Archimedes (about 287 BC, Syracuse, Sicily - 212 BC, ibid.) - ancient Greek scientist, mathematician and mechanic, founder of theoretical mechanics and hydrostatics.

He developed methods for finding areas, surfaces and volumes of various figures and bodies that anticipated integral calculus.

Archimedes was born in 287 BC in the Greek city of Syracuse, where he lived almost his entire life. His father was Phidias, the court astronomer of the ruler of the city of Hiero. Archimedes, like many other ancient Greek scientists, studied in Alexandria, where the rulers of Egypt, the Ptolemies, gathered the best Greek scientists and thinkers, and also founded the famous, largest library in the world.

After studying in Alexandria, Archimedes returned to Syracuse and inherited his father's position.

In theoretical terms, the work of this great scientist was dazzlingly multifaceted. Archimedes' main works concerned various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In his work “Parabolas of Quadrature,” Archimedes substantiated the method for calculating the area of ​​a parabolic segment, and he did this two thousand years before the discovery of integral calculus. In his work “On the Measurement of a Circle,” Archimedes first calculated the number “pi” - the ratio of the circumference of a circle to its diameter - and proved that it is the same for any circle. We still use the system of naming integers invented by Archimedes.

The mathematical method of Archimedes, associated with the mathematical works of the Pythagoreans and with the work of Euclid that completed them, as well as with the discoveries of Archimedes' contemporaries, led to the knowledge of the material space surrounding us, to the knowledge of the theoretical form of objects located in this space, the form of a perfect, geometric form, to to which objects more or less approach and the laws of which must be known if we want to influence the material world.

But Archimedes also knew that objects have more than just shape and dimension: they move, or can move, or remain motionless under the influence of certain forces that move objects forward or bring them into balance. The great Syracusan studied these forces, inventing a new branch of mathematics in which material bodies, reduced to their geometric form, at the same time retain their weight. This geometry of weight is rational mechanics, it is statics, as well as hydrostatics, the first law of which was discovered by Archimedes (the law bearing the name of Archimedes), according to which a force equal to the weight of the fluid displaced by it acts on a body immersed in a liquid.

Once, having raised his leg in the water, Archimedes noted with surprise that his leg became lighter in the water. "Eureka! Found it,” he exclaimed, leaving his bath. The anecdote is amusing, but conveyed this way, it is not accurate. The famous "Eureka!" was pronounced not in connection with the discovery of Archimedes' law, as is often said, but in connection with the law of the specific gravity of metals - a discovery that also belongs to the Syracusan scientist and the detailed details of which are found in Vitruvius.

They say that one day Hiero, the ruler of Syracuse, approached Archimedes. He ordered to check whether the weight of the golden crown corresponded to the weight of the gold allocated for it. To do this, Archimedes made two ingots: one of gold, the other of silver, each of the same weight as the crown. Then he put them one by one in a vessel with water and noted how much its level had risen. Having lowered the crown into the vessel, Archimedes established that its volume exceeded the volume of the ingot. Thus the master’s dishonesty was proven.

A curious comment is from the great orator of antiquity, who saw the “Archimedean sphere” - a model showing the movement of heavenly bodies around the Earth: “This Sicilian had a genius that, it would seem, human nature cannot achieve.”

And finally, Archimedes was not only a great scientist, he was also a man passionate about mechanics. He tests and creates a theory of five mechanisms known in his time and called "simple mechanisms." These are a lever (“Give me a fulcrum,” said Archimedes, “and I will move the Earth”), a wedge, a block, an endless screw and a winch. Archimedes is often credited with inventing the endless screw, but it is possible that he only improved the hydraulic screw that served the Egyptians in draining swamps. Subsequently, these mechanisms were widely used in different countries Mira. Interestingly, an improved version of the water-lifting machine could be found at the beginning of the 20th century in a monastery located on Valaam, one of the northern Russian islands. Today, the Archimedes screw is used, for example, in an ordinary meat grinder.

The invention of the endless screw led him to another important invention, even if it became commonplace - the invention of the bolt, constructed from a screw and a nut.

To those of his fellow citizens who would have considered such inventions insignificant, Archimedes presented decisive proof to the contrary on the day when, by ingeniously adjusting a lever, a screw and a winch, he found a means, to the surprise of onlookers, of launching a heavy galley that had run aground, with all its crew and cargo.

He gave even more convincing evidence in 212 BC. During the defense of Syracuse against the Romans during the Second Punic War, Archimedes designed several war machines that allowed the townspeople to repel the attacks of the superior Romans for almost three years. One of them was a system of mirrors, with the help of which the Egyptians were able to burn the Roman fleet. This feat of his, which was described by Plutarch, Polybius and Titus Livius, of course, aroused greater sympathy among ordinary people than calculating the number "pi" - another feat of Archimedes, very useful in our time for students of mathematics.

Archimedes died during the siege of Syracuse - he was killed by a Roman soldier at a time when the scientist was absorbed in searching for a solution to the problem he had set himself.

It is curious that, having conquered Syracuse, the Romans never became the owners of the works of Archimedes. Only many centuries later they were discovered by European scientists. That is why Plutarch, who was one of the first to describe the life of Archimedes, mentioned with regret that the scientist did not leave a single work.

Plutarch writes that Archimedes died at a very old age. A slab with the image of a ball and cylinder was installed on his grave. It was seen by Cicero, who visited Sicily 137 years after the scientist’s death. Only in the 16th-17th centuries were European mathematicians finally able to realize the significance of what Archimedes had done two thousand years before them.

Archimedes left numerous students. A whole generation of followers, enthusiasts, who, like the teacher, were eager to prove their knowledge with concrete conquests, rushed to the new path opened by him.

The first of these students was the Alexandrian Ctesibius, who lived in the 2nd century BC. Archimedes' mechanical inventions were in full swing when Ctesibius added to them the invention of the gear wheel. (Samin D.K. 100 great scientists. - M.: Veche, 2000)

In his fundamental works on statics and hydrostatics (Archimedes' law), Archimedes gave examples of the application of mathematics in natural science and technology. Archimedes owned many technical inventions (the Archimedes screw, determining the composition of alloys by weighing in water, systems for lifting large weights, military throwing machines), which won him extraordinary popularity among his contemporaries.

Archimedes was educated by his father, the astronomer and mathematician Phidias, a relative of the Syracusan tyrant Hiero II, who patronized Archimedes. In his youth, he spent several years in the largest cultural center of that time, Alexandria of Egypt, where he met Erastosthenes. Then he lived in Syracuse until the end of his life.

During the Second Punic War (218-201), when Syracuse was besieged by the army of the Roman commander Marcellus, Archimedes took part in the defense of the city and built throwing weapons. The scientist’s military inventions (Plutarch spoke about them in his biography of the commander Marcellus) helped to hold back the siege of Syracuse by the Romans for two years. Archimedes is credited with burning the Roman fleet with solar rays directed through a system of concave mirrors, but this is unreliable information. The genius of Archimedes aroused admiration even among the Romans. Marcellus ordered the scientist’s life to be spared, but during the capture of Syracuse, Archimedes was killed.

Archimedes took the lead in many discoveries in the field of exact sciences. Thirteen treatises of Archimedes have reached us. In the most famous of them, “On the Ball and the Cylinder” (in two books), Archimedes establishes that the surface area of ​​a ball is 4 times the area of ​​its largest cross-section; formulates the ratio of the volumes of the ball and the cylinder described near it as 2:3 - a discovery that he valued so much that in his will he asked to erect a monument on his grave with the image of a cylinder with a ball inscribed in it and the inscription of calculation (the monument was seen by Cicero a century and a half later). The same treatise formulated the axiom of Archimedes (sometimes called the axiom of Eudoxus), which plays an important role in modern mathematics.

In his treatise On Conoids and Spheroids, Archimedes examines the sphere, ellipsoid, paraboloid and hyperboloid of revolution and their segments and determines their volumes. In the essay “On Spirals” he explores the properties of the curve that received his name (the Archimedean spiral) and the tangent to it. In his treatise “Measuring the Circle,” Archimedes proposes a method for determining the number π, which was used until the end of the 17th century, and indicates two surprisingly precise limits for the number π:

3·10/71In physics, Archimedes introduced the concept of the center of gravity, established the scientific principles of statics and hydrostatics, and gave examples of application mathematical methods V physical research. The basic principles of statics are formulated in the essay “On the Equilibrium of Plane Figures.”

Archimedes considers the addition of parallel forces, defines the concept of the center of gravity for various figures, and gives a derivation of the law of leverage. The famous law of hydrostatics, which entered science with his name (Archimedes' law), was formulated in the treatise “On Floating Bodies.” There is a legend that the idea of ​​this law came to Archimedes while he was taking a bath, with the exclamation “Eureka!” he jumped out of the bath and ran naked to write down the scientific truth that had come to him.

Archimedes' law: any body immersed in a liquid is acted upon by a buoyant force directed upward and equal to the weight of the liquid displaced by it. Archimedes' law is also true for gases.

F - buoyancy force;
P is the force of gravity acting on the body.

Archimedes built a celestial sphere - a mechanical device on which one could observe the movement of the planets, the Sun and the Moon (described by Cicero; after the death of Archimedes, the planetarium was taken by Marcellus to Rome, where it was admired for several centuries); a hydraulic organ mentioned by Tertullian as one of the wonders of technology (some attribute the invention of the organ to the Alexandrian engineer Ctesibius).

It is believed that in his youth, during his stay in Alexandria, Archimedes invented a water-lifting mechanism (Archimedes screw), which was used to drain the lands flooded by the Nile. He also built an instrument to determine the apparent (angular) diameter of the Sun (Archimedes talks about it in his treatise “Psammit”) and determined the value of this angle.

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 the lack 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 his life path, provided 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 practical applications for it. 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 great heights. This was an important achievement, since Syracuse is located in a mountainous area, and the delivery of water represented 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. The liquid is displaced in a volume that is equal to the volume of the 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.

Name: Archimedes

Years of life: 287 BC e. - 212 BC e.

State: Ancient Greece

Field of activity: Mathematics, geometry, physics, mechanics

Greatest Achievement: Archimedes is responsible for a number of inventions and discoveries that are important and widely used to this day.

The most famous ancient Greek mathematician, Archimedes, was born in the city of Syracuse in Sicily in 287 BC. His father, whose name was Phidias, gave his son a good education. It was he who introduced him to the sciences and instilled a love for them. Perhaps at a young age Archimedes lived for some time in Egypt. He continued his education in Alexandria. The future mathematician studied the works of scientists and became acquainted with the science of geometry. But he spent most of his life in the city of Syracuse, where he was patronized by the ruler Hiero the second. Archimedes corresponded a lot with other mathematicians who lived at that time. These were the Alexandrian scientists Eratosthenes of Cyrene and Conon of Samos.

Archimedes' throwing machines

Archimedes was the defender of Syracuse during the siege of Syracuse in 213 BC. He invented throwing machines that were used to defend the city. He was greatly frightened by the Romans; they threw fire over a long distance; the stones could weigh up to 250 kilograms. But Syracuse was still captured by the Roman general Marcus Claudius Marcellus in the fall of 212 or spring of 211 BC. Archimedes was killed when Roman invaders sacked the city.

Archimedes' inventions

We know more about Archimedes than about other ancient scientists. But all the known facts of his life are more like funny fiction than the truth. His ingenious inventions make a great impression on people's imagination. Thanks to his inventions, mechanics became a science. He also became famous for his military inventions. He proved many theorems. Archimedes derived the number Pi, which is needed to calculate the areas and volumes of figures with many sides. Many people who lived at that time considered him the son of the gods, while others considered him crazy.

Archimedes spiral

All over the world it is believed that he invented a screw, with the help of which water was raised upward from lakes and rivers located at a lower level than the city. The canals filled faster with water rising in a spiral, and this happened without interruption. The inhabitants of Syracuse no longer suffered from lack of moisture. Their fields bore fruit well and the city prospered. The Archimedean screw is still used by residents of developing countries in Asia and Africa.

The meat grinder we all know in its design also contains a screw (auger) that moves the meat to the knives. Even the most ordinary screws are a brilliant invention of Archimedes. Augers are widely used in factories, in various mechanisms and machines. It is impossible to imagine an airplane or a modern ship without a propeller.

Archimedes' bath, Archimedes' force and Archimedes' law

Archimedes formulated the method of the hydrostatic principle. An interesting story is how he determined the ratio of silver and gold in Hiero's wreath by immersing it in water. An anecdotal version is when a naked Archimedes jumps out of the bath and shouts: “Eureka!” - runs around the city. Of course, this is greatly embellished.

Thus, the scientist found out that if an object is lowered into water, it will either drown or end up on the surface. Archimedes found out that this happens under the pressure of a lifting force (or buoyancy). The water that the object displaces has the same volume as the object being lowered. This means that the buoyant force is equal to the weight of the displaced fluid. It was this force that was called Archimedes.

Heat ray

No less mythical are the stories about the large mirrors that Archimedes used to destroy Roman ships by setting them on fire. Archimedes collected many mirrors and directed the rays they reflected to one point. The ships were built of wood and painted with resin, so they quickly caught fire. He studied catoptrics, that is, the reflection of light rays from mirrors.

But perhaps the ships caught fire from fiery arrows or from “fiery projectiles” fired by throwing machines. Later, some researchers tried to repeat this experiment. Some experimenters succeeded. The Romans, who captured Syracuse, demanded that manuscripts with formulas be given to them, and when Archimedes wrote the formulas on the sand with a stick, and then wiped the sand with his foot, refusing to give them up, they killed him.

Archimedes lever

The story is also interesting when he exclaimed: “Give me a fulcrum, and I will turn the whole Earth over!” Archimedes loved his city of Syracuse very much. He equipped the port with a whole system of levers. With their help it was much easier to lift or move loads. And when the Roman ships got very close to the city, its lever cranes easily lifted and overturned the Roman ships.

His invention is considered to be a mechanical device that demonstrates the movement of the Sun, Moon and other planets. It was a planetarium. It was possible to observe the movements of the Sun and planets. But, unfortunately, it was not preserved. He was taken to Rome by the conqueror of Syracuse, Marcellus. Only a few details have survived from this device.

All his work was theoretical in nature, but his interest in mechanics influenced his mathematical thinking. He derived a formula for calculating the area of ​​any sphere, as well as a formula for its volume. This was his pride. According to these records, they found his tomb; it was all covered with moss, grass, and dirt. When they cleared it, they saw that it depicted a sphere inscribed in a cylinder. This happened a century and a half after his death. Found the grave. Archimedes did a lot of work on hydrostatics and theoretical mechanics. He used mechanical theories as a means to solve new mathematical theorems.

There are nine surviving treatises of Archimedes in Greek. A great mathematician and inventor, he was centuries ahead of his time. His theorems include school curriculum in geometry to this day. His “simple” inventions advanced the development of human civilization far forward. He will forever remain in people's memory as a brilliant inventor, mechanic and designer, geometer.

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 in Egypt - scientific and Cultural Center 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 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 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 the sun's rays on them on the orders 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, Archimedes' main mathematical achievements concerned 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 a much more general method for calculating 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 the Equilibrium of Plane Figures” with a 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 essay “Psammit” conveyed information about heliocentric system 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.

Archimedes, an outstanding ancient Greek mathematician, inventor and engineer, lived in the 3rd century BC (287 - 212 BC).

Archimedes' friend Heraclides wrote a biography of the great scientist, but it was lost and now very little is known about his life. Little is known about his life also because almost all the authors who conveyed his biography themselves lived much later. As a result, the biography of Archimedes is filled with legends, some of which have become very popular. However, legends about Archimedes were created during his lifetime. Much less is known about the scientist’s personal life than about his science.

From the biography of Archimedes:

Archimedes was born in the city of Syracuse in Sicily. At that time it was one of the first ancient Greek colonies on the island of Sicily and was called Magna Graecia. It included the territory of modern Southern Italy and Sicily. + Archimedes was born in 287 BC. e. The date of birth is known from the words of the Byzantine historian John Tzetz. He lived in Constantinople in the 12th century. That is, almost one and a half thousand years after Archimedes. He also wrote that the famous ancient Greek mathematician lived 75 years. Such accurate information raises certain doubts, but we have to believe the ancient historian. The biography of Archimedes is known from the works of Titus, Cicero, Polybius, Livy, Vitruvius and other authors who lived later than the scientist himself. It is difficult to assess the reliability of these data.

Archimedes probably spent his childhood in Syracuse. The scientist probably received his primary education from his father. His father, presumably, was the astronomer and mathematician Phidias. Plutarch also claimed that the scientist was a close relative of the ruler of Syracuse, Hiero II.

Being related to such celebrities, Archimedes was able to receive an excellent education: he studied in Alexandria, which at that time was famous as a center of learning. Alexandria of Egypt for several centuries was the cultural and scientific center of civilized Ancient World. There Archimedes met and became friends with many other great scientific figures of his time.

Bust of Archimedes

It was in Alexandria that a young man striving for knowledge established friendly relations with the mathematician and astronomer Conon of Samos and the astronomer, mathematician and philologist Erastothenes of Cyrene - these were famous scientists of that time. Archimedes struck up a strong friendship with them. It continued throughout my life, and was expressed in correspondence.

Also within the walls of the Library of Alexandria, Archimedes became acquainted with the works of such famous geometers as Eudoxus and Democritus. He also learned a lot of other useful knowledge. After training, he returned to his homeland and could fully engage in science, since he did not need funds. In his homeland in Syracuse, Archimedes quickly established himself as an intelligent and gifted person, and lived long years, enjoying the respect of others, and lived there until the end of his life.

Nothing is known about his wife and children, but there is no doubt about his studies in Alexandria, where the famous Library of Alexandria was located.

Archimedes died during the Second Punic War, when Roman troops captured Syracuse after a 2-year siege. The Roman commander was Marcus Claudius Marcellus. According to Plutarch, he ordered that Archimedes be found and brought to him. A Roman soldier came to the house of an outstanding mathematician while he was pondering mathematical formulas. The soldier demanded to immediately go with him and meet with Marcellus. But the mathematician brushed off the obsessive Roman, saying that he must first complete the work. The soldier was indignant and stabbed the smartest resident of Syracuse with a sword.

There is also a version that claims that Archimedes was killed right on the street while he was carrying mathematical instruments in his hands. The Roman soldiers decided that these were valuable objects and stabbed the mathematician to death. But be that as it may, the death of this man outraged Marcellus, since his order was violated. There are other versions of this story, but they agree that the ancient Roman political figure and the military leader Marcellus was extremely upset by the death of the scientist and, uniting with both the citizens of Syracuse and his own subjects, gave Archimedes a magnificent funeral.

140 years after these events, the famous Roman orator Cicero arrived in Sicily. He tried to find the tomb of Archimedes, but none of the local residents knew where it was. Finally, the grave was found in a dilapidated state in the bushes on the outskirts of Syracuse. The gravestone depicted a ball and a cylinder inscribed in it. Poems were engraved underneath them. However, this version does not have any documentary evidence.

In the early 60s of the 20th century, an ancient grave was also discovered in the courtyard of the Panorama Hotel in Syracuse. The hotel owners began to claim that this was the burial place of the great mathematician and inventor of antiquity. But again, they did not provide any convincing evidence. In a word, to this day it is unknown where Archimedes is buried and in what place his grave is located.

Scientific activities and inventions of Archimedes:

The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, and created inventions that served as the starting point for further development Sciences. +Discoveries in the field of mathematics were the scientist’s real passion. According to Plutarch, Archimedes forgot about food and self-care when he was on the verge of another invention in this area. The main direction of his mathematical research was the problems of mathematical analysis.

Even before Archimedes, formulas were invented to calculate the areas of circles and polygons, the volumes of pyramids, cones and prisms. But the scientist’s experience allowed him to develop general techniques for calculating volumes and areas. To this end, he improved the method of exhaustion, invented by Eudoxus of Cnidus, and brought the ability to apply it to a virtuoso level. Archimedes did not become the creator of the theory of integral calculus, but his work subsequently became the basis for this theory.

Also, an outstanding mathematician laid the foundations of differential calculus. From a geometric point of view, he studied the possibility of determining the tangent to a curved line, and from a physical point of view, the speed of a body at any moment in time. The scientist examined a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to a hyperbola, parabola and ellipse. From here we can safely say that this man was ahead of mathematical science by 2 thousand years. Only in the seventeenth century were scientists able to fully understand and reveal all the ideas of Archimedes, which reached those times in his surviving works. The scientist often refused to describe his inventions in books, which is why not every formula he wrote has survived to this day.

The scientist also actively developed mechanical structures. He developed and outlined a detailed theory of the lever and effectively used this theory in practice, although the invention itself was known even before him. Block-lever mechanisms were made in the port of Syracuse. These devices made it easier to lift and move heavy loads, speeding up and optimizing port operations.

He also invented a screw that was used to bail out water. His “Archimedes screw” is still used in Egypt. Archimedes created a theory about the balancing of equal bodies. He proved that a body immersed in a liquid is subject to a buoyant force equal to the weight of the displaced liquid. This idea came to him in the bath. Its simplicity so shocked the outstanding mathematician and inventor that he jumped out of the bath and, dressed as Adam, ran through the streets of Syracuse shouting “Eureka,” which means “found.” Subsequently, this proof was called Archimedes' law. + Great importance have theoretical research as a scientist in the field of mechanics. Based on the proof of the law of leverage, he began to write the work “On the Equilibrium of Plane Figures.” The proof is based on the axiom that equal bodies on equal shoulders will necessarily balance. Archimedes followed the same principle of constructing a book - starting with the proof of his own law - when writing the work “On the Floating of Bodies”. This book begins with a description of Archimedes' well-known law.

The scientist considered the invention of formulas for calculating the surface area and volume of a ball to be a worthy discovery. If in the previous cases described, Archimedes refined and improved other people’s theories, or created quick methods calculation as an alternative to already existing formulas, then in the case of determining the volume and surface of a ball, he was the first. Before him, no scientist had coped with this task. Therefore, the mathematician asked to knock out a ball inscribed in a cylinder on his gravestone.

There is a legend associated with Archimedes' law. One day, the scientist was allegedly approached by Hiero II, who doubted that the weight of the crown made for him corresponded to the weight of the gold that was provided for its creation. Archimedes made two ingots of the same weight as the crown: silver and gold. Next, he placed these ingots in turn in a vessel with water and noted how much its level increased. The scientist then placed the crown in the vessel and discovered that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus, it was discovered that the master had kept some of the gold for himself.

Archimedes became the inventor of the first planetarium. When this device moves, the following is observed: the rising of the Moon and the Sun; the movement of the five planets; disappearance of the Moon and Sun beyond the horizon; phases and eclipses of the moon.

The scientist also tried to create formulas for calculating distances to celestial bodies. Modern researchers suggest that Archimedes considered the Earth to be the center of the world. He believed that Venus, Mars and Mercury revolved around the Sun, and this entire system revolved around the Earth.

His contemporaries also composed numerous legends about the gifted mathematician, physicist and engineer. Legend says that one day Hiero II decided to present Ptolemy, the king of Egypt, with a multi-deck ship as a gift. It was decided to name the watercraft "Syracuse", but it could not be launched. In this situation, the ruler again turned to Archimedes. From several blocks he built a system with the help of which the launch of a heavy vessel was possible with one movement of the hand. According to legend, during this movement Archimedes said: “Give me a point of support, and I will turn the world over.”

The scientist helped his compatriots in naval battles. The cranes he developed grabbed enemy ships with iron hooks, lifted them slightly, and then abruptly threw them back. Because of this, ships turned over and crashed. For a long time, these cranes were considered something of a legend, but in 2005 a group of researchers proved the functionality of such devices by reconstructing them from surviving descriptions.

In 212 BC, during the Second Punic War, the Romans began to storm Syracuse. At this time, Archimedes was already an elderly man, but his mind did not lose its sharpness. Archimedes actively used engineering knowledge to help his people achieve victory. As Plutarch wrote, under his leadership, throwing machines were built, with the help of which the soldiers of Syracuse threw heavy stones at their opponents. When the Romans rushed to the walls of the city, hoping that they would not come under fire, another invention of Archimedes - light throwing devices with close action - helped the Greeks pelt them with cannonballs. Roman galleys scurrying around the port of Syracuse were attacked by special cranes with grappling hooks (Archimedes' claw). With the help of these hooks, the besieged lifted ships into the air and threw them down from a great height. The ships, hitting the water, broke and sank. All these technological advances scared the invaders. So, thanks to the efforts of Archimedes, the Romans’ hope of storming the city failed. They abandoned the assault on the city and moved on to a long siege. In the fall of 212 BC, the colony was taken by the Romans as a result of treason. Archimedes was killed during this incident. According to one version, he was hacked to death by a Roman soldier, whom the scientist attacked for stepping on his drawing.

There is a legend that Archimedes ordered to polish the shields to a mirror shine, and then positioned them in such a way that they reflected sunny color, focused it into powerful beams. They were sent to Roman ships, and they burned. Mentions of these weapons are mere legends, but in recent years experiments have been carried out to determine whether these inventions could actually exist. In 2005, scientists reproduced the cranes, which turned out to be fully functional. And in 1973, Greek scientist Ioannis Sakkas set fire to a plywood model of a Roman ship using a combination of mirrors. He created a cascade of 70 copper mirrors and used it to set fire to a plywood model of a ship, which was located 75 meters from the mirrors. So this legend could well have a practical basis.

However, scientists continue to doubt the existence of “mirror” weapons in Syracuse, since none of the ancient authors mentions it; information about it appeared only in the early Middle Ages - from the 6th century author Anthemius of Trallia. Despite a heroic - and ingenious - defense, Syracuse was eventually conquered.

Legacy of Archimedes:

Archimedes wrote his works in Doric Greek, the dialect spoken in Syracuse. But the originals have not survived. They have come to us in retellings by other authors. All this was systematized and collected into a single collection by the Byzantine architect Isidore of Miletus, who lived in Constantinople in the 6th century. This collection was translated into Arabic in the 9th century, and in the 12th century it was translated into Latin.

During the Renaissance, the works of the Greek thinker were published in Basel in Latin and Greek. Based on these works, Galileo Galilei invented hydrostatic balances at the end of the 16th century.

*Archimedes screw, or auger, is used for lifting and transporting loads and scooping out water. This device is still used today (for example, in Egypt).

*Various types of cranes, which were based on blocks and levers.

*"Celestial Sphere" is the world's first planetarium, with the help of which it was possible to observe the movement of the sun, moon and five then known planets.

*The number close to the number P is the so-called “Archimedean number”: 3 1/7; Archimedes himself indicated the accuracy of the approximation of this number. To solve this problem, he built a circle with 96-gons inscribed and circumscribed around it, the sides of which he then measured.

*Discovery of the fundamental law of physics in general and hydrostatics in particular. This law is named after him and consists of the relationship between the buoyant force, volume and weight of a body immersed in a liquid.

*As the first theorist of mechanics, Archimedes introduced thought experiments into it. The first such experiments were his proofs of the law of the lever and Archimedes' law.

*In 1906, Danish professor Johan Ludwig Heiberg discovered a 174-page prayer collection in Constantinople, written in the 13th century. The scientist found out that it was a palimpsest, that is, text written over old text. At that time, this was common practice, since the tanned goatskin from which the pages were made was very expensive. The old text was scraped off and new text was written on top of it. It turned out that the scraped work was a copy of an unknown treatise by Archimedes. The copy was written in the 10th century. Using ultraviolet and x-ray light, this hitherto unknown work was read. These were works on equilibrium, on measuring the circumference of a sphere and a cylinder, and on floating bodies. Currently, this document is kept in the Baltimore City Museum (Maryland, USA).

*Works of Archimedes: Quadrature of the parabola, On the ball and cylinder, On spirals, On conoids and spheroids, On the equilibrium of plane figures, Epistle to Eratosthenes on the method, On floating bodies, Measurement of the circle, Psammit, Stomachion, Archimedes' problem on bulls, Treatise on construction around the ball of a solid figure with fourteen bases, Book of Lemmas, Book on the construction of a circle divided into seven equal parts, Book on touching circles.

Archimedes: interesting facts

1.Archimedes did not leave any students after himself, because he did not want to create his own school and train successors.

2. Some of Archimedes’ calculations were repeated only fifteen hundred years later by Newton and Leibniz.

3. Some scientists claim that Archimedes was the inventor of the cannon. Thus, Leonardo da Vinci even drew a sketch of a steam cannon, the invention of which he attributed to the ancient Greek scientist. Plutarch wrote that during the siege of Syracuse, the Romans were fired upon by a device that resembled a long tube and “spitted out” cannonballs.

4. Archimedes’ friend Heraclides wrote a biography of the great scientist, but it was lost and now little is known about his life.

5. Some contemporaries considered Archimedes crazy. To demonstrate his skills, the scientist before Hieron pulled the triremes ashore using a system of pulleys.

6. The Roman commander Marcellus, commander of the siege of Syracuse, said: “We will have to stop the war against the geometer.”

7.Archimedes is considered one of the best mathematicians and inventors of all time.

9.According to some legends, during the capture of Syracuse, he was sent in search of a scientist special squad the Romans, who were supposed to capture Archimedes and bring him to command. The scientist died only by an absurd accident.

10. Archimedes’ throwing machines could launch stones weighing up to 250 kg. At that time it was a unique combat vehicle.

11.Archimedes made the world's first planetarium.

12. Contemporaries considered Archimedes almost a demigod, and his military inventions terrified the Romans, who had never encountered anything like this before.

13.The well-known legend about mirrors that burned Roman ships has been repeatedly refuted. Most likely, the mirrors were used only to aim the ballistas, which fired incendiary shells at the Roman fleet. There is also an opinion that the Romans were forced to agree to a night assault on the city precisely because of the use of mirrors by the defenders of Syracuse.

14.The “Archimedes screw” was invented by a scientist back in teenage years and was intended for irrigating fields. Today, screws are used in many industries. And in Egypt they still supply water to the fields.

15. Archimedes considered mathematics his best friend.

Monument to Archimedes

photo from the Internet