How Archimedes died. Biography of Archimedes. Archimedes: interesting facts

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 outlined detailed theory lever and effectively used this theory in practice, although the invention itself was known even before him. Including, based on knowledge in this area, he made a number of block-lever mechanisms in the port of Syracuse. These attachments made lifting and moving heavy loads easier, allowing for faster and better 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 - Archimedes observed when writing the work "On the swimming of bodies." This book begins with a description of the well-known Archimedes' law.

Mathematics and physics

The discoveries in the field of mathematics were the real passion of the scientist. According to Plutarch, Archimedes forgot about food and self-care when he was on the verge of another invention in this area. The main direction of his mathematical research was the problems of mathematical analysis.

Even before Archimedes, formulas were invented 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 improved the method of exhaustion, invented by Eudoxus of Cnidus, and brought the ability to apply it to a virtuoso level. Archimedes did not become the creator of the theory of integral calculus, but his work 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 understand and reveal all the ideas of Archimedes that 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 size 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 corresponds 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 increased. Then the scientist put the crown in the vessel and found that the water did not rise to the level to which it rose when each ingot 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, found that it weighs less in the water, and experienced an inspiration. A similar situation took place, but 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: the planetarium

The scientist also tried to create formulas for calculating distances to celestial bodies. Modern researchers suggest that Archimedes considered the Earth to be the center of the world. He believed that Venus, Mars and Mercury 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-decked ship to Ptolemy, the king of Egypt. It was decided to name the watercraft "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 vessel was possible with the help of one movement of his hand. 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 the help of 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 come 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 and in sea \u200b\u200bbattles... 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 hope of the Romans 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 warrior, whom the scientist attacked for stepping on his drawing.

Other researchers claim that the place of death of Archimedes was 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 a 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 on 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

(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.

Theoretically, 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 a method for calculating the area of \u200b\u200ba parabolic segment, and he did this two thousand years before the discovery of integral calculus. In his work "On the Measurement of a Circle" Archimedes was the first to calculate 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 integer naming system invented by Archimedes.

The mathematical method of Archimedes, associated with the mathematical works of the Pythagoreans and with the work of Euclid that completed them, as well as with the discoveries of Archimedes' contemporaries, led to the knowledge of the material space 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 action 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 regard to the law of the specific gravity of metals - a discovery that also belongs to a 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 established that its volume exceeds the volume of the ingot. So the master's dishonesty was proved.

An interesting review 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 achieve."

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, by cleverly adjusting a lever, a screw and a 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.

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 finding 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 had not left 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.

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

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

Archimedes spent most of his time in the Library of Alexandria. There he studied the works of Democritus and Eudoxus. During his training, Archimedes became close to Eratosthenes and Conon. Friendship has been preserved for many years.

Works and achievements

After completing his studies, Archimedes returned to his native Syracuse and took up the post of astronomer at the court of Hieron II. But not only the stars attracted his attention.

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

The conclusions were detailed in the work "On the equilibrium of plane figures".

A little later, Archimedes wrote an essay "On the measurement of a circle." He managed to calculate the ratio of the diameter of a circle to its length.

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

Gifts of Syracuse

Archimedes made many useful discoveries. All of them were dedicated to the hometown of the scientist. Archimedes actively developed the idea of \u200b\u200busing leverage. In the Syracuse port, he managed to create a whole system of lever-block mechanisms that accelerate the process of transporting heavy, oversized cargo.

With the help of an Archimedean screw, or auger, it became possible to extract water from low-lying reservoirs. Thanks to this, the irrigation canals began to receive moisture without interruption.

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

Archimedean cranes easily turned over the ships of the Romans. This led to the fact that the Roman soldiers abandoned the storming of the city and began a long siege.

Unfortunately, in the end, the city was taken.

Death of a scientist

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

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

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

Other biography options

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

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

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

Archimedes was born in 287 BC in the Greek city of Syracuse, where he lived almost his entire life. His father was Phidias, the court astronomer of the ruler of the city of 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.

It is said that one day Hieron, 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 established that its volume exceeds the volume of the ingot. So the master's dishonesty was proved.

Interesting is the opinion of 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 achieve."

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 the invention of 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.

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 the system of mirrors, with the help of which the Egyptians were able to burn down the Roman fleet. This feat of his, which was told by Plutarch, Polybius and Titus Livy, 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.

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

Archimedes left numerous students. 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.

In his fundamental works on statics and hydrostatics (Archimedes' law), Archimedes gave examples of the application of mathematics in natural science and technology. Archimedes owns many technical inventions (Archimedes' screw, determination of 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 Syracuse 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 participated 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 the burning of the Roman fleet by the sun's rays directed through a system of concave mirrors, but this is unreliable information. Even the Romans admired the genius of Archimedes. Marcellus ordered to save the scientist's life, but during the capture of Syracuse, Archimedes was killed.

Archimedes is the leader 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 a ball and a cylinder" (in two books), Archimedes establishes that the surface area of \u200b\u200ba ball is 4 times the area of \u200b\u200bits largest cross section; formulates the ratio of the volumes of the ball and the cylinder described around it as 2: 3 - a discovery that he treasured so much that in his will he asked to put on his grave a monument depicting a cylinder with a ball inscribed in it and an inscription of calculation (the monument was seen by Cicero a century and a half later). In the same treatise, Archimedes' axiom (sometimes called the Eudoxus axiom) is formulated, playing important role in modern mathematics.

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

In physics, Archimedes introduced the concept of the center of gravity, established the scientific principles of statics and hydrostatics, and gave examples of the application of mathematical methods in physical research. The main provisions of statics are formulated in the essay "On the balance of plane figures."

Archimedes examines the addition of parallel forces, defines the concept of the center of gravity for various figures, gives the derivation of the law of the lever. The famous law of hydrostatics, which entered science with his name (Archimedes' law), is formulated in the treatise "On floating bodies". There is a legend that the idea of \u200b\u200bthis law visited Archimedes when he was taking a bath, with the exclamation of "Eureka!" he jumped out of the bath and ran naked to write down the scientific truth that had come to him.

Archimedes' law: any body immersed in a liquid is subjected to a buoyant force directed upwards 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 it aroused admiration for several centuries); a hydraulic organ, mentioned by Tertullian as one of the miracles of technology (the invention of the organ is attributed by some to the Alexandrian engineer Ctesibius).

It is believed that even 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 his treatise "Psammit") and determined the value of this angle.

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

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

From the biography of Archimedes:

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

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

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

Archimedes bust

It was in Alexandria that the young man striving for knowledge established friendly relations with the mathematician and astronomer Konon of Samos and the astronomer, mathematician and philologist Erastofen of Cyrene - these were famous scientists of that time. Archimedes developed a strong friendship with them. It lasted all my life, and was expressed in correspondence.

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

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

Archimedes died during the Second Punic War, when Roman troops after 2 years of siege captured Syracuse. The Romans were commanded by Mark Claudius Marcellus. According to Plutarch, he ordered to find Archimedes and deliver to him. A Roman soldier came to the house of an outstanding mathematician while he was pondering mathematical formulas. The soldier demanded to go immediately with him and meet with Marcellus. But the mathematician brushed aside the obsessive Roman, saying he had to finish the job first. The soldier was indignant and stabbed the smartest inhabitant of Syracuse with a sword.

There is also a version claiming that Archimedes was killed right on the street when he was carrying mathematical instruments in his hands. The Roman soldiers thought they were valuable items and killed the mathematician. But be that as it may, the death of this man angered Marcellus, since his order was violated. There are still versions 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 both with the citizens of Syracuse and with his own subjects, arranged a magnificent funeral for Archimedes.

140 years after these events, the famous Roman orator Cicero arrived in Sicily. He tried to find the grave of Archimedes, but none of the local residents knew where it was. Finally, the grave was found in a dilapidated state in a thicket of bushes on the outskirts of Syracuse. On the gravestone was a ball and a cylinder inscribed in it. Poems were engraved under them. However, this version has no documentary evidence.

In the early 1960s, an ancient grave was also discovered in the courtyard of the Panorama Hotel in Syracuse. The owners of the hotel began to claim that this was the burial place of the great mathematician and inventor of antiquity. But again, no conclusive evidence was presented. In a word, to this day it is unknown where Archimedes is buried, and in what place his grave is.

Scientific activity and inventions of Archimedes:

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. + Discoveries in the field of mathematics were a real passion of the scientist. According to Plutarch, Archimedes forgot about food and self-care when he was on the verge of another invention in this area. The main direction of his mathematical research was the problems of mathematical analysis.

Also, an outstanding mathematician laid the foundations of differential calculus. From a geometric point of view, he studied the possibility of determining the tangent to a curved line, 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. Hence, we can safely say that this man has outstripped the science of mathematics by 2 thousand years. Only in the seventeenth century, scientists were able to fully understand and reveal all the ideas of Archimedes, which reached those times in his surviving works. The scientist often refused to describe inventions in books, which is why not every formula he wrote has survived to this day.

The scientist also actively developed mechanical structures. He developed and presented a detailed theory of the lever and effectively used this theory in practice, although the invention itself was known even before him. In the port of Syracuse, block-link mechanisms were made. These attachments made lifting and moving heavy loads easier, allowing for faster and better port operations.

He also invented a screw with which water was scooped out. His "Archimedes screw" is still used in Egypt. Archimedes created the theory of balancing equal bodies. He proved that a buoyant force equal to the weight of the displaced fluid acts on a body immersed in a liquid. This idea occurred to him in the bath. She shocked the outstanding mathematician and inventor with her simplicity so much that he jumped out of the bathtub and in Adam's suit ran through the streets of Syracuse shouting "eureka", which means "found." Subsequently, this proof was called the Archimedes law. + 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 necessarily balance. The same principle of constructing the book - starting with the proof of his own law - Archimedes observed when writing the work "On the swimming of bodies." This book begins with a description of the well-known Archimedes' law.

There is a legend associated with Archimedes' law. One day, 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 he put these bars in turn in a vessel with water and noted how much its level had risen. Then the scientist put the crown in the vessel and found that the water did not rise to the level to which it rose when each ingot was placed in the vessel. Thus, it was discovered that the master had kept some of the gold for himself.

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

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 legends, during this movement Archimedes said: "Give me a fulcrum and I will turn the world."

The scientist helped his compatriots in sea 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 capsized and wrecked. 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.

In 212 BC, during the Second Punic War, the Romans began to storm Syracuse. At this time, Archimedes was already an elderly man, but his mind did not lose its sharpness. Archimedes actively used his engineering knowledge to help his people triumph. As Plutarch wrote, throwing machines were built under his leadership, with the help of which the soldiers 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. Roman galleys scurrying about in the port of Syracuse were attacked by special cranes with grabbing hooks (Archimedes' claw). With the help of these hooks, the besieged lifted ships into the air and threw them down from great heights. Ships, hitting the water, crashed and sank. All these technical advances frightened the invaders. So thanks to the efforts of Archimedes, the hope of the Romans to storm the city failed. They abandoned the storming of the city and went over to a long siege. In the fall of 212 BC, the colony was taken by the Romans as a result of treason. Archimedes was killed during this incident. According to one version, he was hacked to death by a Roman soldier, whom the scientist attacked for stepping on his drawing.

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

Nevertheless, scientists continue to doubt the existence of a "mirror" weapon in Syracuse, since none of the ancient authors mentions it; information about him appeared only in the early Middle Ages - from the author of the 6th century Anthimius of Trallius. Despite heroic - and ingenious - defenses, Syracuse was finally subjugated.

Archimedes' legacy:

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

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

* Archimedes screw, or auger - serves for lifting and transporting goods, scooping up water. This device is still used (for example, in Egypt).

* Various types of cranes based on blocks and levers.

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

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

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

* Being the first theorist of mechanics, Archimedes introduced thought experiments into it. The first such experiments were his proof of the law of leverage and the law of Archimedes.

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

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

Archimedes: interesting Facts

1. After himself, Archimedes did not leave students, because he did not want to create his own school and prepare successors.

2. Some calculations of Archimedes were repeated only after one and a half thousand years by Newton and Leibniz.

3.Some scholars claim that Archimedes was the inventor of the cannon. So, Leonardo da Vinci even drew a sketch of a steam cannon, the invention of which he attributed to an ancient Greek scientist. Plutarch wrote that during the siege of Syracuse, the Romans fired at a device that resembled a long pipe and "spit out" the cannonballs.

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

5. Some contemporaries thought Archimedes was crazy. To demonstrate his skills, the scientist in front of Hieron pulled triremes ashore using a block system.

6. The Roman general Marcellus, commander of the siege of Syracuse, said: "We will have to end the war against the geometer."

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

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

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

11 Archimedes built the world's first planetarium.

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

13. The famous legend about the mirrors that burned Roman ships has been repeatedly refuted. Most likely, the mirrors were used only for aiming ballistae, which fired incendiary shells at the Roman fleet. It is also believed that the Romans were forced to agree to the night assault on the city precisely because of the use of mirrors by the defenders of Syracuse.

14. "Archimedes screw" was invented by a scientist in his youth and was intended for irrigation of fields. Today, screws are used in many industries. And in Egypt they still supply water to the fields.

15. Archimedes considered mathematics to be his best friend.

Monument to Archimedes

photo from the Internet

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How Archimedes died. Biography of Archimedes. Archimedes: interesting facts

Engineering

Mathematics and physics

Astronomy

Personal life

Death

Essays

Works and achievements

Gifts of Syracuse

Death of a scientist

Other biography options

Biography score

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