειδέων καὶ σφαιροειδέων - the volumes of segments of paraboloids, hyperboloids and ellipsoids of revolution are determined.
On the equilibrium of plane figures / περὶ ἰσορροπιῶν - the law of lever equilibrium is derived; it is proved that the center of gravity of a plane triangle is at the point of intersection of its medians; the centers of gravity of the parallelogram, trapezoid and parabolic segment are located.
Epistle to Eratosthenes on the method / πρὸς Ἐρατοσθένην ἔφοδος - discovered in 1906, thematically it partially duplicates the work “On the Ball and the Cylinder”, but here the mechanical method of proving mathematical theorems is used.
About floating bodies / περὶ τῶν ὀχουμένων - the law of floating bodies is derived; The problem of equilibrium of the cross section of a paraboloid modeling a ship hull is considered.
Measuring a circle / κύκλου μέτρησις - only an excerpt from this work has reached us. It is in it that Archimedes calculates the approximation for the number \pi.
Psammit / ψαμμίτης - a way to write very large numbers is introduced.
Stomakhion / στομάχιον - a description of the popular game is given.
Archimedes' problem about bulls / πρόβλημα βοικόν - a problem is posed that can be reduced to Pell's equation.
A number of Archimedes' works survive only in Arabic translation:

A treatise on the construction of a corporeal figure with fourteen bases around a ball;
Book of Lemmas;
A book about constructing a circle divided into seven equal parts;
A book about touching circles.

More than two thousand years ago, the entire western part of the coast Mediterranean Sea was engulfed in the flames of a grandiose war. Military operations took place in Italy and Sicily, North Africa and Spain. This war is known in world history as the Second Punic War, in which Rome and Carthage fought for dominance in the Mediterranean.

The famous commander from Carthage, Hannibal, in order to deliver a fatal blow to the very heart of the enemy, conceived a rather bold plan to fight Rome - in Italy itself. In 218 BC new era With a large army and war elephants, he crossed the Pyrenees Mountains, southern Gaul and penetrated through the Alps into Northern Italy. On the fields of Italy, Hannibal defeated three Roman armies in succession and in 216 dealt a crushing blow to the Romans at Cannae. The entire Roman army was destroyed. A number of Roman allies (Capua and others) went over to the side of Carthage. The freedom-loving citizens of the city of Syracuse also rebelled against Roman rule.

Syracuse, one of the greatest cities of antiquity, the center of Greek science and art in the West, was a Greek colony located on the southeastern coast of Sicily. The circumference of the powerful city wall was 23.5 kilometers. For a long time Syracuse was an independent state, the first Greek naval power. But in the 3rd century. BC, Rome advanced on Sicily from the north, and Carthage from the south. During the First Punic War, Sicily was conquered by the Romans, and the people of Syracuse had to accept Roman hegemony.

To punish the disobedient for the uprising, the Roman fleet and army under the leadership of the talented commander Marcus Claudius Marcellus approached the city in 213. Horror took possession of the residents. Marcellus had just stormed another Sicilian city, Leontina, and executed two thousand defectors from the Roman camp. The same fate awaited this city.

More than a hundred Roman ships entered Syracuse harbor. Marcellus formed them in battle order. Penteres tied in pairs with wooden towers, lifting engines and siege weapons came close to the wall. Marcellus signaled for the machines to raise the drawbridges to the level of the walls and lower them onto the walls. Over the lowered bridges, the Roman soldiers were supposed to burst into the city like an indomitable avalanche. The fall of the city seemed inevitable. The assault began from sea and land. But before the vehicles on the penthers had time to raise the drawbridges, before the catapults and ballistae had time to throw their shells, something unexpected happened.

Iron hooks and “paws” suddenly descended from huge levers placed on the battlements of the walls. They clung to the bows of ships, lifted them up, overturned them, smashed them against coastal rocks and cliffs at the foot of the city wall, and drowned them in the depths of the sea. Then Marcellus, according to the Greek historian Plutarch, advanced a ram onto the platform. As he approached the wall, the townspeople threw several stones weighing more than a hundred kilograms at him. They completely destroyed it. The stones were followed by lead balls and huge logs that sank ships in the sea.

The broken Roman ships retreated from the city wall. Marcellus decided to resume the assault at night. He hoped that the vehicles throwing shells would be powerless at night. Shells thrown at random will fly over the heads of the besiegers. But the talented leader of the defense also took this circumstance into account: he positioned his spear-throwing machines so that they constantly threw out short spears that hit the enemy.

The Roman fleet received a well-deserved lesson. The same fate befell the Roman army on the landward side. And here the Roman siege weapons and soldiers were met with iron hooks, hooks, and “scorpions” that picked up the soldiers and threw them onto the stones. The proud Roman had to give up thoughts of taking the city by storm. He decided to go on a blockade and starve the residents to death. But it was difficult for the army to cordon off the entire city, and the residents maintained contact with the outside world.

Archimedes - life and scientific works

Who was this most talented engineer, organizer of defense, builder of ingenious machines, who forced the invincible Roman army to retreat?

It was the greatest physicist and mathematician of antiquity - Archimedes, who applied all his genius abilities to organize the defense of his native city.

Archimedes was born in Syracuse in 287 BC. According to the famous Roman politician and orator Cicero, Archimedes was of low social status and lived poorly. Plutarch claims that Archimedes was already interested in mathematics as a child. A trip to Egypt, where he visited the city of Alexandria, the center of Hellenic culture, had a great influence on the young man. Returning to his homeland, he devoted himself entirely to science and wrote a number of brilliant mathematical works.

Most Greek scientists of the IV-III centuries. BC. was not only condescending, but also somewhat contemptuous of mathematics if it pursued utilitarian goals. Archimedes did not dissociate himself from the people and did not isolate himself in his office from the everyday needs of his fellow citizens. He tried to apply his knowledge to practical life, to make all the achievements of science the property of the people, and often demonstrated his discoveries to the citizens of Syracuse.

Unfortunately, not all of the genius’s works have survived. IN different time The following works of his were found:

1. On the equilibrium of plane figures.
2. About the squaring of a parabola.
3. About floating bodies.
4. About measuring a circle.
5. About the ball and cylinder.
6. About conoids and spheroids, i.e. about bodies learned from the rotation of various figures.
7. About spirals.
8. "Psummit."
9. Individual theorems (lemmas).
10. Stamachion - about the rearrangement of plane figures.

In 1907, a new manuscript “Ephodik” (manual) was found, which contains theorems on the volumes of cones, as well as spheroids and conoids.

The following works of the scientist are considered lost:

1. About a heptagon in a circle.
2. About the contact of circles.
3. About parallel lines.
4. About triangles.
5. About definitions and data.
6. Book "Archai".

In his works “On the Ball and the Cylinder” the scientist proves that the ratio of the volumes of a cone, hemisphere and cylinder with the same bases and heights is equal to the ratio 1: 2: 3.

Among other problems proposed in the second book, there is the famous problem of dividing a ball into two parts by a plane. Archimedes gave correct solution this problem, leading it to a problem of an algebraic nature. Archimedes attached special importance to this work.

In the book about the spiral, the scientist examines the properties of the so-called Archimedean spiral.

In his work “Psammit,” he set out to prove that it was possible to express gigantic numbers.

In his works “On Floating Bodies,” Archimedes establishes the basic principles of hydrostatics and hydrodynamics. This law was found thanks to the following case. The ruler of Syracuse ordered a gold crown from a jeweler. But he was informed that the jeweler had hidden some of the gold and replaced it with silver! The king could not verify the correctness of the report and turned to the scientist with a request to find out how much silver was mixed.

Archimedes, while taking a bath one day, noticed the fact that as much water flowed out of the bath as his body displaced. Delighted by this discovery with the exclamation “Eureka! Eureka!”, he jumped out of the bath and ran undressed to test his theory. Archimedes is credited with up to forty discoveries in the field of mechanics. When the Syracusan king built his famous ship with a displacement of 4000 tons, Archimedes equipped this ship with a stone-throwing machine that threw stones weighing 80 kg and spears over a considerable distance. He built a screw, named after him the Archimedean screw. This is a water-lifting machine in which a helical spiral runs inside a cylindrical pipe. The pipe is open at both ends and placed at an angle. With strong rotation, the pipe captures water at its lower end, the water rises upward in a spiral and pours out at the upper end. There is evidence to suggest that the Archimedes screw was used to drain swamps in Egypt. Later it served as the basis for the construction of a ship propeller and found application in the automotive industry.

The scientist developed the theory of a compound block, lever and screw and applied them in practical life. He used blocks to move large weights. Archimedes famously exclaimed: “Give me a point of support, and I will move the Earth.”

He built a planetarium or “aerial globe” that rotated using a system of blocks. In the planetarium, the movement of the planets around the Earth was visible.

Death of Archimedes

But let's return to the city besieged by the Romans. The siege of the city has been dragging on for three years. Archimedes mobilized all his knowledge by building new machines. To his skillful constructions, popular rumor also added legendary ones (some writers, for example, say that Archimedes allegedly built burning glasses and, with their help, collected the sun's rays, aimed them at Roman ships and burned them).

The class struggle intensified among the besieged. The Syracusan nobility, who supported the side of Rome, entered into negotiations with Marcellus, and the city was taken by the Romans due to the treason of the nobility. Marcellus allowed his soldiers to “loot treasures and capture slaves.” Embittered by the long siege, thirsty for booty, the Roman soldiers rushed like bloodthirsty jackals towards the defenseless city. They broke into homes, robbed jewelry, mercilessly killing residents, including the elderly and children.

Archimedes sat deep in his thoughts over the drawings. He described geometric figures on the floor with a compass, not noticing the orgy of robbery and murder taking place in the city. Suddenly a Roman soldier rushed towards him with a drawn sword. Seeing him enter, Archimedes shielded his geometric drawings from him and said: “Don’t spoil my circles for me.” The warrior, intoxicated by the thirst for profit, in response to the words of Archimedes, dealt him a fatal blow with his sword.

This is how the great luminary of science went out in 212 BC ancient world. Out of respect for the brilliant thinker, Marcellus ordered to bury him with great honor. A cylinder with a ball inscribed in it was placed on the grave (this was the desire of Archimedes himself). But the grave was soon overgrown with bushes. Only in 75 BC. e., the famous Cicero, being a ruler in Sicily, found among the abandoned graves a monument to Archimedes, depicting a cylinder. Cicero exclaims with bitterness: “So one of the most glorious states, which once gave birth to so many learned people, did not know where the tombstone of the sharpest minded of its citizens was.”

After the fall of Greek culture, Archimedes was forgotten. Only the Arabs, who appreciated the mathematical genius of Archimedes, translated some of his works into Arabic.

During the Renaissance, Archimedes' works were brought out of obscurity, published, and aroused the admiration of scientists.

Summing up the scientific and scientific-practical activities of Archimedes, it is clear that he is rightly called the father of physics, physical experience, and physical mechanics. Archimedes founded statics as a mathematical science, gave the foundation to hydrostatics, solved many geometric problems, developed methods for calculating the volume of bodies and the center of gravity, and established a connection between geometry and mechanics.

The greatest mathematician of antiquity, Archimedes, was a patriot who passionately loved his homeland, its independence and culture.

Perhaps, when you hear the word inventor or something similar, the name Archimedes often comes to mind. This ancient thinker was truly an outstanding inventor and left a significant number of discoveries that influenced the development of all mankind in the future.

Archimedes was born in 287 BC on the island of Sicily in the capital - Syracuse. He was born into a rather noble family, his father himself was a mathematician, and he was also known to the tyrant of that city, Hieron the Second. Both of them are with early years noticed in the boy a penchant for knowledge and sent him to adolescence Archimedes studied in Alexandria of Egypt, it was there that the largest library was located, which Herostratus later burned to become famous.

After studying, during which he met many learned men of his time and learned advanced ideas, Archimedes returned to his homeland and actually entered the service of Hieron. The tyrant wants in every possible way for Archimedes to begin developing all sorts of military innovations for the island, but the young scientist adheres to peaceful views and only wants to study the world. So, Archimedes remains on the island and begins to make his discoveries, many of which turn out to be the result of work with Hiero, for example, it was he who wanted the young mathematician to determine the composition of the crown, but without damaging the object itself.

It was then that the invention appeared about the displacement of bodies of different volumes of water, with identical mass. In addition, Archimedes made many discoveries in mathematics, which were no less than a couple of thousand years ahead of the era. That's right, some ideas, such as semi-regular polyhedra or the use of parabolas and hyperbolas to solve equations, were only appreciated and developed by scientists in modern times, after the Middle Ages.

In 212, Syracuse came under attack from Roman troops. The Second Punic War was then underway and Sicily was at a disadvantage between the empire and Carthage. Archimedes made many military inventions in order to defend his own city (throwing guns, reflecting copper plates and much more), however, Syracuse fell, and Archimedes died at the hands of a Roman soldier.

Biography 2

The exact biography of Archimedes, unfortunately, is unknown. Scientists and archaeologists from different eras cited different facts from his life, but they are also based on the works of people who lived much later than Archimedes. According to the most common version, the future mathematician was born in 287 BC. Place of birth was Syracuse (island of Sicily). The boy's father, an astronomer and mathematician, sent his son to study in Alexandria. The favorite place of the future physicist and mathematician was the library of Alexandria, where he studied the works and writings of Democritus, Eudoxus and many other scientists. There Archimedes makes acquaintances that he will carry throughout his life.

The young man loved mathematics from his youth. He devoted all his time to developments in the fields of arithmetic, algebra and geometry. Specialists in these fields were able to understand, classify and develop his ideas only by the 17th century. Archimedes solved complex equations by finding solutions graphically. He calculated the areas and volumes of various geometric figures. Already collected and generalized into unified principles and formulas known methods calculations. He derived and proved postulates and axioms, which not only have not been refuted, but have also been taken as a basis by modern scientists. One of his most important achievements in geometry, in his own words, was to find the surface area and volume of a sphere. He also derived formulas for calculating the volumes of a paraboloid, hyperboloid of revolution and ellipsoid. Before Archimedes, no mathematician had performed these calculations.

In addition to arithmetic, algebra and his beloved geometry, Archimedes applied his knowledge in the field of mechanics and physics, inventing and improving existing structures and mechanisms. For example, Archimedes improved the lever known before his birth, calculating its capabilities and putting it into practice in the port of Syracuse. Some devices and mechanisms based on the principle of leverage have since made hard work much easier.

Astronomy also did not leave him indifferent. The scientist was engaged in determining the distance between space objects, although he did this from an erroneous point of view. After all, in the 3rd century BC. The geocentric theory of the existence of the world was widespread. However, later Archimedes presented the heliocentric theory in one of his works.

A chain of mountains and a crater on the surface of the Moon, an asteroid, streets in several Russian cities, and a street in Amsterdam are named in his honor. Archimedes died during military operations during the Roman attack on Syracuse. For the victory of his homeland, the scientist created throwing mechanisms. Roman troops suffered significantly from these machines. It was decided to keep the city under siege. In 212 BC. Syracuse surrendered and Archimedes was killed.

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The biography of Archimedes is full of blank spots. Historians know little about the life of the outstanding scientist, since the chronicles of that period contain only scant information, but the description of his works tells in sufficient detail about achievements in the field of physics, mathematics, astronomy and technology. His works were far ahead of their era and were appreciated only centuries later, when scientific progress had reached the appropriate level.

Childhood and adolescence

A short biography of Archimedes is available to researchers. He was born in 287 BC. e. in the city of Syracuse, which was located on the east coast of the island of Sicily and at that time was a Greek colony. The father of the future scientist, a mathematician and astronomer named Phidias, instilled in his son a love of science from childhood. Hiero, who later became the ruler of Syracuse, was a close relative of the family, so the boy was provided with an excellent education.

Then, feeling a lack of theoretical knowledge, the young man left for Alexandria, where the most brilliant minds of that era worked. Archimedes spent many hours in the Library of Alexandria, where the largest collection of books was collected. There he studied the works of Democritus, the Greek philosopher, and Eudoxus, the famous mechanic, astronomer, mathematician and physician. During his studies, the future scientist made friends with Eratosthenes, the head of the Library of Alexandria, and Conon. This friendship lasted for many years.

Service at the court of Hiero II

After completing his education, Archimedes returned to his homeland in Syracuse and began work as a court astronomer in the palace of Hiero II. However, it was not only the stars that interested the inquisitive youthful mind. The work on astronomy was not difficult, so the scientist had enough time to study physics, mathematics and engineering. During this period, Archimedes discovered his famous principle of using a lever and outlined his findings in detail in the book “On the Equilibrium of Plane Figures.” Then the world saw another work of the great scientist, which was called “On the Measurement of a Circle,” where the author explained how to calculate the dependence of the diameter of a circle on its length.

The biography of Archimedes the mathematician includes information about the period of study of geometric optics. A gifted young man conducted unique experiments devoted to the study of the refraction of light, and managed to derive a mathematical theorem that has remained relevant to this day. This work contains evidence that the angle of incidence of a ray on a mirror surface is equal to the angle of reflection.

It is useful to get acquainted with the biography of Archimedes and his discoveries, if only because the latter changed the course of the development of science. Through extensive research in mathematics, Archimedes discovered a more advanced way of calculating the area of ​​complex figures than what existed at that time. Later, these studies formed the basis of the theory of integral calculus. Also the work of his hands is the construction of a planetarium: a complex device that clearly and reliably demonstrates the movement of the Sun and planets.

Personal life

short biography Archimedes and his discoveries have been studied quite well, but the scientist’s personal life is shrouded in secrecy. Neither the contemporaries of the great explorer, nor the historians who studied him life path, did not provide any information about his family or possible descendants.

Serving Syracuse

As follows from the biography of Archimedes, his discoveries in physics were of considerable service hometown. After the discovery of the lever, Archimedes actively developed his theory and found useful things for it. practical use. A complex structure consisting of block-lever devices was created in the port of Syracuse. Thanks to this engineering solution, the process of loading and unloading ships was significantly accelerated, and heavy, oversized cargo was moved easily and almost effortlessly. The invention of the screw made it possible to collect water from low-lying reservoirs and raise it to greater height. This was an important achievement, since Syracuse is located in a mountainous area and the delivery of water presented a serious problem. Irrigation canals were filled with life-giving moisture and uninterruptedly supplied the inhabitants of the island.

However, Archimedes presented the main gift to his hometown during the siege of Syracuse by the Roman army in 212 BC. e. The scientist took an active part in the defense and built several powerful throwing mechanisms. After the enemy forces managed to break through the city walls, most of the attackers died under a hail of stones fired from the Archimedean machines.

With the help of huge levers, also created by the scientist, the Syracusans were able to turn over Roman ships and stopped the attack. As a result, the Romans stopped the assault and switched to prolonged siege tactics. Eventually the city fell.

Death

The biography of Archimedes, a physicist, engineer and mathematician, ended after the capture of Syracuse by the Romans in 212 BC. e. The stories of his death, told by various prominent historians of that era, are somewhat different. According to one version, a Roman soldier broke into the house of Archimedes to escort him to the consul, and when the scientist refused to interrupt his work and follow him, he killed him with a sword. According to another version, the Roman nevertheless allowed the drawing to be completed, but on the way to the consul, Archimedes was stabbed to death. The researcher took with him instruments to study the Sun, but the mysterious objects seemed too suspicious to the uneducated guards, and the scientist was killed. At that time he was about 75 years old.

Having received the news of Archimedes' death, the consul was saddened: rumors about the scientist's talent and his achievements reached the ears of the Romans, so the new ruler hoped to attract Archimedes to his side. The body of the deceased researcher was buried with the greatest honors.

Tomb of Archimedes

150 years after the death of Archimedes, whose biography and achievements admired the Roman rulers, a search was organized for the place of the supposed burial. By that time, the scientist’s grave was abandoned and its location forgotten, so the search turned out to be a difficult task. Marcus Tulius Cicero, who ruled Syracuse on behalf of the Roman emperor, wanted to erect a majestic monument at the grave, but, unfortunately, this structure was not preserved. The burial site is located on the territory of the Archaeological Park of Naples, which is located near modern Syracuse.

Archimedes' Law

One of the scientist’s most famous discoveries was the so-called Archimedes’ Law. The researcher determined that any physical body lowered into water exerts upward pressure. Liquid is displaced in a volume equal to the volume physical body, and does not depend on the density of the liquid itself.

Over time, the discovery became overgrown with many myths and legends. According to one of the existing versions, Hieron II suspected that his royal crown was a fake and was not made of gold at all. He instructed Archimedes to investigate and give a clear answer. To draw correct conclusions, it was necessary to measure the volume and weight of the object, and then compare it with a similar gold bar. It was not difficult to find out the exact weight of the crown, but how to calculate its volume? The answer came while the scientist was taking a bath. He realized that the volume of the crown, like any other physical body immersed in a liquid, is equal to the volume of the displaced liquid. It was at this moment that Archimedes exclaimed: “Eureka!”

Archimedes considered his best friend not man, but mathematics.

The throwing machines that the scientist built during the storming of Syracuse by Roman troops could lift stones weighing up to 250 kg, which was an absolute record at that time.

Archimedes invented the screw while still a young man. Thanks to this invention, water flowed to higher elevations and irrigated fields, and the Egyptians still use this mechanism for irrigation.

Although the biography of Archimedes is full of mysteries and gaps, his achievements in the field of science are undeniable. Most of the discoveries made by scientists almost 2300 years ago are still used today.

Archimedes was born in 287 BC, in Syracuse. A relative of the future scientist was Hiero, who later became the ruler of Syracuse, Hiero II. Archimedes' father Phidias, an outstanding astronomer and mathematician, was at court. For this reason, the boy received a decent education.

Realizing that he lacked theoretical knowledge, the young man soon went to study in Alexandria, where the brightest minds of antiquity worked at that time.

Archimedes spent most of his time in the Library of Alexandria. There he studied the works of Democritus and Eudoxus. During his studies, Archimedes became close to Eratosthenes and Conon. The friendship remained for many years.

Works and achievements

Having completed his studies, Archimedes returned to his native Syracuse and took up the post of astronomer at the court of Hiero II. But it was not only the stars that attracted his attention.

The position of astronomer was not onerous. Archimedes had the opportunity to study mechanics, physics and mathematics. At this time, the researcher applied the principle of leverage to solve several problems in geometry.

The conclusions were presented in detail in the work “On the equilibrium of plane figures.”

A little later, Archimedes wrote the essay “On the Measurement of a Circle.” He managed to calculate the ratio of the diameter of a circle to its length.

When studying the short biography of Archimedes, you should know that he also paid attention to geometric optics. He conducted several interesting experiments on the refraction of light. The theorem has survived to this day. It proves that against the background of the reflection of a ray of light from a mirror surface, the angle of incidence is equal to the angle of reflection.

Gifts to Syracuse

Archimedes made many useful discoveries. All of them were dedicated to the scientist’s hometown. Archimedes actively developed ideas for using leverage. In the port of Syracuse, he managed to create a whole system of lever-block mechanisms that speed up the process of transporting heavy, bulky cargo.

With the help of an Archimedean screw, or auger, it became possible to extract water from low-lying reservoirs. Thanks to this, irrigation canals began to receive moisture uninterruptedly.

The main service to Syracuse was provided by Archimedes in 212. The scientist took an active part in the defense of Syracuse, which was besieged by Roman troops. Archimedes managed to create several powerful throwing machines. When the Romans rushed into the city, many of them fell under the blows of stones thrown from these machines.

Archimedes' cranes easily turned over Roman ships. This led to the fact that the Roman soldiers abandoned the assault on the city and began a long siege.

Unfortunately, in the end, the city was taken.

Death of a Scientist

The account of the death of Archimedes was related by John Tzetz, Plutarch, Diodorus Siculus and Titus Livy. The details of the death of the great scientist vary. One thing is common: Archimedes was killed by a certain Roman soldier. According to one version, the Roman did not wait for Archimedes to complete the drawing, and for refusing to follow the consul, he stabbed him with a sword.

Another version says that the scientist was killed on the way to Marcellus. The Roman soldiers found the instruments for measuring the Sun that Archimedes carried in his hands suspicious.

Consul Marcellus, having learned about the death of the scientist, was upset. The body of Archimedes was buried with great honors, and his relatives were shown “great respect.”

Other biography options

• Archimedes once exclaimed, “Give me a fulcrum and I will move the Earth!” In the eyes of his contemporaries, the outstanding scientist was practically a demigod.
• According to legend, the Syracusans managed to burn several Roman ships. This was done with the help of huge mirrors, the amazing properties of which were also discovered by Archimedes.

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