Where did Archimedes live in what city. Archimedes and his discoveries. Getting electricity from radio waves

The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, created inventions that served as a starting point for the further development of science. Legends about Archimedes were created during his lifetime. The scientist spent several years in Alexandria, where he met and became friends with many other great scientists of his time.

The biography of Archimedes is known from the works of Titus, Polybius, Livy, Vitruvius and other authors who lived later than the scientist himself. It is difficult to assess the degree of reliability of these data. It is known that Archimedes was born in the Greek colony of Syracuse, located on the island of Sicily. His father, presumably, was the astronomer and mathematician Phidias. also claimed that the scientist was a close relative of the kind and skillful ruler of Syracuse Hieron II.

Probably, Archimedes spent his childhood in Syracuse, and at a young age went to Alexandria of Egypt to get an education. For several centuries this city was the cultural and scientific center of the civilized Ancient World. The scientist, presumably, received his primary education from his father. After living for several years in Alexandria, Archimedes returned to Syracuse and lived there until the end of his life.

Engineering

The scientist actively developed mechanical structures. He presented a detailed theory of the lever and effectively used this theory in practice, although the invention itself was known directly before him. Including, based on knowledge in this area, he made a number of block-link mechanisms in the port of Syracuse. These attachments made it easier to lift and move heavy loads, allowing you to speed up and optimize port operations. And the "Archimedes screw", designed to scoop out water, is still used in Egypt.

Archimedes' inventions: Archimedes screw

The theoretical research of the scientist in the field of mechanics is of great importance. Based on the proof of the law of leverage, he began to write the work "On the balance of plane figures." The proof is based on the axiom that on equal shoulders, equal bodies will balance out of necessity. The same principle of constructing the book - starting with the proof of his own law - was observed by Archimedes when writing the work "On the Swimming of Bodies". This book begins with a description of the well-known Archimedes' law.

Mathematics and physics

Discoveries in the field of mathematics were a real passion of the scientist. According to Plutarch, Archimedes forgot about food and personal 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 for calculating the areas of a circle and polygons, the volumes of a pyramid, a cone and a prism. But the scientist's experience allowed him to develop general techniques for calculating volumes and areas. To this end, he perfected 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 later became the basis for this theory.

Also, the 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, from a physical point of view - the speed of a body at any time. The scientist investigated a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to hyperbola, parabola and ellipse. Only in the seventeenth century, scientists were able to fully realize and reveal all the ideas of Archimedes, which have come down to those times in his surviving works. The scientist often refused to describe inventions in books, which is why not every formula he wrote has survived to this day.

Archimedes' inventions: "solar" mirrors

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

The discovery of the scientist in the field of physics was a statement that is known as Archimedes' law. He determined that a buoyant force exerts pressure on any body immersed in a liquid. It is directed upward, and in magnitude is equal to the weight of the liquid that was displaced when the body was placed in the liquid, regardless of what the density of this liquid is.

There is a legend associated with this discovery. Once, the scientist was allegedly approached by Hieron 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 bars of the same weight as the crown: silver and gold. Then, in turn, he placed these ingots in a vessel with water and noted how much its level had risen. Then the scientist put a crown in the vessel and found 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.

There is a myth that a bathtub helped Archimedes make a key discovery in physics. While swimming, the scientist allegedly lifted his leg slightly in the water, discovered that it weighs less in the water, and experienced an inspiration. A similar situation took place, however, with its help, the scientist discovered not the Archimedes law, but the law of the specific gravity of metals.

Astronomy

Archimedes became the inventor of the first planetarium. When this device moves, observe:

• rising of the moon and sun;
• movement of five planets;
• the disappearance of the Moon and the Sun beyond the horizon;
• phases and eclipses of the moon.

Archimedes' inventions: planetarium

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

Personal life

Much less is known about the scientist's personal life than about his science. His contemporaries also composed numerous legends about the gifted mathematician, physics and engineer. Legend says that one day Hieron II decided to present a multi-deck ship to Ptolemy, the king of Egypt. It was decided to name the water vessel "Syracuse", but it was not possible to launch it.

In this situation, the ruler again turned to Archimedes. From several blocks, he built a system with which the descent of a heavy ship was possible with one hand movement. According to legend, during this movement, Archimedes said:

"Give me a foothold, and I will turn the world."

Death

In 212 BC, during the Second Punic War, Syracuse was besieged by the Romans. Archimedes actively used his engineering knowledge to help his people triumph. So, he designed throwing machines with which the warriors of Syracuse threw heavy stones at opponents. When the Romans rushed to the walls of the city, hoping that there they would not fall under fire, another invention of Archimedes - light throwing devices of close action - helped the Greeks to throw cannonballs at them.

Archimedes' inventions: the catapult

The scientist helped his compatriots in naval battles. The cranes developed by him captured enemy ships with iron hooks, slightly lifted them, and then abruptly threw them back. Because of this, the ships overturned and suffered a wreck. For a long time, these cranes were considered something of a legend, but in 2005 a group of researchers proved the operability of such devices, reconstructing them according to surviving descriptions.

Archimedes' inventions: lifting machine

Thanks to the efforts of Archimedes, the Romans' hope to storm the city failed. Then they decided to go over to the 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.

Other researchers claim that Archimedes was killed in his laboratory. The scientist was allegedly so keen on research that he refused to immediately follow the Roman soldier, who was ordered to escort Archimedes to the commander. He, in anger, pierced the old man with his sword.

There are also variations of this story, but they agree that the ancient Roman politician and military leader Marcellus was extremely upset by the death of the scientist and, having united with the citizens of Syracuse and with his own subjects, arranged a magnificent funeral for Archimedes. Cicero, who discovered the destroyed grave of the scientist 137 years after his death, saw on it a ball inscribed in a cylinder.

Essays

• The square of the parabola
• About ball and cylinder
• About spirals
• About conoids and spheroids
• On the balance of plane figures
• Message to Eratosthenes about the method
• About floating bodies
• Circle measurement
• Psammit
• Stomachion
• Archimedes' problem on bulls
• Treatise on the construction of a corporeal figure with fourteen bases near a ball
• Book of lemmas
• A book on constructing a circle divided into seven equal parts
• A book about touching circles

ARCHIMEDES

OK. 287 - c. 212 BC NS.

Archimedes is an ancient Greek scientist, mathematician and mechanic from Syracuse. He developed methods for finding the areas of surfaces and volumes of various figures and bodies. His mathematical works were far ahead of their time and were correctly evaluated only in the era of the creation of differential and integral calculus. Archimedes is a pioneer of mathematical physics, one of the founders of mechanics as a science. Mathematics in his works is systematically applied to the study of the problems of natural science and technology. Archimedes owns various technical inventions.

Archimedes was born in Syracuse (Sicily) and lived in this city during the 1st and 2nd Punic Wars. It is believed that he was the son of the astronomer Phidias. He began his scientific career as a mechanic and technician. Archimedes traveled to Egypt and became close to Alexandrian scholars, including Conon and Eratosthenes. This was the impetus for the development of his outstanding abilities. Archimedes was close to the Syracuse king Hieron II. During the 2nd Punic War, Archimedes organized an engineering defense of Syracuse from the Roman troops. His war machines forced the Romans to abandon their attempts to take the city by storm and forced them to go to a long siege. During the capture of the city by the troops of Marcellus, Archimedes was killed by a Roman soldier, whom, according to legend, he met with the words "do not touch my drawings." On the grave of Archimedes, a monument was erected with the image of a ball and a cylinder described around it. The epitaph indicated that the volumes of these bodies are related as 2: 3 - the discovery of Archimedes, which he especially appreciated.

The works of Archimedes show that he was perfectly familiar with the mathematics and astronomy of his time, and amaze with the depth of penetration into the essence of the problems under consideration. A number of works are in the form of messages to friends and colleagues. Sometimes Archimedes previously communicated his discoveries to them without proof, adding several incorrect sentences with subtle irony.

In the IX-XI centuries. Archimedes' works were translated into Arabic, from the XIII century. they appear in Western Europe in Latin translation. Since the XVI century. Archimedes' printed editions begin to appear, in the 17th-19th centuries. they are being translated into new languages. The first edition of individual works of Archimedes in Russian dates back to 1823. Some of Archimedes' works did not reach us or are known only in fragments, and his "Epistle to Eratosthenes" was found only in 1906.

The central theme of the mathematical works of Archimedes is the problem of finding the areas of surfaces and volumes. Archimedes initially found the solution to many problems of this type, using mechanical considerations, essentially reducing to the method of "indivisible", and then rigorously proved by the method of exhaustion, which he significantly developed. Archimedes' consideration of two-sided estimates of the error in carrying out integration processes allows us to consider him a predecessor not only of I. Newton and G. Leibniz, but also G. Riemann. Archimedes calculated the area of ​​an ellipse, a parabolic segment, found the surface area of ​​a cone and a sphere, the volume of a sphere and a spherical segment, as well as various bodies of revolution and their segments. Archimedes investigated the properties of the so-called. Archimedean spiral. Gave the construction of a tangent to this spiral, found the area of ​​its turn. Here he acts as the predecessor of the methods of differential calculus. Archimedes also considered one problem of the isoperimetric type. In the course of his research, he found the sum of an infinite geometric progression with a denominator of 1/4, which was the first example of the appearance of an infinite series in mathematics. In the study of one problem, which reduces to a cubic equation, Archimedes clarified the role of the characteristic, which later became known as the discriminant. Archimedes owns a formula for determining the area of ​​a triangle through its three sides (incorrectly referred to as Heron's formula). Archimedes gave a (not completely exhaustive) theory of semiregular convex polyhedra ( Archimedean bodies). Of particular importance is Archimedes axiom: of unequal segments, the smaller one, being repeated a sufficient number of times, will surpass the larger one. This axiom defines the so-called. Archimedean ordering, which plays an important role in modern mathematics. Archimedes built a notation that allows you to write and name very large numbers. He calculated with great precision the value of the number pi and indicated the margin of error.

Mechanics was constantly in the circle of interests of Archimedes. In one of his first papers, he investigated the distribution of loads between beam supports. The definition of the center of gravity of a body belongs to Archimedes. Applying, in particular, integration methods, he found the position of the center of gravity of various figures and bodies. Archimedes gave a mathematical derivation of the laws of the lever. He is credited with the proud phrase: "Give me where to stand, and I will move the Earth." Archimedes laid the foundations for hydrostatics. He formulated the main provisions of this discipline, including the famous Archimedes' law... The last work of Archimedes is devoted to the study of the equilibrium of floating bodies. At the same time, he distinguishes stable equilibrium positions. Archimedes invented the water-lifting mechanism, the so-called. Archimedes screw, which was the prototype of ship, as well as propellers. They say that Archimedes found a solution to the problem of determining the amount of gold and silver in the sacrificial crown of Hieron, when he sat down in the bath, and ran home naked with a shout of "eureka!" ("found!").

Archimedes also studied astronomy. He constructed an instrument for determining the apparent (angular) diameter of the Sun and found the value of this angle with amazing accuracy. At the same time, Archimedes introduced a correction for the size of the pupil. He was the first to bring observations to the center of the Earth. Finally, Archimedes built the celestial sphere - a mechanical device on which it was possible to observe the movements of the planets, the phases of the moon, solar and lunar eclipses.

Archimedes is an ancient Greek scientist, physicist, mathematician and engineer from Syracuse (the island of Sicily), who lived in 287-212 BC. In addition to the many discoveries made in the field of mathematics, especially in geometry, he also became the founder of mechanics, hydrostatics, and the author of a number of other significant inventions. He owns many significant discoveries in the field of mathematics and physics. For example, the ratio of the length and diameter of a circle, the scientific substantiation of the action of the lever, and others. The life of a scientist can be judged by his works and essays by other ancient Greek figures. Among them are Titus Livy, Polybius, Cicero, Vitruvius. Archimedes developed a love for the exact sciences since childhood, since the scientist's father was also a mathematician. To get a decent education and as much knowledge as possible, the scientist went to Alexandria - the cultural and scientific center of the ancient world. Upon his return to Syracuse, the scientist began to intensively engage in scientific work. It was during this period that the law of hydrostatics appeared, later called the Archimedes law. His engineering skills were fully developed during the Roman siege. For defense purposes, he created special throwing machines. Unfortunately, the Romans still took Syracuse, and the scientist was killed in the process. Some of the treatises of Archimedes have reached the present day, which speak of the genius of the scientist. Among them are "On a ball and a cylinder", "On floating bodies", "On spirals", "On the balance of plane figures" and others. Many discoveries were made in the field of astronomy. So, for example, Archimedes built the first planetarium, with the help of which it was possible to observe the movement of several planets, the rising of the Sun and the Moon, the phases of the eclipse of the Moon, etc. In one of his writings, he mentions the heliocentric system of the world. In memory of Archimedes, a crater and an asteroid are named after him. Name: Archimedes Years of life: 287 BC NS. - 212 BC NS. State: Ancient Greece Field of activity: Mathematics, geometry, physics, mechanics Greatest achievement: Archimedes owns 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, 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, instilled love for them. Perhaps at a young age, Archimedes lived for some time in Egypt. He continued his education in Alexandria. As a future mathematician, he studied the works of scientists, got 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 Hieron II. Archimedes corresponded a lot with other mathematicians who lived at that time. These were the Alexandrian scholars Eratosthenes of Cyrene and Konon of Samos. Archimedes' throwing machines Archimedes was the protector of Syracuse during their siege in 213 BC. He invented the 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 250 kilograms. But Syracuse was still captured by the Roman general Marcus Claudius Marcellus in the fall of 212 or in the spring of 211 BC. Archimedes was killed when the Roman invaders plundered 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 impress people's imaginations. Thanks to his inventions, mechanics became a science. He also became famous for his military inventions. He proved many theorems. Archimedes deduced 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 lifted up from lakes and rivers that are at a lower level than the city. The canals were quickly filled with water rising upward in a spiral, and this happened without interruption. The people of Syracuse no longer lacked moisture. Their fields yielded well, the city flourished. The Archimedean screw is still used by residents of developing countries in Asia and Africa. The well-known meat grinder in its design also contains a screw (auger) that moves the meat to the knives. Even the most ordinary cogs are a brilliant invention of Archimedes. Augers are widely used in factories, in various mechanisms, machines. It is impossible to imagine an airplane or a modern ship without a propeller. Archimedes bath, Archimedean force and Archimedes' law Archimedes formulated the method of the hydrostatic principle. An interesting story is about how he determined the ratio of silver and gold in Hieron's wreath by submerging it in water. Anecdotal version, when naked Archimedes jumps out of the bath and shouts: "Eureka!" - runs around the city. Of course, this is heavily embellished. Thus, the scientist found out that if an object is lowered into water, then it will either drown or be on the surface. Archimedes found out that this happens under the pressure of the lifting force (or buoyancy). The water displaced by the object has the same volume as the dropped object. This means that the buoyancy force is equal to the weight of the displaced fluid. It was this force that received the name Archimedean. Heat ray No less mythical are the stories about the large mirrors that Archimedes used to destroy Roman ships by setting fire to them. Archimedes collected many mirrors, directed the rays reflected by them to one point. The ships were built of wood and painted with resin paint, so they quickly caught fire. He was engaged in catoptrics, that is, the reflection of light rays from mirrors. But it is possible that the ships caught fire from fiery arrows or from "fiery projectiles" fired by throwing machines. Later, some researchers tried to repeat this experiment. Some of the experimenters succeeded. The Romans, who captured Syracuse, demanded to give them manuscripts with formulas, and when Archimedes wrote the formulas on the sand with a stick, and then rubbed off the sand with his foot, refusing to give them away, they killed him. Archimedes Lever An interesting story is also when he exclaimed: "Give me a fulcrum, and I will turn the whole Earth!" Archimedes was very fond of his city of Syracuse. 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. In it one could observe the movements of the Sun and planets. But, unfortunately, it has not survived. He was taken to Rome by the conqueror Syracuse Marcellus. Only a few details have survived from this device. All of his work was theoretical, 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, his tomb was found, it was all covered with moss, grass, mud. When they cleaned it, they saw that it had a sphere inscribed in a cylinder. This happened a century and a half after his death. I found the grave. Archimedes has many works on hydrostatics and theoretical mechanics. He applied mechanical theories as a means of solving 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 are included in the school curriculum in geometry to this day. His "simple" inventions pushed the development of human civilization far ahead. He will forever remain in the memory of people as a brilliant inventor, mechanic and designer, geometer. (287 - 212 BC) Archimedes was born in 287 BC (because of this, many facts of his biography were lost) 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 studied, like many other ancient Greek scientists, 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 the position of his father. In theoretical terms, the work of this great scientist was dazzlingly multifaceted. Archimedes' main works dealt with various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In the essay "Parabola of Quadrature", Archimedes substantiated the method for calculating the area of ​​a parabolic segment, and he did it 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 to the 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 who 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 in this space, the form of a perfect, geometric form, to which objects are more or less approaching and the laws of which must be known if we want to influence the material world. But Archimedes also knew that objects have not only 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, retain their weight at the same time. 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 stated with surprise that the leg became lighter in the water. "Eureka! Found it, ”he exclaimed, coming out of his bath. The anecdote is amusing, but, conveyed in 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 with respect to the law of the specific gravity of metals - a discovery that also belongs to the Syracuse scientist and the detailed details of which we find in Vitruvius. It is said that once Heron, the ruler of Syracuse, turned to Archimedes. He ordered to check whether the weight of the gold crown corresponds to the weight of the gold set on it. For 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, 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 master's dishonesty was proved. Interesting is the opinion of Cicero, the great orator of antiquity, who saw the "Archimedean sphere" - a model showing the movement of heavenly bodies around the Earth: "This Sicilian possessed a genius that, it would seem, human nature cannot reach." And finally, Archimedes was not only a great scientist, he was also a man with a passion for mechanics. He tests and creates a theory of five mechanisms known in his time and called "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 inventing the endless screw, but it is possible that he only improved the hydraulic screw that served the Egyptians when draining swamps. Subsequently, these mechanisms were widely used in different countries of the world. 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 common, the invention of a bolt constructed from a screw and a nut. To those of his fellow citizens who would consider such inventions insignificant, Archimedes presented decisive proof of the opposite on the day when he, cleverly adjusting a lever, a screw and a winch, found a means, to the surprise of onlookers, to launch a heavy galley that had run aground, with everything her crew and cargo. He gave an even more convincing proof in 212 BC. While defending Syracuse from the Romans during the second Punic War, Archimedes constructed several combat vehicles 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 which the Egyptians were able to burn down the Roman fleet. This feat of his, which was told by Plutarch, Polybius and Titus of Livia, of course, aroused more sympathy from 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 looking for a solution to his problem. It is curious that, having conquered Syracuse, the Romans did not acquire the works of Archimedes. Only after many centuries were they 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 with the image of a ball and a cylinder was installed on his grave. It was seen by Cicero, who visited Sicily 137 years after the death of the scientist. Only in the 16th-17th centuries did European mathematicians finally realize the significance of what Archimedes had done two thousand years before them. He left numerous disciples. A whole generation of followers, enthusiasts, who were eager, like the teacher, to prove their knowledge by concrete conquests, rushed to the new path opened by him. The first of these disciples was the Alexandrian Ctesibius, who lived in the 2nd century BC. Archimedes' inventions in the field of mechanics were in full swing when Ctesibius added to them the invention of the cogwheel.

 

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