The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, and created inventions that served as the starting point for further development 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 scientific figures 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 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 good and skillful ruler of Syracuse, Hiero II.
Archimedes probably spent his childhood in Syracuse, and at a young age he went to Alexandria in Egypt to receive an education. For several centuries this city was cultural and scientific center 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 devices made it easier to lift and move heavy loads, speeding up and optimizing port operations. And the “Archimedes screw”, designed for scooping up water, is still used in Egypt.
Archimedes' inventions: Archimedes' screw Great value have theoretical research as a scientist in the field of mechanics. Based on the proof of the law of leverage, he began to write the work “On Equilibrium” flat figures" The proof is based on the axiom that on equal shoulders equal bodies will be balanced if necessary. Archimedes followed the same principle of constructing a book - starting with the proof of his own law - when writing the work “On the Floating of Bodies”. This book begins with a description of Archimedes' well-known law.
Mathematics and Physics
Discoveries in the field of mathematics were the scientist's real passion. According to Plutarch, Archimedes forgot about food and self-care when he was on the verge of another invention in this area. The main direction of his mathematical research was the problems mathematical analysis.
Even before Archimedes, formulas were invented to calculate the areas of circles and polygons, the volumes of pyramids, cones and prisms. But the scientist’s experience allowed him to develop general techniques to calculate volumes and areas. To this end, he improved the method of exhaustion, invented by Eudoxus of Cnidus, and brought the ability to apply it to a virtuoso level. Archimedes did not become the creator of the theory of integral calculus, but his work subsequently became the basis for this theory.
The mathematician also laid the foundations of differential calculus. WITH geometric point From a physical point of view, he studied the possibility of determining the tangent to a curved line, and from a physical point of view, the speed of a body at any moment in time. The scientist examined a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to a hyperbola, parabola and ellipse. Only in the seventeenth century were scientists able to to the fullest to realize and reveal all the ideas of Archimedes that reached those times in his surviving works. The scientist often refused to describe his inventions in books, which is why not every formula he wrote has survived to this day.
Archimedes' inventions: "solar" mirrors The scientist considered the invention of formulas for calculating the surface area and volume of a ball to be a worthy discovery. If in the previous cases described, Archimedes refined and improved other people’s theories, or created quick methods calculation as an alternative to already existing formulas, then in the case of determining the volume and surface of a ball, he was the first. Before him, no scientist had coped with this task. Therefore, the mathematician asked to knock out a ball inscribed in a cylinder on his gravestone.
The scientist's discovery in the field of physics was a statement that is known as Archimedes' law. He determined that any body immersed in a liquid is subject to pressure by a buoyant force. 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. One day, the scientist was allegedly approached by Hiero II, who doubted that the weight of the crown made for him corresponded to the weight of the gold that was provided for its creation. Archimedes made two ingots of the same weight as the crown: silver and gold. Next, he placed these ingots in turn in a vessel with water and noted how much its level increased. The scientist then placed the crown in the vessel and discovered that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus it was discovered that the master had kept part of the gold for himself.
There is a myth that a bath helped Archimedes make a key discovery in physics. While swimming, the scientist allegedly lifted his leg slightly in the water, discovered that it weighed less in the water, and experienced an epiphany. A similar situation took place, but with its help the scientist discovered not Archimedes’ law, but the law of the specific gravity of metals.
Astronomy
Archimedes became the inventor of the first planetarium. When moving this device observe:
- moon and sun rising;
- the movement of the five planets;
- disappearance of the Moon and 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 to be the center of the world. He believed that Venus, Mars and Mercury revolved around the Sun, and this entire system revolved around the Earth.
Personal life
ABOUT personal life much less is known about the scientist than about his science. His contemporaries also composed numerous legends about the gifted mathematician, physicist and engineer. Legend says that one day Hiero II decided to present Ptolemy, the king of Egypt, with a multi-deck ship as a gift. It was decided to name the watercraft "Syracuse", but it could not be launched.
In this situation, the ruler again turned to Archimedes. From several blocks he built a system with the help of which the launch of a heavy vessel was possible with one movement of the hand. According to legend, during this movement Archimedes said:
“Give me a foothold and I will change the world.”
Death
In 212 BC, during the Second Punic War, Syracuse was besieged by the Romans. Archimedes actively used engineering knowledge to help his people achieve victory. Thus, he designed throwing machines, with the help of which the warriors of Syracuse threw heavy stones at their opponents. When the Romans rushed to the walls of the city, hoping that they would not come under fire, another invention of Archimedes - light throwing devices with close action - helped the Greeks pelt them with cannonballs.
Archimedes' inventions: catapult The scientist helped his compatriots in naval battles. The cranes he developed grabbed enemy ships with iron hooks, lifted them slightly, and then abruptly threw them back. Because of this, ships turned over and crashed. For a long time these cranes were considered something of a legend, but in 2005 a group of researchers proved the functionality of such devices by reconstructing them from surviving descriptions.
Archimedes' inventions: lifting machine Thanks to the efforts of Archimedes, the Romans' hope of storming the city failed. Then they decided to go on a 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 the place where Archimedes died was his laboratory. The scientist was allegedly so carried away by his research that he refused to immediately follow the Roman soldier who was ordered to take Archimedes to the military leader. He, in anger, pierced the old man with his sword.
There are still variations of this story, but they agree that the ancient Roman politician and the military leader Marcellus was extremely upset by the death of the scientist and, uniting with both the citizens of Syracuse and his own subjects, gave Archimedes a magnificent funeral. Cicero, who discovered the scientist’s destroyed grave 137 years after his death, saw on it a ball inscribed in a cylinder.
Essays
- Quadrature of a parabola
- About the ball and cylinder
- About spirals
- About conoids and spheroids
- On the equilibrium of plane figures
- Epistle to Eratosthenes on Method
- About floating bodies
- Circle measurement
- Psammit
- Stomachion
- Archimedes' Bull Problem
- Treatise on the construction of a corporeal figure with fourteen bases around a ball
- Book of Lemmas
- A book about constructing a circle divided into seven equal parts
- Book about touching circles
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 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, a young man striving for knowledge established friendships 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 smart and a gifted person, and lived for many years, enjoying the respect of others.
Died outstanding personality 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 man made a very great contribution to the development of mathematics. He managed to find general method when 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 acted upon by 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 high altitude. 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, 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 languages. 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 is known to have lived in Syracuse. This is Sicily.
At the same time that Hannibal was at war with Rome, the Greek Syracuse found itself in the unpleasant position of having to choose: they had to join one of the warring parties. There was no chance of maintaining neutrality. In the city itself there were different opinions about who to join. Better, of course, to the winner. But the situation was changing.
Syracuse, sending a detachment of 8 thousand soldiers, took part in the resistance to the Romans Leontin. The city fell. Horrors were told about its fall: the Romans killed everyone - warriors, civilians, everything was plundered. Titus Livius, the Roman historian, does not deny that 2,000 defectors were flogged and executed on the orders of the Roman commander Marcellus.
Syracuse decided that the Romans would do even worse to their richer city.
Roman troops began their assault on Syracuse simultaneously from land and sea. And then they encountered Archimedes.
Archimedes was born in 287 BC. in the family of the mathematician and astronomer Phidias and was a relative of the Syracusan king Hiero II. He continued his education in Alexandria. He made interesting astronomical observations, determined the diameter of the Sun and the distances between the planets, invented a “celestial globe” that made it possible to study the movements of the planets, the phases of the Moon, solar and lunar eclipses. He worked a lot in the field of mechanics, on the invention of various kinds of tools, on solving mathematical and physical problems.
It is obvious that he saw his civic duty in protecting the fatherland from invaders.
Map of Syracuse.
Siege of Syracuse.
Marcellus stormed the wall of Achradina from the sea with 60 quinqueremes; From some ships, slingers, archers, and spearmen fired at the wall; he ordered other ships to be connected in twos and, having installed siege weapons on them, to be brought close to the fortifications.
Roman quinquereme.
Archimedes hit distant ships with catapults, and to defeat nearby ones he organized loopholes in the walls. When Roman ships entered the dead zone right under the walls, an “iron paw” fell on them: grabbing the bow of the ship with its paw, they placed the ship on the stern or even lifted it above the sea, and then abandoned it, the ship lost its crew, crashed, and sank.
Loopholes in the walls.
Option "iron paw".
Another.
The assault from the sea was unsuccessful.
The same goes for sushi. Archimedes' weapons threw stones, arrows, spears, and blocks at the heads of the Romans.
Marcellus abandoned attempts to take the city by storm and proceeded to blockade.
Polybius complements and clarifies Livy's story. The same with Plutarch. According to him, Marcellus cried out: “Shouldn’t we stop fighting this geometer-Briareus, who, sitting calmly by the sea, destroys our ships and, at the same time showering us with so many arrows, surpasses the hundred-armed giants?” In the end, Archimedes inspired such terror in the Roman soldiers that they fled in panic when they saw a piece of rope or a log above the city wall.
There was no talk of taking the city by storm. The blockade also turned out to be ineffective: food was regularly imported to Syracuse from Carthage. Marcellus placed his hopes only on the “fifth clone” - the pro-Roman Syracusans.
As was established, in one place the city wall was relatively low. But it was here that she was especially vigilantly guarded. In the besieged city, the usual three-day celebration in honor of Artemis was going on, wine was generously distributed to the people.
Late at night, a Roman detachment of a thousand soldiers entered the city. Panic began. However, Ahradina and the island of Ortigia were not going to give up.
While negotiations were taking place in the Roman camp, clashes began in Syracuse itself. In this situation, Marcellus began the assault on Achradina and landed troops on Ortygia. Now the capture has been successful. He gave Akhradin to be plundered. Titus Livius: “Many disgusting examples of malice have been revealed, many of greed.” During this orgy of violence and robbery, Archimedes died, busy drawing on the sand. Livy says that the Roman soldier did not know who he was facing, and Marcellus was allegedly upset by this death: he was concerned about the burial of the great scientist, and protected his relatives from violence.
Ortygia. Modern look.
Plutarch gives three stories about the death of Archimedes.
According to the first, Archimedes was busy drawing and did not pay attention to the Roman soldiers. When one of them demanded him to Marcellus, Archimedes said that he had not yet solved the problem, and the angry warrior stabbed him to death. The second one is similar to the first one. And the third tells that Archimedes was going to Marcellus with his instruments, when the soldiers, mistaking them for treasures, killed him for the purpose of robbery.
Zonarra tells the following: "The Romans killed many others and Archimedes." Marcellus did not order him to spare the scientist, did not grieve over his death, and, moreover, did not punish anyone.
Marcellus, who unleashed robberies and murders in captured Syracuse, may have considered it necessary to express sadness about the death of Archimedes: it was not profitable for the Romans, who needed the support of the Greeks, to appear in the role of murderers and rapists exterminating best representatives Hellenic thought. The comparison with Hannibal, who had Greek writers on his staff, was extremely unpleasant.
Cicero says that Marcellus dedicated one of Archimedes’ “spheres”, celestial globes, to the Temple of Courage, and took the other for himself: this relic was passed down in his family from generation to generation. A sad relic - the creation of a brilliant man you killed.
Marcellus.
However, in Syracuse captured by Rome, mentioning the name of Archimedes - the uncompromising enemy of Rome - was apparently unsafe. His grave was abandoned and forgotten. Only Cicero already in the 1st century. It was with great difficulty that I was able to find her.
Archimedes Square in Syracuse.
It's her. Fountain of Artemis, in whose honor the festival was held.
A statue of Archimedes with a bronze hyberbolic mirror, with a system of which he allegedly burned the Roman fleet. But that's another story.
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, brought to their geometric shape, retain their heaviness 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 fluid displaced by it acts on a body immersed in a liquid.
Once, having raised his leg in the water, Archimedes noted with surprise that his leg became lighter in the water. "Eureka! Found it,” he exclaimed, leaving his bath. The anecdote is amusing, but conveyed this way, it is not accurate. The famous "Eureka!" was pronounced not in connection with the discovery of Archimedes' law, as is often said, but in connection with the law of the specific gravity of metals - a discovery that also belongs to the Syracusan scientist and the detailed details of which are found in Vitruvius.
They say that one day Hiero, the ruler of Syracuse, approached Archimedes. He ordered to check whether the weight of the golden crown corresponded to the weight of the gold allocated for it. To do this, Archimedes made two ingots: one of gold, the other of silver, each of the same weight as the crown. Then he put them one by one in a vessel with water and noted how much its level had risen. Having lowered the crown into the vessel, Archimedes established that its volume exceeded the volume of the ingot. Thus the master’s dishonesty was proven.
A curious comment is from the great orator of antiquity, who saw the “Archimedean sphere” - a model showing the movement of heavenly bodies around the Earth: “This Sicilian had a genius that, it would seem, human nature cannot achieve.”
And finally, Archimedes was not only a great scientist, he was also a man passionate about mechanics. He tests and creates a theory of five mechanisms known in his time and called " simple mechanisms" These are a lever (“Give me a fulcrum,” said Archimedes, “and I will move the Earth”), a wedge, a block, an endless screw and a winch. Archimedes is often credited with inventing the endless screw, but it is possible that he only improved the hydraulic screw that served the Egyptians in draining swamps. Subsequently, these mechanisms were widely used in different countries Mira. Interestingly, an improved version of the water-lifting machine could be found at the beginning of the 20th century in a monastery located on Valaam, one of the northern Russian islands. Today, the Archimedes screw is used, for example, in an ordinary meat grinder.
The invention of the endless screw led him to another important invention, even if it became commonplace - the invention of the bolt, constructed from a screw and a nut.
To those of his fellow citizens who would have considered such inventions insignificant, Archimedes presented decisive proof to the contrary on the day when, by ingeniously adjusting a lever, a screw and a winch, he found a means, to the surprise of onlookers, of launching a heavy galley that had run aground, with all its crew and cargo.
He gave even more convincing evidence in 212 BC. During the defense of Syracuse against the Romans during the Second Punic War, Archimedes designed several war machines that allowed the citizens to repel the attacks of the superior Romans for almost three years. One of them was a system of mirrors, with the help of which the Egyptians were able to burn the Roman fleet. This feat of his, which was described by Plutarch, Polybius and Titus Livius, of course, aroused greater sympathy among ordinary people than calculating the number "pi" - another feat of Archimedes, very useful in our time for students of mathematics.
Archimedes died during the siege of Syracuse - he was killed by a Roman soldier at a time when the scientist was absorbed in searching for a solution to the problem he had set himself.
It is curious that, having conquered Syracuse, the Romans never became the owners of the works of Archimedes. Only many centuries later they were discovered by European scientists. That is why Plutarch, who was one of the first to describe the life of Archimedes, mentioned with regret that the scientist did not leave a single work.
Plutarch writes that Archimedes died at a very old age. A slab with the image of a ball and cylinder was installed on his grave. It was seen by Cicero, who visited Sicily 137 years after the scientist’s death. Only in the 16th-17th centuries were European mathematicians finally able to realize the significance of what Archimedes had done two thousand years before them.
Archimedes left numerous students. On new way, discovered by him, a whole generation of followers, enthusiasts, who were eager, like the teacher, rushed to prove their knowledge with concrete conquests.
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 the 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 through a system of concave mirrors sun rays, but this is false 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 Sphere and the Cylinder” (in two books) Archimedes establishes that the surface area of the sphere is 4 times more area its largest cross section; formulates the ratio of the volumes of the ball and the cylinder described near it as 2:3 - a discovery that he valued so much that in his will he asked to erect a monument on his grave with the image of a cylinder with a ball inscribed in it and the inscription of calculation (the monument was seen by Cicero a century and a half later). The same treatise formulated the axiom of Archimedes (sometimes called the axiom of Eudoxus), which plays an important role in modern mathematics.
In his treatise On Conoids and Spheroids, Archimedes examines the sphere, ellipsoid, paraboloid and hyperboloid of revolution and their segments and determines their volumes. In the essay “On Spirals” he explores the properties of the curve that received his name (the Archimedean spiral) and the tangent to it. In his treatise “Measuring the Circle,” Archimedes proposes a method for determining the number π, which was used until the end of the 17th century, and indicates two surprisingly precise limits for the number π:
3·10/71In physics, Archimedes introduced the concept of the center of gravity, established scientific principles statics and hydrostatics, gave examples of the application 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 one could observe the movement of the planets, the Sun and the Moon (described by Cicero; after the death of Archimedes, the planetarium was taken by Marcellus to Rome, where it was admired for several centuries); a hydraulic organ mentioned by Tertullian as one of the wonders of technology (some attribute the invention of the organ to the Alexandrian engineer Ctesibius).
It is believed that in his youth, during his stay in Alexandria, Archimedes invented a water-lifting mechanism (Archimedes screw), which was used to drain the lands flooded by the Nile. He also built an instrument to determine the apparent (angular) diameter of the Sun (Archimedes talks about it in his treatise “Psammit”) and determined the value of this angle.
The ancient Greek scientist Archimedes was an inventor, mathematician, designer, engineer, physicist, astronomer and mechanic. He founded the field of mathematical physics. The researcher also developed methods for finding volumes, surfaces and areas different bodies and figures, anticipating integral calculus. He is the author of many inventions. The name of the scientist is associated with the appearance of the laws of leverage, the introduction of the term “center of gravity” and research in the field of hydrostatics. When the Romans attacked Syracuse, it was Archimedes who organized the engineering defense of the city.
In times of high technology and scientific discoveries, we are accustomed to perceive achievements as something ordinary, forgetting that the foundations of existing knowledge were laid by ancient scientists. They were the pioneers. And Archimedes of Syracuse was generally a genius. After all, he confirmed most of his own ideas in practice. Our contemporaries successfully use them in their work, although they do not even know who their author was. The biography of Archimedes has survived to this day only from legends and memories. We invite you to familiarize yourself with it.
Childhood and studies
Archimedes, short biography who will be presented below, was born in the city of Syracuse around 287 BC. e. His childhood occurred during the period when King Pyrrhus waged wars with the Carthaginians and Romans, trying to create a new Greek state. Hiero, a relative of Archimedes, who later became the ruler of Syracuse, especially distinguished himself in this war. Phidias (the boy's father) was a close associate of Hiero. This allowed him to give Archimedes good education. But the young man lacked theoretical knowledge, and he went to Alexandria, which was a scientific center at that time. Here the Ptolemies, the rulers of Egypt, gathered the best Greek scientists and thinkers of that time. Also in Alexandria there was the largest library in the world, where Archimedes studied mathematics and the works of Eudoxus, Democritus, etc. for a long time. In those years, the future researcher became friends with the astronomer Konon, geographer and mathematician Eratosthenes. Then he carried on frequent correspondence with them.
First profession
After his studies, Archimedes, whose brief biography is known to all scientists, returned to Syracuse and inherited the position of Phidias - court astronomer. Thanks to Hieron, a time of peace came to the city. To withdraw from participation in the First, he paid Rome a huge indemnity. In his General History, Polybius described him as follows: “Hieron came to power without fame, wealth, or any gifts of fate. He did not offend anyone, did not expel, did not kill, and ruled for 54 years...” Nevertheless, Hiero, like his successors, paid great attention to strengthening the city, preparing for possible military battles.
Scientific works
The position of astronomer was not onerous, and Archimedes was free to engage in other activities. In theoretical terms, his research was multifaceted. Archimedes's first works were devoted to mechanics. He also relied on it in some mathematical works. For example, a researcher applied the lever principle to solve several geometric problems. He outlined the mathematical conclusions he had made in his work “On the Equilibrium of Plane Figures.” This work of the scientist became the cornerstone of the “Parabola of Quadrature” (integral calculus), which will be discovered 2000 years later. And in the essay “On the Measurement of a Circle,” the researcher calculated the ratio to its length, or, in other words, (3.14). In addition, everyone still uses the system of naming integers he invented.
Scientific achievements
The biography of Archimedes describes two of his most significant scientific achievements: the doctrine of the center of gravity and the formulation of the principle of leverage. He also laid the foundations of hydrostatics. Only at the end of the 16th and beginning of the 17th century were these ideas developed by Pascal, Galileo, Stevin and other scientists who used what he described in his work “On Floating Bodies.” This essay was the first attempt to test in practice the fundamental assumption about the structure of matter by creating its model. Archimedes not only proved several main points about the physical characteristics of the atoms of a liquid, but also confirmed a number of atomistic ideas of Democritus. In this work, the scientific genius of the researcher manifested itself with particular force. The results he obtained could only be proven in the 19th century.
Other studies
As the biography of Archimedes says, in addition to mechanics, physics and mathematics, he was engaged in meteorological and geometric optics. The scientist also conducted a number of experiments on There is numerous information that Archimedes wrote a large work - “Catoptrics”, but, unfortunately, it has not reached us. Based on the quotations preserved from it, it can be assumed that the researcher knew about the incendiary effect of concave lenses, conducted experiments on the refraction of light in water and air, and also had an idea of the properties of images in concave, convex and In addition to quotations, only one theorem survived, proving that when a ray of light is reflected from a mirror, the angle of incidence equal to angle reflections.
Defense of Syracuse
Archimedes' discoveries in the field of engineering brought him the greatest fame, which crossed the boundaries of not only countries, but also centuries. His engineering genius manifested itself especially clearly in 214 BC. e. during the siege of his native Syracuse. Archimedes was already in his seventh decade. This was one of the greatest triumphs in the life of a scientist. Here he proved himself not only as an inventor, but also as an outstanding builder. Everyone knows that ancient buildings consisted of solid walls. Archimedes installed loopholes and embrasures in them, intended for middle and lower combat. Created by him in peacetime combat vehicles allowed to defend Syracuse from the attack of the Romans for three years.
Recent years
As you can see, scientific life Archimedes was bright and rich. IN recent years He was engaged in computational and astronomical activities. Titus Livius (Roman writer) called him “a unique observer of the stars and sky.” And although not a single astronomical work of Archimedes has reached us, there is no doubt about the authenticity of this characteristic. This type of activity is evidenced by the story about the astronomical sphere he created, and the essay “Psammit”, where the scientist tries to count the number of grains of sand in the Universe.
There is a moment in the researcher’s essay that can be classified as “Archimedes’ discovery.” The scientist was the first in the history of science to compare two systems of the world - heliocentric and geocentric. Archimedes wrote: “Most astronomers believe that the world is a sphere contained between the centers of the Earth and the Sun.” Thus, he was aware of the size of the world and understood that it was finite. This allowed the researcher to complete his calculations.
Conclusion
This ends the biography of Archimedes. He appeared before us as an engineer, researcher, theorist and popularizer of science. The combination of practical thinking with mathematical talent and organizational skills was rare at that time. Archimedes entered the history of science as shining example a researcher who managed to harmoniously combine theory with practice. Undoubtedly, he is an exemplary scientist from whom other generations of researchers should take an example. The mathematical physics proposed by Archimedes was not taken seriously either by his descendants or by the scientists of the Middle Ages. If we talk about researchers who were ahead of their time, then Archimedes was a record holder among them. Only in the 16th and 17th centuries were European mathematicians able to realize the importance and significance of his scientific contribution. Since then, the ancient Greek scientist had many enthusiastic followers who were eager to prove their own theories with concrete achievements. And now, in memory of this genius, the scientists who made the discovery repeat the same exclamation as Archimedes: “Eureka! I found it."
