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

Developed anticipating integral calculus methods for finding areas, surfaces and volumes of various figures and bodies.

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 Hieron. 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 again and inherited his father's position.

In theoretical terms, the work of this great scientist was blindingly multifaceted. The main works of Archimedes concerned various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In his work “Parabola 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 the 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, connected 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 that surrounds us, to the knowledge of the theoretical form of objects located in this space, the form of a perfect, geometric form, to which objects more or less approach and whose laws 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 stationary 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, retain at the same time their heaviness. 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 liquid displaced by it acts on a body immersed in a liquid.

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

It is said that one day Archimedes was approached by Hiero, the ruler of Syracuse. He ordered to check whether the weight of the golden crown corresponds to the weight of the gold allotted to 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 in turn in a vessel with water, noted how much its level had risen. Having lowered the crown into the vessel, Archimedes found that its volume exceeds the volume of the ingot. So the dishonesty of the master was proved.

The review of the great orator of antiquity, who saw the "Archimedean sphere" - a model showing the movement of heavenly bodies around the Earth, is curious: "This Sicilian possessed a genius that, it would seem, human nature cannot achieve."

And, finally, Archimedes was not only a great scientist, he was, moreover, a man passionate about mechanics. He tests and creates a theory of five mechanisms known in his time and referred to as "simple mechanisms". This is a lever (“Give me a fulcrum,” said Archimedes, “and I will move the Earth”), a wedge, a block, an endless screw and a winch. It is Archimedes who is often credited with the invention of the infinite screw, but it is possible that he only improved the hydraulic screw, which served the Egyptians in draining swamps. Subsequently, these mechanisms were widely used in different countries Peace. 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 Archimedean screw is used, for example, in an ordinary meat grinder.

The invention of the infinite screw led him to another important invention, even if it had become commonplace, the invention of a bolt constructed from a screw and a nut.

To those of his fellow citizens who would consider such inventions worthless, Archimedes presented decisive evidence to the contrary on the day when, by cunningly fitting a lever, screw and winch, he found a means, to the surprise of onlookers, to launch a heavy galley that had run aground, with everything her crew and cargo.

Even more convincing proof he gave in 212 BC. During the defense of Syracuse from the Romans during the Second Punic War, Archimedes designed several fighting machines that allowed the townspeople to repel the attacks of the outnumbered Romans for almost three years. One of them was a system of mirrors, with which the Egyptians were able to burn the Roman fleet. This feat of his, which Plutarch, Polybius and Titus Livy told about, 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 the moment when the scientist was absorbed in the search for a solution to the problem set before him.

It is curious that, having conquered Syracuse, the Romans did not become the owners of the works of Archimedes. Only after many centuries they were discovered by European scientists. That is why Plutarch, 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 ripe old age. A plate depicting a sphere and a cylinder was placed on his grave. She was seen by Cicero, who visited Sicily 137 years after the scientist's death. Only in the XVI-XVII centuries, European mathematicians were finally able to realize the significance of what was done by Archimedes two thousand years before them.

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

The first of these students was the Alexandrian Ctesibius, who lived in the 2nd century BC. The inventions of Archimedes in the field of mechanics 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 the fundamental works on statics and hydrostatics (the law of Archimedes), Archimedes gave examples of the application of mathematics in natural science and technology. Archimedes owns many technical inventions (Archimedean screw, determining the composition of alloys by weighing in water, systems for lifting heavy 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 Hieron 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 military inventions of the scientist (Plutarch told about them in the biography of the commander Marcellus) for two years helped to restrain the siege of Syracuse by the Romans. Archimedes is credited with burning the Roman fleet with sun rays directed through a system of concave mirrors, but this is unreliable information. The genius of Archimedes was admired even by the Romans. Marcellus ordered to save the scientist's life, but during the capture of Syracuse, Archimedes was killed.

Archimedes holds the primacy in many discoveries from the field of exact sciences. Thirteen treatises of Archimedes have come down to us. In the most famous of them - "On the ball and the cylinder" (in two books), Archimedes establishes that the surface area of ​​​​the ball is 4 times the area of ​​\u200b\u200bits largest section; formulates the ratio of the volumes of the ball and the cylinder described next to it as 2:3 - a discovery that he cherished so much that in his will he asked to put a monument on his grave with the image of a cylinder with a ball inscribed in it and an inscription of the 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 the treatise "On Conoids and Spheroids" Archimedes considers a sphere, an ellipsoid, a paraboloid and a 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 the treatise "Measuring the Circle", Archimedes offers a method for determining the number π, which was used until the end of the 17th century, and indicates two surprisingly accurate limits for the number π:

3 10/71 In physics, Archimedes introduced the concept of the center of gravity, established the scientific principles of statics and hydrostatics, gave examples of the application mathematical methods V physical research. The main provisions 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 the derivation of the law of the lever. 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 visited Archimedes when 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' principle: any body immersed in a liquid is subjected to a buoyant force directed upward and equal to the weight of the liquid displaced by it. Archimedes' law is also valid for gases.

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

Archimedes built the celestial sphere - a mechanical device on which it was possible to 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 for several centuries it aroused admiration); a hydraulic organ, mentioned by Tertullian as one of the marvels 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 a device for determining the apparent (angular) diameter of the Sun (Archimedes talks about it in the treatise Psammit) and determined the value of this angle.

Archimedes made many discoveries in geometry, laid the foundations of mechanics, hydrostatics, and was the author of a number of important inventions.

Scientific discoveries of the scientist Archimedes

Scientific discoveries the ancient Greek scientist Archimedes influenced the development of physics, geometry, mechanics and other sciences.

The story is widely known when the king of the city of Syracuse, Hieron, instructed Archimedes to check whether he was deceived by a jeweler who was supposed to make him a crown of pure gold. Thinking about how to solve this problem. Archimedes somehow went into the bathhouse and there, plunging into the bath, 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 jumped naked into the street shouting "Eureka" (ancient Greek εὕρηκα - found). At this point, the basic law of hydrostatics was discovered: the law of Archimedes.

His mathematical work was far ahead of its time. He is one of the creators of mechanics as a science, he owns various technical inventions.

One of them is helical shaft (auger), which is located inside the meat grinder. When it is rotated, it grabs the pieces of meat and advances them under the knives. Such a shaft is called by the name of the inventor, the screw of Archimedes. Only Archimedes invented it not at all for a meat grinder, but for a water-lifting device to irrigate the fields. The Archimedes (infinite) screw has been successfully used to lift water for two thousand years. Back in the 20s of our century in the Crimea one could see the "Archimedean worm", which was used to pump out a thick saline solution. The Archimedes screw served as the prototype for aircraft propellers and ship propellers, as well as conventional screws and nuts. At present, the Archimedean screw is used in various machines and mechanisms, for moving parts in factories, lifting bulk cargo, and even as an all-terrain vehicle mover.

Archimedes developed the idea of ​​using the lever. So the scientist created a whole complex of block-lever mechanisms in the port of Syracuse, which greatly facilitated and accelerated the process of transporting heavy loads.

widely known and military inventions Archimedes, thanks to whom it was possible long time hold the defense of Syracuse from Roman troops.

As a military engineer, he prepared ahead of time for an enemy attack and built many different defensive vehicles.

Archimedes built machines adapted to throw projectiles at any distance. So, if the enemy sailed from afar, Archimedes hit him with long-range stone-throwing guns and plunged him into a difficult, helpless position. If the shells began to fly over the enemy, Archimedes used smaller machines, each time in accordance with the distance, and inspired such horror on the Romans that they did not dare to attack or approach the city on ships. Archimedes invented and applied mechanisms that turned enemy ships over.

The inventions of Archimedes frightened the Romans so much that when they only saw a log or a rope showing above the wall, they shouted that Archimedes was directing some kind of machine at them, retreated and fled.

There is also a legend that Archimedes ordered the soldiers to polish the shields to a shine and direct the sunlight reflected from them onto the Roman ships, which led to their ignition.

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

The biography of Archimedes is full of white spots. Historians know little about the life of an outstanding scientist, since the chronicles of that period contain only scarce information, but the description of his works tells in sufficient detail about achievements in the field of physics, mathematics, astronomy and technology. His work was far ahead of its time and was appreciated only centuries later, when scientific progress reached the appropriate level.

Childhood and youth

A brief 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, from childhood instilled in his son a love of science. Hieron, 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 departed 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. In the process of learning, the future scientist made friends with Eratosthenes, the head of the Alexandrian Library, and Konon. This friendship lasted for many years.

Service at the court of Hieron II

After completing his education, Archimedes returned to his homeland in Syracuse and began working as a court astronomer in the palace of Hieron II. However, not only the stars were interested in the inquisitive youthful mind. Work on astronomy was not difficult, so that the scientist had enough time to study physics, mathematics and engineering. During this period, Archimedes discovered his famous principle of using a lever and detailed his developments in the book On the Balance 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 on the study of the refraction of light, and managed to derive a mathematical theorem that has retained its relevance to this day. This work contains evidence that the angle of incidence of a beam 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 to calculate 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 are well studied, but the personal life of the scientist is shrouded in a veil of secrecy. Neither the contemporaries of the great explorer, nor the historians who have studied his life path, provided any data about his family or possible descendants.

Service to Syracuse

As follows from the biography of Archimedes, his discoveries in physics did a great service to his native city. After the discovery of the lever, Archimedes actively developed his theory and found useful practical applications for it. In the port of Syracuse, a complex structure was created, consisting of block-lever devices. Thanks to this engineering solution, the process of loading and unloading ships was significantly accelerated, and heavy, oversized cargo was moved easily and with little or no effort. The invention of the screw made it possible to collect water from low-lying reservoirs and raise it to a great height. 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 native city 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 troops managed to break through the city walls, most of the attackers died under a hail of stones fired from Archimedes' machines.

With the help of huge levers, also created by the scientist, the Syracusans were able to turn over the Roman ships and stop the attack. As a result, the Romans stopped the assault and switched to the tactics of a long siege. 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 stop work and follow him, he killed him with a sword. According to another version, the Roman nevertheless allowed the drawing to be completed, but Archimedes was stabbed to death on the way to the consul. The researcher took with him instruments for studying 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.

Upon receiving the news of the death of Archimedes, the consul was saddened: rumors about the talent of the scientist 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 alleged burial. By that time, the scientist's grave was abandoned, and its location was forgotten, so the search turned out to be a difficult task. Mark Thulius Cicero, who ruled Syracuse on behalf of the Roman emperor, wished to erect a majestic monument on the grave, but, unfortunately, this structure has not been preserved. The burial place is located on the territory of the Archaeological Park of Naples, which is located near modern Syracuse.

Law of Archimedes

One of the most famous discoveries of the scientist was the so-called Law of Archimedes. 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 opening has acquired 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 sort it out 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. Finding out the exact weight of the crown was not difficult, but how to calculate its volume? The answer came at the moment when 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 liquid being displaced. It was at this moment that Archimedes exclaimed, "Eureka!"

Archimedes considered his best friend not man, but mathematics.

Throwing machines, which the scientist built during the assault on 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 the highlands and irrigated the 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.

If only... Oh, if the great states of antiquity would pay a little more attention to their glorious inventors - at least in the same way that current governments do not skimp on financing high-tech military programs, then - who knows what language we would be talking to you now and in what country did you live in? What would happen if Leonardo da Vinci or Nikola Tesla got the opportunity to develop their talents to the full extent?

About and da Vinci we have already written. It's time to pay tribute to another, perhaps the very first technical genius of mankind. A great mathematician, physicist, engineer and astronomer, underestimated during his lifetime and accidentally killed by an illiterate soldier - he could hasten the scientific and technological revolution by almost two thousand years, if ...

Who are you, Mr. Archimedes?

Archimedes (artist Domenico Fetti, 17th century).

Any stories about great people usually begin with their biography. Alas, in the case of Archimedes, we will have to be content with only a set of unconfirmed facts. There are many legends about the life of this scientist, but there is very little reliable information.

The birthplace of the inventor was Sicily, the city of Syracuse. He spent most of his life there. The date of his birth - 287 BC - was established on the basis of the testimony of the Byzantine historian John Price (12th century), who wrote that Archimedes lived for 75 years and died in 212 BC.

In his writings, the inventor mentioned that his father was the astronomer and mathematician Phidias, who came from a noble Syracusan family. Apparently, at a young age the boy was sent to study in Alexandria - the largest Cultural Center that time. In the future, he actively communicated with the mathematicians of the Alexandrian school (for example, with Erastofen), and this suggests the idea that Archimedes used the works of the Alexandrian Euclid as "textbooks". The subject of his further research also coincided with the "Euclidean science" and significantly developed it - this is, first of all, the theory of numbers, as well as planimetry and geometry.

Having studied in Alexandria, Archimedes returned home and got a “job” at the court of his distant relative, the Syracusan tyrant Heron II. There are many legends about how Archimedes performed the most ingenious tasks of Heron, but in reality the ruler, most likely, did not attach much practical importance to his research and patronized the outstanding scientist only because his presence in Syracuse significantly increased the cultural status of the city.

Being “under the wing” of an enlightened monarch for most of his life, the inventor could work calmly - and he worked, and so fruitfully that today the word “Archimedes” is unknown only to those who live in the forest, pray to the wheel and faint at the form of an airplane.

Syracuse is one of the most influential and beautiful cities in the ancient Mediterranean. It was founded in the 8th century BC under the name Sirako (“swamp”, because there really was a swamp near the city). Heron II wisely ruled Syracuse for 50 years: he avoided major wars, developed jurisprudence, science and art. His heir - the young Jerome - ascended the throne in 215 and almost immediately led the city to collapse, quarreling with Rome. Syracuse fell due to the fact that some of the townspeople decided to negotiate the terms of a peace treaty and opened a small door in the wall for the Romans, but they burst inside and quickly crushed the resistance.

The troops of the Roman consul Marcellus besieged Syracuse for a very long time (about 8 months). The reason for the delay was allegedly that the great scientist, in the face of the threat of invasion, switched from pure mathematics to mechanics and began to create amazing combat devices to protect his native city. Moreover - according to some evidence, Archimedes personally led the defense of the city and disposed of its technical resources.

The Romans were not stupid. Having appreciated the defensive innovations of the Greeks, Marcellus ordered his soldiers not to touch the brilliant engineer when capturing the city, apparently planning to lure him into his service. It is not difficult to imagine what kind of military mechanisms Archimedes could have invented while working for the practical and cruel Romans.

However, history decreed otherwise. According to legend, one of the legionnaires found a scientist in the garden of his house, when he was studying the drawings on the sand, not paying any attention to street fighting. Either the Roman did not recognize this Greek, or he deliberately violated the order of the commander (they say that Archimedes told the soldier not to touch his drawings - “circles”, but in what exact terms he did this remains unclear) - in any case, the greatest mind of his time was simply hacked to death on the spot.

Death of Archimedes. Engraving from an 18th century Italian book.

Plutarch (45-120) reports that, according to the will of Archimedes, a ball enclosed in a cylinder was placed on his grave, indicating that the ratio of their volumes is 2/3. In his work "On the Sphere and the Cylinder" Archimedes proved the same multiplicity of the ratio of the surface area of ​​these two figures.

Word and deed

It is enough just to take a glimpse of the “know-how” of Archimedes to understand how much this man was ahead of his time and what our world could turn into if high technologies were assimilated in antiquity as quickly as they are today. Archimedes specialized in mathematics and geometry, two of the most important sciences that underlie technological progress. The revolutionary nature of his research is evidenced by the fact that historians consider Archimedes one of the three greatest mathematicians of mankind (the other two are Newton and Gauss).

In terms of innovation, this Greek was head and shoulders above all European mathematicians until the Renaissance. In a society where a completely terrible system of calculation was used, and in a language where the word "myriad" (ten thousand) was synonymous with "infinity", he developed a clear science of numbers and "counted" them up to 10 64 .

Archimedes laid the foundations for integral calculus and the theory of ultrasmall numbers. He proved that the ratio of the circumference of a circle to its diameter is equal to the ratio of the area of ​​a circle to the square of its radius. The scientist, of course, did not call this ratio the "Pi number", but quite accurately determined its value in the range from 3 + 10/71 (about 3.1408) to 3 + 1/7 (about 3.1429).

Only a few treatises of Archimedes have survived to our time. Most of them perished in two fires in the Library of Alexandria - only a few translations into Arabic and Latin have survived. For example, in the work "On the balance of planes" the author studied the centers of gravity of various figures. There is a legend according to which Heron asked Archimedes to visually illustrate the "effect" of the lever, known from his famous phrase "Give me a fulcrum and I will turn the whole world!" (Plutarch quotes her differently: "If there were another Earth, I would stand on it and move this one").

The inventor ordered to pull a large ship ashore and fill it with cargo, after which he stood near the chain hoist (reel block) and began to pull the rope tied to the ship without any visible effort. The latter, to the surprise of those present, "floated" on land, as on water.

Other works are no less significant: “On Conoids and Spheroids”, “On Spirals”, “Measurement of a Circle”, “Squaring a Parabola”, “Psammit” (“Calculation of Grains of Sand” - here the scientist proposed a way to find out the number of grains of sand contained in the volume of everything of the world, that is, he described a system for writing super-large numbers).

Separately, it should be said about his work in the field of mechanics. Here he really was a pioneer, in many ways reminiscent of Leonardo da Vinci.

According to Diodorus Siculus, Roman slaves in Spain drained entire rivers using a device that Archimedes developed during a visit to Egypt. It was the so-called "Archimedes screw" - a powerful and at the same time very simple screw pump. However, some evidence suggests that a similar device was invented 300 years earlier to irrigate the Hanging Gardens of Babylon (the so-called "Gardens of Babylon").

Archimedes allegedly invented a mosaic game - "stomachion" (from flat bone pieces of different geometric shapes it is necessary to make recognizable figures - a person, an animal, etc.). He is also credited with the creation of the odometer (a device that measures the distance traveled).

During the siege of Syracuse, Archimedes built many amazing devices, of which two of the most effective can be distinguished. The first is the "Paw of Archimedes", a unique lifting machine and a prototype of a modern crane. Outwardly, it looked like a lever protruding beyond the city wall and equipped with a counterweight. Polybius in " world history”Wrote that if a Roman ship tried to land near Syracuse, this “manipulator”, under the control of a specially trained machinist, grabbed its bow and turned it over (the weight of Roman triremes exceeded 200 tons, and the penter could reach all 500), flooding the attackers.

A crane is also a weapon!

The Romans were shocked to see Archimedes' machines in action. Plutarch writes that sometimes it came to the point of absurdity: when they saw some kind of rope or log on the wall of Syracuse, the invincible Roman legionnaires fled in a panic, thinking that another infernal mechanism would now be used against them.

Similar machines knocked down Roman siege ladders from the walls, while Archimedes' long-range and incredibly accurate catapults bombarded their ships with stones. But even more surprising was the second "surprise" - a beam weapon.

Realizing the futility of trying to take the city by storm, the Roman fleet (according to various sources, about 60 ships) anchored near the city. According to legend, Archimedes constructed a large mirror, or handed out small concave mirrors to the soldiers (historians do not have a single point of view - sometimes polished copper shields even appear here), with the help of which he “concentrated” sunlight on the enemy fleet and burned it to the ground.

Cicero wrote that after Syracuse was plundered, Marcellus took out two devices from there - "spheres", the creation of which is attributed to Archimedes. The first was a kind of planetarium, and the second modeled the movement of the stars across the sky, which suggested the presence of a complex gear mechanism in it.

Until recently, this evidence was considered doubtful, but in 1900, near the Greek island of Antikythera, at a depth of 43 meters, the remains of a ship were found, from which the remains of a certain device were raised - an “advanced” system of bronze gears dating back to 87 BC. This proves that Archimedes could well create a complex mechanism - a kind of "computer" of ancient times.

Antikythera - perhaps the oldest gear mechanism in the world

Hyperboloid engineer Archimedes

Could a cunning Greek really feed the fish in the sea near Syracuse with fried Romans? This myth has been tested several times - and with varying results. The most interesting was the experiment of the Massachusetts Institute of Technology, conducted in 2005.

Ancient sources describe the design of the Archimedean "hyperboloid" in a very contradictory way - whether it was bronze shields, or a giant reflector. The researchers suggested that Archimedes could hardly have made a huge (and therefore very vulnerable) reflector, and chose the option with shields, replacing them with 127 mirrors about 30 by 30 centimeters in size.

The experimenters did not aim to completely recreate the conditions for using the "hyperboloid". The model of the ship was made of solid oak, although more combustible woods, such as cypress, were used to build Roman ships. The ship's sides were dry, although in reality they are open to the waves. The distance to the target is 30 meters, but in fact it was much more (at least the distance of the arrow). In addition, the layout remained stationary, and the Roman ships moved slightly, even when anchored in the bay of Syracuse.

Mirrors were pointed at the ship and covered with curtains. A problem immediately arose - the "weapon" was on stands, and not in the hands of the Greek soldiers. The sight had to be constantly adjusted, because due to the movement of the Sun across the sky, the rays shifted by 1.5 meters every 10 minutes. Clouds also did not facilitate the work - the power of the "laser" periodically fell.

What came of it? "Weapon of Vengeance" worked for only 10 minutes, but the effect exceeded all expectations. Immediately after the opening of the mirrors, the wood began to char, then smoke appeared and almost immediately after it - a bunch of bright flames. The fire was extinguished after 3 minutes. A through hole appeared in the side of the ship.

The mobility of real targets, the long distance to them, the poor reflective qualities of bronze - all this speaks against the legend of Archimedes. However, the inventor had many reflectors at his disposal (the number of soldiers with polished shields on the walls of the city was in the hundreds) and he was not limited in time. Archimedes really could achieve the effect of a "laser", but not in quality, but in quantity.

In the experiment, the mirrors were flat, which cannot be said about the shields of the Greeks. If the reflectors they used were concave, their "range" would exceed 30 meters.

Too little historical information has survived to recreate the weapons of Archimedes as they really could be. It is reasonable to talk not about the refutation of the myth, but about the theoretical possibility of a "solar laser". The experiment showed that physics does not contradict history. This inspires optimism, so the legend of the "death rays" of Archimedes can be considered conditionally true.

• Modern Syracuse has almost no traces of its former greatness. Tourists are often taken to the so-called "Tomb of Archimedes" in the Grotticelli necropolis. In fact, this Roman burial does not contain the remains of the famous scientist.
• The Archimedes Palimpsest is a Christian book compiled in the 12th century from "pagan" parchments from the 10th century. To do this, the old letters were washed away from them, and a church text was written on the material received. Fortunately, the palimpsest (from the Greek palin - again and psatio - I erase) was made of poor quality, so the old letters were visible through the light (and even better - under ultraviolet light). In 1906, it turned out that these were three previously unknown works of Archimedes.
• There is a legend about how King Heron instructed Archimedes to check if the jeweler had mixed silver into his golden crown. The integrity of the product could not be violated. Archimedes could not complete this task for a long time - the solution came by chance when he lay down in the bathroom and suddenly noticed the effect of liquid displacement (he shouted: “Eureka!” - “Found it!”, And ran naked into the street). He realized that the volume of a body immersed in water is equal to the volume of water displaced, and this helped him to expose the deceiver.
• One of the large lunar craters (82 kilometers wide) was named after Archimedes.

* * *

Archimedes is the most suitable candidate for creating the image of an ancient inventor who designed steam tanks and flying machines hundreds of years before the birth of Christ (this genre is usually called "sandalpunk" - by analogy with "cyberpunk" or "dieselpunk", where the word "sandal" means sandalwood, as well as sandals in which the ancient Greeks walked). By today's standards, the writings of Archimedes are high school level. However, do not forget that they were made over 2000 years ago and were ahead of their time by at least the 17th century. Thanks to this, the hero of our article can rightfully be called one of the greatest geniuses of mankind.

ARCHIMEDES AND HIS DISCOVERIES

(research)

Introduction

For more than 20 centuries, and with each subsequent century, more and more often, the creative tension of human thought ends with a satisfied - emotional exclamation "EUREKA!" ("FOUND!"). I found a solution to a new problem, a problem - EUREKA! I came up with a new solution method - EUREKA! Made a discovery - EUREKA! According to legend, this exclamation, which has become winged, marking the triumph of reason, was given to mankind by the greatest Archimedes - the most famous in the galaxy of original mathematicians Ancient Greece. It was about him that the 17th-century English mathematician John Wallis (1616-1703) said: “This scientist had amazing insight. He laid the foundations of almost all discoveries, the development of which our age is proud of. So what discoveries did this great scientist make? The purpose of this work- to get acquainted with the scientific discoveries of Archimedes. Tasks: 1. Study the literature on this issue

2. List the discoveries made by Archimedes and describe some of them

3. Carry out some experiments proposed by Archimedes

4. Make up a quiz

Chapter I

Stories about the life of Archimedes are found in the ancient historians Polybius (II century BC) and Titus Livius (I century BC), in the writers Cicero (I century BC), Plutarch (I-II century BC). .v.) and others.

Archimedes was born in Syracuse on the island of Sicily. Father of Archimedes, astronom and mathematician Phidias was one of the close associates of the king of Syracuse Hieron. Phidias gave his son a good education, encouraging his son to creative knowledge of astronomy, mechanics and mathematics. Later, the desire to deepen theoretical knowledge led him to Alexandria (Egypt) - the then world scientific center. Here he met the famous astronomer Conon and the mathematician Eratosthenes, worked hard in the richest library, studied the works of scientists Democritus, Eudoxus and others. Euclid's Elements was Archimedes' reference book throughout his life. In Alexandria, his first brilliant successes were achieved in theoreticalRussian mechanics and its practical applications. A remarkable invention of his was a machine for watering the fields (“snail screw”), which had and still hasstill of great economic importance in Egypt, where the rains are almostdoes not happen and where is everyone Agriculture based on artificial irrigationresearch institutes. Archimedes was always so keen on science that he had to force
tear away from the workplace to eat or forcibly take to the bathhouse,where he kept meditating on geometric shapes which heHe drew with his finger on the soapy body. There are many legends about this scientist, his life and scientific activity.

One of the legends tells about the discovery of buoyancy by Archimedes. King Hieron ordered the master a crown of pure gold. When the order was completed, the king wanted to check if the master had replaced part of the gold given to him with silver, and turned to Archimedes, who at that time was the king's adviser. Archimedes could not immediately solve the problem assigned to him. He began to look for a solution, never stopping thinking about it even when he was busy doing other things. Otherwise, the fabulous event that formed the basis of the legend would not have happened.

It happened, as they say, in the bath. Soaped with ashes, Archimedes decided to plunge into the bath. The water rose in the tub as Archimedes sank into it. If he had not paid attention to this before, now this phenomenon interested him; he got up - the water level dropped, he sat down again - the water rose. "EUREKA! Eureka! I found!". He jumped out of the bath and ran for the precious crown.

The ancient legend knows the whole world,
Like enjoying a hot bath
Archimedes discovered his law
Associating it with a strange trick.

Radiant jumped out Archimedes

From the hot bath, where he washed,

And straight from the bath, as was not

dressed,

He started running somewhere.

A painting worthy of the brush of the gods,
On the street warmed by the sun,
Dotted line leaving wet traces
Archimedes is running undressed.

A crowd of Syracusans rushes after,

In a frenzy of racing

And rejoices loudly when Archimedes

Shouted "EUREKA!" - loudly.

Found! He found the desired answer
Who searched so hard!

"Found!" - Archimedes shouted in ecstasy,

"Found!" - repeated fervently.

To this day, in all schools of the world, Archimedes' law of bodies immersed in a liquid is being studied.

Once a schoolgirl sympathetically complained: “Poor geniuses! They were forced to reveal what we went through at school.”

Another legend tells...

King Hieron built a giant as a gift to the Egyptian king Ptolemya noble and luxurious ship "Sirokosia", but the people of the king were not able to launch this ship into the water. Archimedes built a machine by which oneonly a man, the king himself, launched the ship into the water. After that, the king exclaimed: “From now on, no matter what our Archimedes says, we will consider it true!” Archimedes developed the theory of the lever. There is another figurativeproud statement that has survived the ages: “Give me a foothold, and Imove the earth!" Of course, these words are nothing more than poetic hyperbole.

Chapter II

The following works of Archimedes have come down to us:

Treatise "On the Sphere and Cylinder". In it, Archimedes outlined his method for calculating the volume of a ball and, much more difficultly, the surface of a ball. And he was very proud of the discovery of a beautiful result - "the volume of a ball inscribed in a cylinder is one and a half times less than the volume of the cylinder and that the surfaces of these bodies also apply."

“Of course,” Archimedes writes in the preface to the treatise, “these properties have always been inherent in these bodies, but they remained unknown to all geometers; not one of them even noticed that these bodies are commensurate with each other.

This discovery delighted Archimedes so much that he even bequeathed to carve a figure of a cylinder with an inscribed ball on his future tombstone, which was subsequently carried out.

Treatise "Squaring the parabola". In it, Archimedes finds the area of ​​a segment of a parabola.

Treatise on Spirals. Archimedes defines the spiral as a line,
described by a point moving uniformly along a straight line, in turn uniformly rotating around one of its points.

Treatise "On conoids and spheroids".

Treatise "Method" . In this work, the volumes of bodies are found.

Treatise "Measurements of the circle". This is one of the most famous works of Archimedes, from which, however, only a small fragment has come down to us. It provides evidence for the following:

Area of ​​a circle.

The ratio between the area of ​​a circle and the area of ​​a square built on its diameter11:14

The ratio of any circle to its diameter

3 < < 3

Treatise "Psammit" ("calculus of grains of sand").

IN 3rd century BC people did not yet know that the natural series is infinite. In this work, Archimedes developed a system that made it possible to express an arbitrarily large number and showed that the natural series is infinite. And the number of grains of sand in the universe is no more than 10 65 .

Treatise "On Floating Bodies". Here, among others, the Law of Archimedes is formulated.

Treatise "On the equilibrium of plane figures". Archimedes finds the center of gravity of a triangle, parallelogram, trapezoid, parabolic segment, sets out the proof of the law of equilibrium of a lever.

Archimedes thus developed, along with theoretical mathematics and
practical mathematics.

"First in Mathematical Physics"

Archimedes was the creator of science, he discovered new truths, created new theories. Therefore, the amazement and respect with which his contemporaries treated him and now those who are close to mathematics, mechanics and applied sciences are understandable.

Of the mathematical discoveries of Archimedes, the calculation was of particular importance
lengths of curves, areas and volumes of figures by such methods that after
2 thousand years were used to create integral and differential calculus. One of the creators of this theory, Leibniz, wrote in the 17th century about the teachings of Archimedes: “Carefully reading the writings of Archimedes, one ceases to be surprised at everything the latest discoveries geometry."

This is a unique fact in the history of mathematics - the scientist was 18 centuries ahead of his time.

And he raised mechanics to a level that it could not surpass for 19 centuries, before Galileo.

"The world's first planetarium"

The amazing invention of Archimedes - a mechanical celestial globe - a kind of planetarium, demonstrating all visible movements celestial bodies on models and even the phases of the moon, carried out with the help of special mechanisms. On the surface of the globe, stars and 12 zodiac constellations are marked, through which the Sun moves, passing one constellation per month. It was the first planetarium on earth, which for many centuries was an unsurpassed creation of theoretical mechanics. It is first mentioned in the 1st century BC, and the last one belongs to the Roman poet Claudian in the 5th century.

The sky charter, the laws of the gods, the harmony of the world -

All the Syracuse old man wisely brought to earth.

The air hidden within, various luminaries move

Just in marvelous ways, making creation alive.

The false zodiac runs, the appointed move is carried out

The face of the fake moon comes again every month,

Proud of bold art, bringing your world into rotation,

The stars of the highest heavens are ruled by the mind of man.

"Don't touch my circles!"

The high moral character of Archimedes also captivates. He was a true patriot of his city. In 212 BC. during the second Punic War, the Roman legions moved to conquer Carthogen. On their way was the hometown of Archimedes - Syracuse. Roman troops under the command of Marcellus besieged the city from two sides, and none of the besieged hoped for salvation. It was here that Archimedes set in motion his machines, which

he himself designed and built. The defense of the city rested on the ingenious engineering ingenuity of Archimedes. With the help of several dozen well-polished shields of Syracusan warriors, collecting reflected sunbeams at one point, he set fire to the galleys of the Romans, who approached the walls of the city from the sea.

telling about the siege of Syracuse by the Roman commander Marcellus: “The land army was struck by a hail of projectiles, stones, the weight of which reached a quarter of a ton, and thrown with great swiftness. As for the fleet, suddenly, from the height of the walls, logs descended onto ships and drowned them. Then iron claws and beaks seized ships, lifted them into the air nose up, stern down and then immersed them in the water. And then the ships were brought into rotation, and, circling, fell on pitfalls and cliffs at the foot of the walls. Every minute they saw some ship raised in the air. Terrible sight!"

“Well, we will have to stop the war against the mathematician,” sadly
joked Marcellus, withdrawing the fleet and ground army from the walls of Syracuse and proceeding to their long siege.

Nevertheless, after 8 months of defense, taking advantage of the lack of proper vigilance, the Romans finally managed to break into the city. The capture of Syracuse was accompanied by incredible acts of cruelty, murders and robberies.

Archimedes was among those killed. The gray-haired 75-year-old elder was sitting and thinking intensely over the geometric figures inscribed in the sand, when a Roman soldier burst in and rushed at him with a sword. Archimedes only had time to shout out: "Don't touch my circles!" - how the soldier's sword struck him.

Archimedes went down in history as one of the first scientists to work on the howl.
well, and as the first victim of the war among the people of science.

He was thoughtful and calm
I am fascinated by the mystery of the circle ...
Above him is an ignorant warrior
He swung his rogue sword.

The thinker drew with inspiration, Squeezing only the heart of a heavy burden: "Is it possible for my creations to burn Among the ruins of Syracuse?"

And Archimedes thought: “I will droop

Am I head to laugh at the enemy?

With a firm hand he took the compass

Spent the last arc.

Already the dust swirled over the road,

That is the path to slavery, to the yoke of chains.

"Kill me, but just don't touch me,

Oh, barbarian, these drawings!

According to another version of the legend, the soldier killed Archimedes for his refusal to obey the order to go with the soldier to Marcellus. One way or another, but the exclamation "do not spoil my circles!" became an aphorism - a commandment of high morality for all subsequent eras.

Dmitry Kedrin's poem "Archimedes".

No, the Sage is not always ridiculous and narrow, deaf to the affairs of the Earth: Already on the road in Syracuse

There were Roman ships.

Above the curly-haired mathematician, the Soldier raised a short knife,

And he, on a sandbank, entered the circle into the drawing.

Ah, if death were a dashing guest, I was also lucky to meet,

Like Archimedes drawing with a cane

In the minute of death - the number!

And the famous poet of Montenegro, Zhuvdiya Hodzic, as if rethinking the last words of Archimedes, wrote an excited poem.

Do what you want with me
Hang me on a star hook

Tame with wet chains, burn your legs and break your arms

Aim in the heart of me and our widows,

But don't touch my circles!

On the thirsty waters,
Drive under the scorching sun
Let everyone test their sword on me,
Drop on your knees and torture

« But don't touch my circles!

Scythians or termite powder Hanging over us in the future Sprinkle dynamite under me.

We'll save Syracuse in circles.

Do not forgive me other people's debts.

But don't touch my circles!

With a weak, weary hand

I will move the north and south, days and nights.

Don't give me peace for a moment

Burn your eyes with slaked lime.

I lie in the face of your courts.

But don't touch my circles!

"Don't touch my circles!"

Cicero - the famous Roman orator and politician - tracked down the tomb of Archimedes when, in 76 BC. was in Sicily. They found a grave obelisk with an engraved ball inscribed in a cylinder. In the 136 years that have passed since the death of Archimedes, his tomb has been abandoned and forgotten. In Syracuse, nevertheless, an original monument to Archimedes was erected with a model of a concave mirror in hand. According to legend, with the help of such a mirror, Archimedes set fire to enemy ships that threatened Syracuse. The mirror has the form of a spherical segment, the radius of curvature of which is approximately 1 m.

Centuries have passed,

The scientific feat is not forgotten.

Nobody knows who the killer is

But everyone knows who was killed.

The works of Archimedes greatly reinforced the belief of people that the universe is moving on mathematical principles. Law and order exist in nature, and mathematics is the key to understanding this order.

"The Challenge is a Legend"

Once the king ordered Archimedes to establish how much gold would be needed so that it would be equal in mass to the mass of an elephant. But there were no such scales to weigh this huge load. I wonder how - and quite simply - Archimedes solved this problem?

ANSWER. Archimedes solved the problem by placing an elephant on a large raft and noting the level to which the raft was submerged in water. Then the elephant was removed from the raft and began to load the raft with ingots until the raft was loaded to the marked level. In this position, the weight of the raft with gold was equal to the weight of the raft with the elephant, and, therefore, the gold weighed as much as the elephant.

"How to weigh the area?"

Archimedes proposed an ingenious way to approximate the area of ​​a drawn flat figure by weighing: draw the figure on a sheet of homogeneous material, cut it out, weigh it on an accurate balance, and then weigh a square with a side equal to the scale unit of the figure cut out of the same material, and divide the first result to the second.

(Number weight display π )

Draw a circle of radius R \u003d l dm on cardboard, carefully cut out the circle, determine the mass with the help of scales. Meaning pi = t.

"Hieron's Challenge"

King Hieron ordered a crown of pure gold from the master. When the order was completed, the king wanted to check if the master had replaced part of the gold given to him with silver and turned to Archimedes, who at that time was the king's adviser.

Solving the problem from the point of view of physics:

Given:

P in air =20N

P in water = 18.75N

 water =1000

 gold =19320

Find:  crown

Compare  crown with  gold.

Solution:

F arch \u003d P in air - P in water \u003d 1.25N

F arch \u003d  W V body g  V body \u003d
=
\u003d 1.25 * 10 -4 N

P in air =mg  m crown = ==2 (kg)

m \u003d V  crown   crown \u003d =
10 4 =1,6*10 4 =16000is less than the density of gold. So the master deceived the king.

Solution of the problem from the point of view of mathematics.

Pure gold loses a 20th part of its weight in water, and silver a 10th part. We have uncovered the deception, but let's follow the example of Archimedes and find out how much gold the master replaced with silver?

The crown has lost 1.25H=H in weight, while it should have lost 1H. This is because it contains silver, which does not lose in water. share of the weight, and . There should be enough silver in the crown so that the crown loses not 1H, but H in water, i.e. more than N.

So, in the crown there were 5 N of silver and 15 N of gold.

Toy "Underwater inhabitant"

(Float Descartes)

Blow the contents out of the egg. Attach "handles" and "legs" of plasticine.

Pour water into the egg, close it with your index finger, turn it over and lower it into a vessel with water. By pouring in and out of water, we make the toy float. Now fill the jar with water to the brim, tighten with a rubber film, tying the neck of the vessel with a thread.

By pressing on the film, you will make the "little man" dance up and down.

Experiences:

At the table.

Dissolve in a glass filled with ¾ boiling water, 2-3 pieces of sugar. Place a teaspoon obliquely near the surface of the liquid and pour strong tea on it in a thin stream. The golden layer of tea will sit on top of the sweetened boiling water without mixing with it. Why?

Three cans and three potatoes.

Prepare three approximately identical small potatoes, three half-liter jars, table salt, a vessel of water.

Pour water into 1 jar, a very strong solution into 2. Half fill the third jar with strong brine, and carefully pour over it pure water so that the liquids do not mix (see previous experience). If you put potatoes in all three jars, how will they settle down? Why? Test your reasoning empirically.

Quiz "On the water and under water."

Why is it easier to stay on the water when swimming on your back?

Answer: it is easier to swim on your back, because. while the largest part of the human body is immersed in water. This increases the buoyancy force.

Why are life belts made from cork?

1. Why do ships, leaving the mouths of the rivers to the open sea, have less draft?

Answer: The density of sea water is 1050  fresh water density

In training, divers must put together a wooden box underwater. What is the difficulty of the task?

Answer: The difficulty lies in the following: nails, a hammer fall down, and boards float up. The hammer handle, escaping from the hands, is located vertically, etc.

When we stand on the rocky bottom of a river or sea in shallow water, near the shore, our legs hurt, and when we go deeper, the pain decreases. Why?

Answer: The greater part of the human body is immersed in water, the greater the buoyancy force. This leads to a decrease in the pressure force of the foot on the bottom  according to Newton's III law, the pressure of the bottom on the feet decreases.

Conclusion

Working on the chosen topic, we studied a lot of literature that tells about the life and work of Archimedes, his discoveries. We found in the studied literature confirmation that Archimedes is a really great scientist who made many discoveries not just theoretical, but those that were used by man in ancient times. This scientist deserves to be known by everyone. We have done some experiments that turned out to be interesting, they confirm the laws of physics. In the course of the work, we made a quiz to test the knowledge of students. The work on this topic was interesting and useful. We think that the material we have selected will be useful to both students and teachers of our school.