Archimedes of Syracuse. Archimedes and his discoveries

Archimedes was born in 287 BC in the family of a court astronomer, ruler of the city of Hiero. He studied in Alexandria, where there were the best Greek scientists and thinkers, as well as the largest library in the world. But still he returned to his hometown and lived there all his life.

Archimedes' discoveries

Not only his name, but also his discoveries are legendary. Archimedes' works are devoted to physics, mechanics, but mainly mathematics. With his discoveries, he simplified work and gave impetus to the development of science. The law of leverage laid the foundation for the study of spirals, a method for determining areas and volumes, centers of gravity of geometric figures and much more - these are all his discoveries.

• Mechanics

The famous ancient Greek scientist introduced into mechanics such a concept as the center of gravity - in any body there is one single fulcrum on which its weight can be concentrated. Archimedes said: “Give me a fulcrum and I will move the earth!”
Archimedes' discoveries include many mechanical structures, such as the lever. He, of course, was known before him, but it was Archimedes who outlined his complete theory and successfully applied it in practice, which made it easier to lift and transport heavy loads. And the screw invented by Archimedes for scooping up water is still used in Egypt. Also included in the list of his devices is a “snail” - an invention for watering crops, as well as devices capable of quickly throwing stones with a huge mass of about 250 kilograms.

• Astronomy

An ancient Greek scientist built a planetarium where you can observe the movement of the five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, and the disappearance of bodies beyond the horizon. Archimedes calculated the distance to the planets: according to his ideas, the world system was centered on the Earth, and the planets Mercury, Venus and Mars revolved around the Sun and Earth.

• Mathematics

Archimedes discovered the semiregular polyhedra that now bear his name. But the main discovery is considered to be a general method for calculating areas or volumes. He established that a sphere and cones with a common vertex inscribed in a cylinder are related like two cones: sphere: cylinder - 1:2:3. Archimedes proved that the area of ​​a segment of a parabola cut off from it by a straight line is 4/3 of the area of ​​the triangle inscribed in this segment. He easily found tangents to an ellipse, hyperbola and parabola and calculated extrema - his calculus methods formed the basis of differential calculus. In addition, it was Archimedes who calculated the number “pi” - the ratio of the circumference of a circle to its diameter.

He considered his best discovery to be the determination of the surface and volume of a ball, so at his grave he asked to knock out a ball inscribed in a cylinder. So, even thinking about death, he cannot forget about mathematics.

Archimedes is an outstanding ancient Greek mathematician, inventor and engineer who lived in the 3rd century BC. e. This man was born in 287 BC. e. in the city of Syracuse in Sicily. At that time it was a colony of Ancient Greece and was called Magna Graecia. It included the territory of modern Southern Italy and Sicily.

The date of birth is known from the words of the Byzantine historian John Tzetz. He lived in Constantinople in the 12th century. That is, almost one and a half thousand years after Archimedes. He also wrote that the famous ancient Greek mathematician lived 75 years. Such accurate information raises certain doubts, but let us show respect for the outstanding minds of antiquity and accept the indicated dates and figures as the truth.

Biography of Archimedes

So, an outstanding resident of Magna Graecia was born in 287 BC. e., and died in 212 BC. e. His father was an astronomer named Phidias, about whom nothing is known. Family ties with the tyrant of Syracuse, Hieron II, are also suggested. The most detailed biography of Archimedes was written by his friend Heraclides. But this work was lost, and therefore the details of the life of the mathematician and inventor remained unclear. 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.

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

It was within the walls of the Library of Alexandria that Archimedes became acquainted with the works of such famous geometers as Eudoxus and Democritus. He also gained much other useful knowledge and after a few years returned to his homeland in Syracuse. There he quickly established himself as an intelligent and gifted person, and lived for many years, enjoying the respect of those around him.

An outstanding personality died during the Second Punic War, when Roman troops captured Syracuse after a 2-year siege. The Roman commander was Marcus Claudius Marcellus. According to Plutarch, he ordered that Archimedes be found and brought to him. A Roman soldier came to the house of an outstanding mathematician while he was pondering mathematical formulas. The soldier demanded to immediately go with him and meet with Marcellus.

But the mathematician brushed off the obsessive Roman, saying that he must first complete the work. The soldier was indignant and stabbed the smartest resident of Syracuse with a sword. There is also a version that claims that Archimedes was killed right on the street while he was carrying mathematical instruments in his hands. The Roman soldiers decided that these were valuable objects and stabbed the mathematician to death. But be that as it may, the death of this man outraged Marcellus, since his order was violated.

Archimedes is killed by a Roman soldier

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

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

This outstanding person made a very great contribution to the development of mathematics. He was able to find a general method for calculating volumes and areas using infinitesimal quantities. That is, it was he who laid the foundation for integral calculus. He also proved that the ratio of circumference to diameter is a constant. He laid the foundation for differential calculus, that is, he did everything that mathematicians were able to continue only in the 17th century. From here we can safely say that this man was ahead of mathematical science by 2 thousand years.

In mechanics, he developed a lever and began to successfully apply it in practice. In the port of Syracuse, block-lever mechanisms were made that raised and lowered heavy loads. He also invented the Archimedes screw, which was used to bail out water. Created a theory about the balancing of equal bodies.

He proved that a body immersed in a liquid is subject to a buoyant force equal to the weight of the displaced liquid. This idea came to him in the bath. Its simplicity so shocked the outstanding mathematician and inventor that he jumped out of the bath and, dressed as Adam, ran through the streets of Syracuse shouting “Eureka,” which means “found.” Subsequently, this proof was called Archimedes' law.

Archimedes' claw lifts a Roman ship

During the long siege of Syracuse by the Romans, Archimedes was already an elderly man, but his mind did not lose its sharpness. As Plutarch wrote, under his leadership, throwing machines were built that threw heavy stones at Roman soldiers. Close range throwing machines were also made. They destroyed enemies near the walls by dropping barrels of boiling resin and stone cannonballs on them.

Roman galleys scurrying around the port of Syracuse were attacked by special cranes with grappling hooks (Archimedes' claw). With the help of these hooks, the besieged lifted ships into the air and threw them down from a great height. The ships, hitting the water, broke and sank. All these technological advances scared the invaders. They abandoned the assault on the city and moved on to a long siege.

There is a legend that Archimedes ordered the shields to be polished to a mirror shine, and then arranged them in such a way that, reflecting the color of the sun, they focused it into powerful rays. They were sent to Roman ships, and they burned. Already in our time, the Greek scientist Ioannis Sakkas created a cascade of 70 copper mirrors and, with its help, set fire to a plywood model of a ship, which was located at a distance of 75 meters from the mirrors. So this legend could well have a practical basis.

A focused sunbeam sets a ship on fire

And, of course, the outstanding inventor could not ignore astronomy, because at that distant time it was extremely popular. He tried to determine the distance from the Earth to the planets, but was guided by the fact that the center of the world is the Earth, and the Sun and Moon revolve around it. At the same time, he assumed that Mars, Mercury and Venus revolve around the Sun.

Legacy of Archimedes

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

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

In 1906, Danish professor Johan Ludwig Heiberg discovered a 174-page prayer collection written in the 13th century in Constantinople. The scientist found out that it was a palimpsest, that is, text written over old text. At that time, this was common practice, since the tanned goatskin from which the pages were made was very expensive. The old text was scraped off and new text was written on top of it.

It turned out that the scraped work was a copy of an unknown treatise by Archimedes. The copy was written in the 10th century. Using ultraviolet and x-ray light, this hitherto unknown work was read. These were works on equilibrium, on measuring the circumference of a sphere and a cylinder, and on floating bodies. Currently, this document is kept in the Baltimore City Museum (Maryland, USA).

Archimedes (287-212 BC), ancient Greek philosopher and scientist.

Native and citizen of Syracuse (island of Sicily). He received his education in Alexandria, the greatest cultural center of the ancient world.

Archimedes made a number of important mathematical discoveries (in the field of the relationship between the length and diameter of a circle, geometric progression, etc.). The highest achievements of a scientist in the field of physics are the scientific substantiation of the action of a lever and the discovery of the law according to which any body immersed in a liquid is subject to a buoyant force directed upward and equal to the weight of the liquid displaced by it (Archimedes' law).

During the 2nd Punic War (218-201 BC), Syracuse, which had sided with Carthage, was subjected to a Roman siege. Archimedes became famous for his active participation in the defense of the city. He created many combat vehicles that delayed the capture of Syracuse for a long time. The possibility of the existence of some of these mechanisms is still in doubt among a number of scientists (despite direct evidence from ancient authors). So, Archimedes seemed to be able to focus sunlight using a giant mirror and direct the resulting beam at enemy ships.

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

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

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

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

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

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

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

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

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

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

And finally, Archimedes was not only a great scientist, he was also a man passionate about mechanics. He tests and creates a theory of five mechanisms known in his time and called “simple mechanisms”. These are a lever (“Give me a fulcrum,” said Archimedes, “and I will move the Earth”), a wedge, a block, an endless screw and a winch. Archimedes is often credited with inventing the endless screw, but it is possible that he only improved the hydraulic screw that served the Egyptians in draining swamps. Subsequently, these mechanisms were widely used in different countries 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 commonplace - the invention of the bolt, constructed from a screw and a nut.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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