What Archimedes invented. The tale of the scientist Archimedes, who cost an entire army

Date of birth: 287 BC NS.
Died: 212 BC NS.
Place of birth: Syracuse city, Greece

Archimedes- a famous ancient Greek scientist. Archimedes famous for his works in physics, mathematics and mechanics. The scientist is the author of numerous discoveries in geometry, the founder of hydrostatics and mechanics. Archimedes is also known as an inventor.

The ancient Greek scientist was born in Syracuse. The father of the future inventor Phidias was a mathematician and astronomer. His father's hobby was passed on to Archimedes and over time, this hobby for the exact sciences, became the work of the entire life of the ancient scientist.

Alexandria became for Archimedes the city where he could get an education. In ancient times, this city was considered a cultural and scientific center. In Alexandria, Archimedes was able to meet such famous scientists as Eratsfen and Konon.

At that time, about 700 thousand manuscripts were collected in the Alexandria Library. Archimedes spent a lot of time in the library and got acquainted with the works of geometers. The knowledge acquired in Alexandria greatly helped the scientist in his future work.

After graduation, Archimedes returned to his hometown. He was greeted there with open arms, the scientist could not think about how to make a living, was engaged in discoveries and wrote scientific works.

The sources of his activities during this period have practically not been preserved in history. Legends about Archimedes were already composed during his lifetime, and after many centuries, confusion with facts from his life only intensified.

The so-called Archimedes screw or auger made it possible for the inhabitants of the city to extract more water from reservoirs. Thanks to this, the irrigation canals began to receive uninterrupted water, and the inhabitants of Syracuse did not have to worry about their harvest.

The main merit of Archimedes is his participation in the second Punic War, which was fought in 212 BC. He was then 75 years old, he was an active participant in the defense of the city and put his inventions into practice.

Archimedes created powerful stone throwing machines that stopped the Romans on the outskirts of the city. Cranes invented by Archimedes overturned enemy ships.

The Romans could not take the city, since the inventions of Archimedes stood on the defense. Then the legionnaires went over to a long siege. There is a legend that the Syracusans were able to burn several enemy ships with the help of large mirrors.

This legend has no confirmation, and most likely the inhabitants of Syracuse burned ships with the help of throwing machines.

The Romans still managed to capture the city, despite the efforts of Archimedes, as a result of betrayal. The scientist himself was killed during the assault. There is also no reliable information about this, since there are several versions of the story of his death left in history.

Byzantine Ioann Tsets wrote that during the assault Archimedes was busy drawing on the sand. The legionary stepped on this blueprint, and the scientist lunged at the soldier with a cry. At that moment he was killed.

According to Plutarch's version, the Roman commander Marcellus sent his soldier after Archimedes. But Archimedes did not follow the legionnaire, and he stabbed him in anger.

According to Diodorus Siculus, the legionnaire tried to drag Archimedes to the commander, the scientist began to resist and threatened to start his machines. Since the Romans were afraid of these inventions, the soldier did not wait and killed the inventor.

The commander Marcellus gave an honorable burial for Archimedes, and the soldier who stabbed Archimedes was beheaded.

There is another version, according to which Archimedes met with Marcellus in order to show his inventions. The legionnaires embraced the glitter of glass and metal parts machines for the glitter of gold and killed Archimedes in the hope of getting the loot.

The dilapidated tomb of Archimedes was found by Cicero in 75 BC.

Archimedes' achievements:

Archimedes laid the foundations of the exact sciences
Solved problems related to mathematical analysis
Applied new method solutions of cubic equations.
Calculated all semiregular polyhedra
I learned to determine the density of bodies by immersing them in a liquid.
Improved leverage system
Designed the Archimedes screw
He wrote the essay "Psammit", where he opened the topic of the heliocentric system of the universe.

Dates from the biography of Archimedes:

287 BC NS. - born in Syracuse
212 BC NS. - died during the siege of Syracuse at the hands of a Roman legionary

Interesting Archimedes Facts:

The Roman general Marcellus, during the siege of Syracuse, wanted to end the war against Archimedes
While taking a bath, Archimedes saw that his body was heavier than water and the brilliant idea of ​​determining the density of bodies came to him
Created a throwing machine
Archimedes would be a respected person in his homeland, and the Romans, who had never encountered such weapons before, were afraid of his military vehicles.
After Archimedes, there were no students left, since he did not want to create his own school and raise new scientists
Archimedes' screw was invented by him in his youth and was used to fill irrigation canals. Today, these screws are used in different areas
Archimedes is considered one of the world's best inventors and mathematicians.
Contemporaries considered the scientist crazy. He demonstrated his skills in front of the ruler of Syracuse, pulling triremes ashore using a block system
According to some legends, during the storming of Syracuse, a detachment of legionnaires was sent for Archimedes. His death was an absurd accident.
Archimedes' calculations many thousands of years later were repeated by Newton and Leibniz
Created a planetarium
Heraclides wrote a biography of Archimedes, but it is lost, and today there are no reliable facts about the life of the great scientist
The math was best friend Archimedes
Some scholars call Archimedes the inventor of the cannon. Plutarch, illuminating the storming of Syracuse, wrote that during the storming of the city, the legionnaires were fired at from a device with a long pipe, from which the balls flew
The legend of the mirrors, with the help of which the inhabitants of the besieged city destroyed Roman ships, has been refuted many times. But historians say that mirrors were used to aim rock-throwing machines that fired at the Roman fleet.

A native and citizen of Syracuse. Educated in Alexandria, the greatest cultural center of the ancient world.

Archimedes made a number of important mathematical discoveries. The highest achievements of the scientist in the field of physics are the scientific substantiation of the action of the lever and the discovery of the law, according to which a buoyant force acts on every body immersed in a liquid, directed upwards and equal to the weight of the liquid displaced by it.

During the 2nd Punic War, Syracuse, who had gone over to the side of Carthage, was subjected to a Roman siege. Archimedes became famous for his active participation in the defense of the city. He created many war machines that delayed the capture of Syracuse for a long time. The possibility of the existence of some of these mechanisms is still questioned by a number of scientists. So, Archimedes seems to have managed to focus sunlight using a giant mirror and direct the resulting beam at enemy ships.

During the capture of Syracuse, the scientist was killed by Roman soldiers.

Archimedes is an ancient Greek scientist, physicist, mathematician and engineer from Syracuse who lived in 287-212 BC. In addition to the many discoveries made in the field of mathematics, especially in geometry, he also became the founder of mechanics, hydrostatics, and the author of a number of other significant inventions. He owns many significant discoveries in the field of mathematics and physics. For example, the ratio of the length and diameter of a circle, the scientific substantiation of the action of the lever, and others.

Some of the treatises of Archimedes reached the present day, which speak of the genius of the scientist. Among them are "On a ball and a cylinder", "On floating bodies", "On spirals", "On the balance of plane figures" and others. Many discoveries were made in the field of astronomy. So, for example, Archimedes built the first planetarium, with the help of which it was possible to observe the movement of several planets, the rising of the Sun and the Moon, the phases of the eclipse of the Moon, etc. In one of his writings, he mentions the heliocentric system of the world. In memory of Archimedes, a crater and an asteroid are named after him.

Greek mechanic, physicist, mathematician, engineer. Born and spent most of his life in Syracuse. Studied in Alexandria. He was an advisor to the king of Sicily, Hieron II. According to legend, with the help of a system of mirrors reflecting the sun's rays, he burned the Roman fleet that laid siege to Alexandria. Considered the inventor of the catapult. He established the rule of the lever, in connection with which the saying is attributed to him: "Give me a fulcrum and I will move the Earth."

Archimedes brilliantly combined the talents of an engineer-inventor and a theoretical scientist. In addition to military vehicles, he designed a planetarium and a propeller for lifting water, which is still in use. He wrote treatises: “On spirals”, “On a ball and a cylinder”, “On conoids and spheroids”, “On levers”, “On floating bodies”, etc. He calculated the volume of a sphere and the value of the number pi. I counted the number of grains of sand in the volume of the globe.

Once King Hieron II asked Archimedes to determine if jewelers had mixed silver with gold when they made his crown. To do this, it was necessary to find out not only the weight, but also the volume of the product. Archimedes solved a difficult problem gracefully: he lowered the crown into the water and determined the volume of the displaced liquid. They say the thought came to him when he was taking a bath. Joyful, he jumped out into the street in what he was shouting: "Eureka!" ...

Many legends are associated with the name of Archimedes, the authenticity of which can hardly be confirmed. Of course, he could not use mirrors to burn enemy ships. But the story with the royal crown is quite plausible.

It is said that Hieron invited him to raise most of it with little force. The scientist invented a mechanism with the help of which he pulled a heavily loaded trire to the shore. One of the historians of science has suggested that Archimedes used his screw in conjunction with a gear system. True, most likely this story was invented in order to brighten up the engineering genius of Archimedes. Greek sailors, apparently, knew how to pull ashore even large ships with the help of levers and blocks, but was Archimedes alone able to cope with such a task? Hardly.

Rumors about the planetarium he created are considered more reliable. In the center was the Earth, the Sun, the Moon and several planets revolving around it, set in motion by some kind of mechanism. Cicero mentioned this building with enthusiasm, without leaving detailed description... It is assumed that similar ones were created on the basis of the Archimedean planetarium in the Middle Ages.

Outstanding discoveries of Archimedes

The ancient Greek scientist Archimedes was an inventor, mathematician, designer, engineer, physicist, astronomer and mechanic. He founded such a direction as mathematical physics. The researcher also developed ways of finding volumes, surfaces and areas of various bodies and figures, anticipating integral calculus. He is the author of many inventions. The name of the scientist is associated with the emergence of the laws of the lever, 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 used to perceiving achievements as something commonplace, forgetting that the foundations of existing knowledge were laid by ancient scientists. They were the pioneers. And Archimedes of Syracuse was so 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 study

Archimedes, short biography who will be presented below, was born in the city of Syracuse in about 287 BC. NS. His childhood fell on the period when King Pyrrhus waged wars with the Carthaginians and the Romans, trying to create a Greek state of a new type. Particularly distinguished in this war was Hieron, a relative of Archimedes, who later became the ruler of Syracuse. Phidias was an associate of Hieron. This allowed him to give Archimedes a good education... But the young man lacked theoretical knowledge, and he went to Alexandria, which was at that time a scientific center. The best Greek scientists and thinkers of that time were gathered here by the Ptolemies, the rulers of Egypt. Also in Alexandria was the world's largest library, where Archimedes studied mathematics and the works of Eudoxus, Democritus, etc. for a long time. In those years, the future explorer made friends with the astronomer Konon, the geographer and mathematician Eratosthenes. Then he kept up a frequent correspondence with them.

Sources: allbiograf.ru, citaty.su, www.sdamna5.ru, biopeoples.ru, fb.ru

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In general, we have outlined the life of an inventor, his scientific and inventive achievements. In this article we will try to list the inventions of Archimedes with a more detailed explanation.

We present a list of inventions of Archimedes for quick navigation:

Improving leverage

“Be at my disposal another land on which
I could get up, I would move ours. "
(c) Archimedes

Archimedes, of course, was not the one who invented the lever, since it is a fairly simple device, but he was the one who theoretically described the principles of its operation and, understanding these principles, was able to develop and improve it. He also explained the principle of multistage transmission.

In his work "On the equilibrium of planes or centers of gravity of planes" Archimedes writes the following:

Bodies of the same weight, which are equidistant from the center, will be in equilibrium, but if the distance of one of them is changed, then the balance will be disturbed in favor of the body that is at a more distant distance from the center.
If you take two bodies of the same weight, which are equidistant from the center, and add additional weight to one of them, then the balance is disturbed in favor of more weight.

Leverage principle and mathematical relationship

Worm-gear

Many historians believe that Archimedes also managed to invent the worm gear. Considering that Archimedes invented the water-raising propeller, there is no doubt that he could have guessed before this invention. Later he described a screw with a special half-notch, which slid along the screw along its thread. But for the era of Heron, this mechanism seems outdated, since in his time screws and nuts already existed. It is possible that Heron described exactly the invention of Archimedes, having read some of his works that have not reached us.

Connecting pulley

A pulley is a wheel along which a rope or chain can be installed. A person pulling from one end of the rope can lift the weight at the other end of the rope. The pulley wheel acts as a fulcrum, reducing the force required to lift a load. Archimedes invented a whole pulley system to lift and move loads

The pulley system can be further complicated to obtain greater strength gains.

The consistent complication of the pulley system and calculations for them show that it is possible to achieve a 4-fold reduction in the required force.

King Chieron, having heard that Archimedes can move any heavy objects from the place did not believe him and asked to prove it. The timing was right, because in Syracuse there was just a problem with a huge ship (the ship was named after the city), which could not be taken out of the harbor. It should be noted that the ship was stunningly beautiful and reached 55 meters in length. According to Plutarch, Archimedes managed to get the ship out of Syracuse harbor using a complex system of levers and pulleys.

Archimedes screw

"Eureka!"
(c) Archimedes

Also, this invention is sometimes called "Archimedes' snail" or water screw. The device is designed for raising water, for example, for irrigating fields. The Archimedes screw is a spiral that rotated inside the pipe, transferring water upward on the helical blades. The spiral rotation was set by rotating a special handle from above. The handle itself could be rotated by both a person and cattle or horse, and in later times it was possible to use water wheel or windmill.. In addition to water, it can be transported to the top by means of a screw granular materials such as ash or sand.

Perhaps this is one of the oldest known devices for raising water. The screw is still used in small power plants and even on farms. Since 1980, the state of Texas in the United States has used eight Archimedes propellers with a diameter of about 3.6 meters to deal with storm runoff. The propeller is powered by a 551 kilowatt engine and can pump up to 500 thousand liters of water per minute.

Archimedes screw used in Texas in the USA

The main advantage of the Archimedes screw is that the ingress of debris into the mechanism does not lead to disruptions in the operation of the device. For example, with the help of the screw, you can even lift the fish along with the water, while the screw will continue to work.

Detailed explanation of how the Archimedes screw works:

A huge Archimedes screw installed at a hydroelectric power station:

And in this video, the Archimedes screw was made from Lego:

Iron hand or claw of Archimedes

Archimedes' claw was a weapon that the inventor invented during the siege of him hometown Syracuse. The city had to be defended from the fleet of the Roman Empire, so it was necessary to develop effective methods to sink the fleet directly from the fortress walls.

The exact design of the device is not known to us, but we roughly understand the principles on which it was based. If you have read carefully about the invention of pulleys and levers, then it will not be difficult to understand the principle of the claw.

The principle of operation of the claw of Archimedes

Archimedes' claw was a system of pulleys, ropes and beams. At one end of the rope there was a hook that was thrown onto the enemy ship and hooked under the belly of the ship. On the back side the ropes behind the wall were already at the ready bulls and people who began to pull the rope. As a result, multi-ton ships were turned over or thrown on stones, scattering the enemy's fleet and crew around the walls.

The pitiful Roman fleet is nothing against the mind of Archimedes!

In our time, two whole groups of people tried to build the claw of Archimedes and sink the ship. We suggest looking at both attempts and making sure that the device was functional.

Catapults, ballistae and scorpions

A painting depicting the siege of Syracuse.

During the siege of Syracuse, Archimedes built artillery that could cover whole line ranges. While the attacking ships were at great distance, he fired from catapults and ballistae, pelting enemy ships with huge stones and logs. If the ships approached the fortress walls for an assault, then they were met by a whole stream of arrows from "scorpions" (small catapults throwing steel darts). By the way, it is worth noting that it was Archimedes who suggested making the loopholes, which was an innovation in the fortification of that time. From small openings, archers successfully fired at the advancing Romans. Thus, the Romans did not succeed in approaching the walls of Syracuse, and if they did, they suffered huge losses.

True, from a historical point of view, Archimedes was not the one who first invented all these structures, but he clearly made his own modifications to them (for example, improved accuracy) and successfully used them for defense.

Fire mirrors

Well, this invention for its time definitely strikes any fantasy. Archimedes figured out how to burn enemy ships with the sun. In some articles, this invention is even called "death rays". How was it organized?

The Romans set up near the city with their 60 quinquerems. Archimedes was educated enough optically to make convex mirrors. Presumably it was not one mirror, but a whole system of mirrors heading to one place to focus the rays. The system most likely consisted of 24 mirrors, which were combined into one frame and rotated by means of hinges, changing the angles of rotation.

How mirrors work

In fact, it is not completely clear what exactly Archimedes used mirrors for. It is likely that he did not burn the fleet with them, but only blinded the archers on the ships. There is also a version according to which special shells were thrown at the ships with the help of catapults, which were then set on fire with the help of mirrors, so one might think that these were mirrors burning ships. And there is also a version that mirrors were used only for aiming catapults.

In 1973, the Greek scientist Ionnis Saccas became interested in the possibility of burning a fleet using mirrors, so he set up an experiment. 60 Greek sailors held 70 mirrors, each of which was copper-plated and measured 1.5 meters by 1 meter. The mirrors were directed to a plywood model of the ship, 50 meters away. The mirrors quietly set fire to the model, which proved the practical possibility of setting fire to the fleet with the help of mirrors.

In 2005, the Mythbusters repeated the experience, albeit in a slightly different way. They used convex mirrors in the amount of 500 pieces and with a smaller area. They managed to burn the sail on the model only after 1 hour, so their experiment showed that burning a fleet with mirrors is not very convincing.

Odometer

Archimedes odometer

Aristotle creates an odometer around 330 BC. This device made it possible to measure the distance traveled, which was indispensable when creating maps or when building large structures.

The odometer principle is simple. The wheels rotate and drive two gears. After certain distances, the gears release a small ball, which falls into a special container. At the end of the path, you can count the balls and find out which path you have done.

As a result, the Romans took Syracuse through bribery. The traitors opened the gates for them, and Archimedes was killed. Cicero later described the return of the Romans to Rome, saying that among the spoils of war there was also a beautiful mechanical planetarium invented by Archimedes. The planetarium showed the movement of five planets and an eclipse. This reconstruction showed the daily movement of stars around the Earth, eclipses of the Sun and Moon, and their movement along the ecliptic.

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.

In theoretical terms, the work of this great scientist was dazzlingly multifaceted. Archimedes' main works dealt with various practical applications of mathematics (geometry), physics, hydrostatics and mechanics. In the essay "Parabola of Quadrature", Archimedes substantiated a 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 to the diameter - and proved that it is the same for any circle. We still use the system of naming integers invented by Archimedes.

Archimedes' mathematical method associated with mathematical work 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 more or less approach and laws which you need to know if we want to influence the material world.

But Archimedes also knew that objects have not only shape and dimension: they move, or can move, or remain motionless under the influence certain forces that move objects forward or balance. The great Syracusean studied these forces, inventing a new branch of mathematics, in which material bodies, reduced to their geometric shape, 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 about the law specific gravity metals - a discovery that also belongs to the Syracuse scientist and the detailed details of which we find in Vitruvius.

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 found that its volume exceeds the volume of the ingot. So the master's dishonesty was proved.

An interesting review 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 Peace. Interestingly, an improved version of the water-lifting machine could be found at the beginning of the 20th century in a monastery located on Valaam, one of the northern Russian islands. Today the Archimedes screw is used, for example, in an ordinary meat grinder.

The invention of the endless screw led him to another important invention, even if it became common, the invention of a bolt constructed from a screw and a nut.

To those of his fellow citizens who would consider such inventions insignificant, Archimedes presented decisive proof of the opposite on the day when he, cleverly adjusting a lever, a screw and a winch, found a means, to the surprise of onlookers, to launch a heavy galley that had run aground, with everything her crew and cargo.

He gave an even more convincing proof in 212 BC. While defending Syracuse from the Romans during the second Punic War, Archimedes constructed several combat vehicles that allowed the townspeople to repel the attacks of the superior Romans for almost three years. One of them was a system of mirrors with which the Egyptians were able to burn down the Roman fleet. This feat of his, which was told by Plutarch, Polybius and Titus Livy, of course, aroused greater sympathy from ordinary people than calculating the number "pi" - another feat of Archimedes, very useful in our time for students of mathematics.

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

It is curious that, having conquered Syracuse, the Romans did not acquire the works of Archimedes. Only after many centuries were they discovered by European scientists. That is why Plutarch, one of the first to describe the life of Archimedes, mentioned with regret that the scientist did not leave a single work.

Plutarch writes that Archimedes died at a ripe old age. A slab with a ball and a 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 did European mathematicians 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.

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. (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 (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 until the end of his life he lived in Syracuse.

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 directed through a system of concave mirrors sunbeams, 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 ​​a ball is 4 times the area of ​​its largest 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), which plays an important role in modern mathematics, is formulated.

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 application 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, and gives the derivation of the law of leverage. 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 ​​this 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 the treatise "Psammit") and determined the value of this angle.

Perhaps, with the word inventor or something similar, the name of Archimedes appears quite often in the mind. This ancient thinker was indeed an outstanding inventor and left a significant amount of discoveries that influenced the development of all mankind in the future.

Archimedes was born in 287 BC on the territory of the island of Sicily in the capital - Syracuse. He was born into a fairly noble family, his father was a mathematician himself, and he was also known to the tyrant of that city, Hieron II. Both are with early years noticed in the boy a penchant for knowledge and sent Archimedes in adolescence to study in Alexandria of Egypt, it was there that there was the largest library, which Herostratus later burned to become famous.

After training, during which he met many pundits of his time and assimilated advanced ideas, Archimedes returned to his homeland and actually entered the service of Hieron. The tyrant in every possible way wants Archimedes to start developing all kinds of military innovations for the island, and the young scientist adheres to peace-loving views and wants to do only the study of the world. So, Archimedes remains on the island and begins to make his discoveries, many of which turn out to be the result of work with Hieron, for example, it was he who wanted the young mathematician to determine the composition of the crown, but without damaging the object itself.

It was then that the invention appeared about the displacement of bodies of different volumes of water, with an identical mass. In addition, Archimedes made many discoveries in mathematics, which were no less ahead of the era by a couple of thousand years. That's right, some ideas, such as semiregular polyhedra or the use of parabolas and hyperbolas to solve equations, scientists were able to appreciate and develop only in the new time, after the Middle Ages.

In 212, Syracuse came under Roman pressure. Then there was the second Punic War and Sicily was at a disadvantage between the empire and Carthage. Archimedes made many military inventions in order to defend his own city (throwing weapons, reflecting copper plates and much more), nevertheless, Syracuse fell, and Archimedes died at the hands of a Roman soldier.

Biography 2

Unfortunately, the exact biography of Archimedes is unknown. Scientists and archaeologists different eras various facts from his life were given, but they are also based on the works of people who lived much later than Archimedes. According to the most widespread version, the future mathematician was born in 287 BC. The birthplace was Syracuse (the island of Sicily). The boy's father, an astronomer and mathematician, sent his son to study in Alexandria. The favorite place of the future physicist and mathematician was the library of Alexandria, where he studied the works and writings of Democritus, Eudoxus and many other scientists. In the same place, Archimedes makes acquaintances that he will carry through his whole life.

The young man loved mathematics from his youth. He devoted all his time to developments in the field of arithmetic, algebra and geometry. Specialists in these fields were able to understand, classify and develop his ideas only by the 17th century. Archimedes decided complex equations finding solutions graphically. Calculated areas, volumes different kinds geometric shapes... He collected and generalized already known calculation methods into uniform principles and formulas. Derived and proved postulates and axioms, which are not only not refuted, but also taken as a basis by modern scientists. One of his most important achievements in geometry, in his own words, was to find the surface area and volume of a sphere. He also derived formulas for calculating the volumes of a paraboloid, a hyperboloid of revolution and an ellipsoid. Before Archimedes, no mathematician had performed these calculations.

In addition to arithmetic, algebra and geometry so beloved by him, Archimedes applied his knowledge in the field of mechanics and physics, inventing and improving already existing structures and mechanisms. For example, Archimedes improved the lever known before his birth, calculating its capabilities and applying it in practice in the port of Syracuse. Some devices and mechanisms based on the principle of leverage have since made heavy work much easier.

Astronomy also did not leave him indifferent. The scientist was engaged in determining the distance between space objects, although he did it from an erroneous point of view. Indeed, in the 3rd century BC. the geocentric theory of the existence of the world was spread. However, later Archimedes presented the heliocentric theory in one of his works.

A chain of mountains and a crater on the surface of the Moon, an asteroid, streets in several cities of Russia and a street in Amsterdam are named in his honor. Archimedes died during the hostilities during the Roman advance on Syracuse. For the victory of his homeland, the scientist created throwing mechanisms. The Roman troops suffered significantly from these machines. It was decided to keep the city under siege. In 212 BC. Syracuse surrendered and Archimedes was killed.