What did Archimedes invent? The tale of the scientist Archimedes, who cost an entire army

The famous scientist of the Antiquity era, Archimedes was born in 287 BC. in Sicily, in the city of Syracuse. John Tsetse told the world about this in his writings. Archimedes himself did not leave his descendants an autobiography, memoirs, memoirs. He devoted his life entirely to mathematics, physics, geometry, and engineering. He used the talent of the writer, but for other purposes.

By area, Syracuse was the largest locality ancient world. The largest cultural centers were, of course, Athens, Rome. But even in Syracuse, civilization flourished: the future scientist in childhood had the opportunity to get a good education, devote a lot of time to lessons, moreover, subjects that were somehow abstract, philosophical. Oratory, popular in those days, did not captivate him. Most likely because Syracuse was far from the capital. He did not become a great architect, did not get rich through trade deals, agriculture. Fascinated by the world of numbers and ideas, its illusiveness and realism, he invented and discovered invisible laws.

Most researchers believe that his father is a mathematician, astronomer Phidias. Archimedes himself mentions it in the treatise "Calculation of grains of sand". Nowhere else, from the found documents of that era, this name does not sound. But it is difficult to understand who exactly we are talking about - the text can be translated in different ways. In one interpretation, it says about Phidias that he was the son of Acupatrus, and in another - the father of Archimedes. Plutarch claimed that Archimedes came from a very influential family: the ruler of Syracuse, Hieron II was his relative.

In his youth, the future great scientist went to Egypt, the city of Alexandria, to start his career in the field of science. He did not know much, there was much to learn. It housed a magnificent library, with a huge number of manuscripts. Many famous scientists also lived in this city. In Alexandria, Archimedes made friends with the notorious astronomer Konon of Samos, poet, mathematician, geographer Eratosthenes of Cyrene.

After training, he again came to Syracuse. He quickly created a name for himself, a reputation as a genius. Success brought him, however, not reasoning. His discoveries were useful to the state. He did not hesitate to put them into practice. For example, he is believed to have discovered the law of Archimedes by measuring the king's crown, trying to figure out how much gold it contained and how much impurities. However, he also corresponded with other scientists, discussed achievements, shared his successes.

In those days, there was a constant war between different states for territory. But this did not prevent civilization from developing. Ancient Greece was a formidable opponent. Glorious warriors, industrious farmers lived in it. Archimedes, on the other hand, was characterized by fanaticism, he was crazy in love with science, he served the truth. In 212 BC. The war for Syracuse began with the Romans. It was Archimedes who invented a formidable weapon, throwing machines with aimed fire. Thanks to his efforts, the attacks were repelled. But the city was under siege, and soon, all in the same year 212, it was captured by cunning - a traitor helped. Archimedes died in that battle. He was 75 years old. The battle for Syracuse, the inventions of the scientist are described in the writings of Plutarch, Titus Livius, Anthemius of Tralles.

Biography of Archimedes about the main thing

Archimedes is an outstanding ancient Greek mathematician, engineer and inventor of his time. He was born in 287 BC. in the city of Syracuse in Sicily. Phidias' father was a physicist and mathematician who was at court.

Archimedes received an excellent education, but he understood that he still lacked the theoretical knowledge that had been given earlier. Therefore, he spent all his free time in the Alexandrian Library. After graduation, he began working at the court as an astronomer, created a planetarium. Since it was fashionable at that time to study astronomy, everyone believed that the Sun and the Moon revolve around the Earth, but only Archimedes suggested that it was all the planets that revolved around the Sun. In addition, he studied mechanics, physics and mathematics, he outlined his works in his works “On the Equilibrium of Plane Figures”, followed by the essay “On Changing the Circle”.

The scientist has a lot of discoveries, which he shined on his homeland. He managed to recreate a whole lever-and-block mechanism that allows you to transport heavy loads much faster.

Also, Archimedes has many works related to algebra, geometry, arithmetic. Developed a comprehensive method for calculating the areas of various figures. He created the theory of balancing equal bodies.

One of the versions of death is that the great scientist was killed during the Second Punic War, when after a long defense they took Syracuse. Mark Claudius Marcellus gave the order to find Archimedes and bring him to him. A soldier was sent for him, he went to the house of a scientist who during this period made mathematical calculations. The soldier demanded to come to the Romans, to which Archimedes answered only after I finished the calculations, but the angry soldier stabbed the most brilliant man of that time with his sword. He lived only 75 years.

The most important. For children and schoolchildren and its discovery

Interesting Facts and dates from life

Nick. bitter

Other Scientific Tales Nick. Gorky were published in the journal "Science and Life" in 2010-2013.

Domenico Fetti. Archimedes reflects. 1620. Painting from the Old Masters Gallery, Dresden.

Edward Vimon. Death of Archimedes. 1820s.

Tomb of Archimedes in Syracuse. Photo: Codas2.

Ortigia Island, the historic center of Syracuse, the hometown of Archimedes. Along these coasts, Archimedes burned and sank the Roman galleys. Photo: Marcos90.

Greek theater in Syracuse. Photo: Victoria|photographer_location_London, UK.

Archimedes flips the Earth with a lever. Ancient engraving. 1824

Depiction of Archimedes on the Fields Gold Medal, the highest award among mathematicians. The inscription in Latin: "Transire suum pectus mundoque potiri" - "To overcome your human limitations and conquer the Universe." Photo by Stefan Zakhov.

Each new fairy tale writer and astrophysicist, Doctor of Physical and Mathematical Sciences Nikolai Nikolaevich Gorkavy (Nik. Gorkavy) - this is a story about how the important discoveries in some area of ​​science. And it is no coincidence that Princess Dzintara and her children, Galatea and Andrei, became the heroes of his popular science novels and fairy tales, because they are from the breed of those who seek to “know everything”. The stories told by Dzintara to children were included in the collection "Star Vitamin". It turned out to be so interesting that readers demanded a sequel. We invite you to familiarize yourself with some of the tales from the future collection "Creators of Times". Before you - the first publication.

The greatest scientist of the ancient world, the ancient Greek mathematician, physicist and engineer Archimedes (287-212 BC) was from Syracuse, a Greek colony on the largest island in the Mediterranean - Sicily. The ancient Greeks, the creators of European culture, settled there almost three thousand years ago - in the 8th century BC, and by the time of the birth of Archimedes Syracuse was a flourishing cultural city, where their philosophers and scientists, poets and orators lived.

The stone houses of the townspeople surrounded the palace of the king of Syracuse Hieron II, high walls protected the city from enemies. Residents liked to gather in stadiums where runners and discus throwers competed, and in bathhouses, where they not only washed, but rested and exchanged news.

That day in the baths on the main square of the city it was noisy - laughter, screams, splashing of water. Young people swam in a large pool, and people of respectable age, holding silver goblets with wine in their hands, carried on a leisurely conversation on comfortable beds. The sun looked into patio baths, illuminating the opening of the door leading to a separate room. In it, in a small pool that looked like a bath, a man was sitting alone, who behaved quite differently from the others. Archimedes - and it was he - closed his eyes, but by some elusive signs it was clear that this man was not sleeping, but was thinking hard. In recent weeks, the scientist has become so deep in his thoughts that he often forgot even about food, and his family had to make sure that he did not remain hungry.

It began with the fact that King Hieron II invited Archimedes to his palace, poured him the best wine, asked about his health, and then showed him a golden crown made for the ruler by a court jeweler.

I do not understand jewelry, but I understand people, - Hieron said. - And I think that the jeweler is deceiving me.

The king took a bar of gold from the table.

I gave him exactly the same ingot, and he made a crown out of it. The weight of the crown and the ingot is the same, my servant checked it. But I have no doubts whether silver is mixed into the crown? You, Archimedes, are the greatest scientist of Syracuse, and I ask you to check this, because if the king puts on a false crown, even the street boys will laugh at him ...

The ruler handed the crown and ingot to Archimedes with the words:

If you answer my question, you will keep the gold for yourself, but I will still be in your debt.

Archimedes took a crown and an ingot of gold, left the royal palace and has since lost peace and sleep. If he cannot solve this problem, then no one can. Indeed, Archimedes was the most famous scientist of Syracuse, studied in Alexandria, was friends with the head of the Library of Alexandria, mathematician, astronomer and geographer Eratosthenes and other great thinkers of Greece. Archimedes became famous for his many discoveries in mathematics and geometry, laid the foundations of mechanics, he has several outstanding inventions to his credit.

The puzzled scientist came home, put the crown and the ingot on the scales, lifted them by the middle and made sure that the weight of both objects was the same: the scales swayed at the same level. The density of pure gold was known to Archimedes, it was necessary to find out the density of the crown (weight divided by volume). If there is silver in the crown, its density should be less than that of gold. And since the weights of the crown and the ingot are the same, then the volume of the false crown must be greater than the volume of the gold ingot. The volume of an ingot can be measured, but how can one determine the volume of a crown with so many teeth and petals of complex shape? This is the problem that tormented the scientist. He was an excellent geometer, for example, he solved a difficult problem - determining the area and volume of a ball and a cylinder circumscribed around it, but how to find the volume of a body of complex shape? We need a fundamentally new solution.

Archimedes came to the bathhouse to wash off the dust of a hot day and refresh his head, tired of thinking. Ordinary people while swimming in the bath, they could chat and chew figs, and Archimedes did not leave the thought of an unsolved problem day or night. His brain searched for a solution, clinging to any clue.

Archimedes took off his tunic, put it on a bench and went to a small pool. Water splashed in it three fingers below the edge. When the scientist plunged into the water, its level rose noticeably, and the first wave even splashed onto the marble floor. The scientist closed his eyes, enjoying the pleasant coolness. Thoughts about the volume of the crown habitually swirled in my head.

Suddenly Archimedes felt that something important had happened, but could not understand what. He opened his eyes in annoyance. From the side of the large pool came voices and someone's heated argument - it seems about last law ruler of Syracuse. Archimedes froze, trying to comprehend what really happened? He looked around: the water in the pool did not reach the edge of just one finger, and after all, when he entered the water, its level was lower.

Archimedes got up and left the pool. When the water calmed down, it was again three fingers below the edge. The scientist again climbed into the pool - the water obediently rose. Archimedes quickly estimated the size of the pool, calculated its area, then multiplied it by the change in water level. It turned out that the volume of water displaced by his body is equal to the volume of the body, if we assume that the densities of water and the human body are almost the same, and each cubic decimeter, or cube of water with a side of ten centimeters, can be equated to a kilogram of the weight of the scientist himself. But when immersed, the body of Archimedes lost weight and floated in the water. In some mysterious way, the water displaced by the body took away his weight ...

Archimedes realized that he was on the right path - and inspiration carried him on his mighty wings. Is it possible to apply the found law on the volume of the displaced fluid to the corona? Of course! It is necessary to lower the crown into the water, measure the increase in the volume of liquid, and then compare it with the volume of water displaced by the gold ingot. Problem solved!

According to legend, Archimedes, with a triumphant cry “Eureka!”, which means “Found!” in Greek, jumped out of the pool and, forgetting to put on a tunic, rushed home. It was necessary to urgently check your decision! He ran through the city, and the people of Syracuse waved their hands in greeting. Still, it is not every day that the most important law of hydrostatics is discovered, and not every day you can see a naked man running along the central square of Syracuse.

The next day, the king was informed of the arrival of Archimedes.

I solved the problem, - said the scientist. - There is indeed a lot of silver in the crown.

How did you know it? - the ruler asked.

Yesterday, in the baths, I guessed that a body that is immersed in a pool of water displaces a volume of liquid equal to the volume of the body itself, and at the same time loses weight. Returning home, I conducted many experiments with scales immersed in water, and proved that a body in water loses exactly as much weight as the liquid it displaces weighs. Therefore, a person can swim, but a gold bar cannot, but it still weighs less in water.

And how does this prove the presence of silver in my crown? the king asked.

Tell them to bring a vat of water, - Archimedes asked and took out the scales. While the servants were dragging the vat to the royal chambers, Archimedes placed the crown and ingot on the scales. They balanced each other.

If there is silver in the crown, then the volume of the crown is greater than the volume of the ingot. This means that when immersed in water, the crown will lose more weight and the scales will change their position, - said Archimedes and carefully immersed both scales in the water. The cup with the crown immediately rose up.

You are truly a great scientist! - exclaimed the king. - Now I can order a new crown for myself and check whether it is real or not.

Archimedes hid a grin in his beard: he understood that the law he had discovered the day before was much more valuable than a thousand golden crowns.

The law of Archimedes has remained in history forever; it is used in the design of any ships. Hundreds of thousands of ships plow the oceans, seas and rivers, and each of them keeps on the surface of the water thanks to the force discovered by Archimedes.

When Archimedes grew old, his measured studies in science suddenly ended, however, as did the quiet life of the townspeople - the rapidly growing Roman Empire decided to conquer the fertile island of Sicily.

In 212 BC. a huge fleet of galleys filled with Roman soldiers approached the island. The superior strength of the Romans was obvious, and the commander of the fleet had no doubt that Syracuse would be captured very quickly. But that was not the case: as soon as the galleys approached the city, powerful catapults struck from the walls. They threw heavy stones so precisely that the invaders' galleys were shattered into splinters.

The Roman commander was not at a loss and ordered the captains of his fleet:

Come to the very walls of the city! At close range, catapults will not be afraid of us, and archers will be able to shoot accurately.

When the fleet with losses broke through to the city walls and prepared to storm it, the Romans were in for a new surprise: now light throwing machines threw a hail of cannonballs at them. The lowered hooks of powerful cranes hooked the Roman galleys by the bows and lifted them into the air. The galleys turned over, fell down and sank.

The famous historian of antiquity Polybius wrote about the storming of Syracuse: "The Romans could quickly take possession of the city if someone removed one elder from among the Syracusans." This elder was Archimedes, who designed throwing machines and powerful cranes to protect the city.

The quick capture of Syracuse did not work out, and the Roman commander gave the command to retreat. The heavily depleted fleet retreated to a safe distance. The city steadfastly held on thanks to the engineering genius of Archimedes and the courage of the townspeople. The scouts reported to the Roman commander the name of the scientist who created such an impregnable defense. The commander decided that after the victory he needed to get Archimedes as the most valuable military trophy, because he alone was worth the whole army!

Day after day, month after month, men were on duty on the walls, shooting from bows and loading catapults with heavy stones, which, alas, did not reach the goal. The boys brought water and food to the soldiers, but they were not allowed to fight - they were still small!

Archimedes was old, he, like the children, could not shoot his bow as far as the young and strong men but he had a powerful brain. Archimedes gathered the boys and asked them, pointing to the enemy galleys:

Want to destroy the Roman fleet?

We are ready, tell us what to do!

The wise old man explained that he would have to work hard. He told each boy to take a large copper sheet from the already prepared stack and put it on even stone slabs.

Each of you must polish the leaf so that it shines like gold in the sun. And then tomorrow I'll show you how to sink the Roman galleys. Work, friends! The better you polish copper today, the easier it will be for us to fight tomorrow.

Are we going to fight ourselves? asked the little curly-haired boy.

Yes, - said Archimedes firmly, - tomorrow you will all be on the battlefield on a par with the soldiers. Each of you will be able to accomplish a feat, and then legends and songs will be composed about you.

It is difficult to describe the enthusiasm that seized the boys after the speech of Archimedes, and they energetically undertook to polish their copper sheets.

The next day, at noon, the sun was burning in the sky, and the Roman fleet was motionless at anchor in the outer roadstead. The wooden sides of enemy galleys warmed up in the sun and oozed resin, which was used to protect ships from leaks.

On the fortress walls of Syracuse, where enemy arrows did not reach, dozens of teenagers gathered. In front of each of them stood a wooden shield with a polished copper sheet. The shield supports were made so that the sheet of copper could be easily turned and tilted.

Now we will check how well you polished the copper, ”Archimedes turned to them. - I hope everyone knows how to let the sunbeams?

Archimedes approached the little curly-haired boy and said:

Catch the sun with your mirror and direct the sunbeam into the middle of the side of the big black galley, just under the mast.

The boy rushed to follow the instructions, and the soldiers crowded on the walls looked at each other in surprise: what else did the cunning Archimedes start up?

The scientist was pleased with the result - a light spot appeared on the side of the black galley. Then he turned to the rest of the teenagers:

Point your mirrors in the same place!

Creaked wooden poles, copper sheets rattled - a flock of sunbeams ran to the black galley, and its side began to fill with bright light. The Romans poured onto the decks of the galleys - what is happening? The commander-in-chief came out and also stared at the sparkling mirrors on the walls of the besieged city. Gods of Olympus, what else have these stubborn Syracusans come up with?

Archimedes instructed his army:

Keep your eyes on the sunbeams - let them always be directed to one place.

In less than a minute, smoke billowed from a glowing spot on the side of the black galley.

Water, water! the Romans shouted. Someone rushed to scoop outboard water, but the smoke quickly gave way to flames. Dry tarred wood burned beautifully!

Move the mirrors to the next galley on the right! commanded Archimedes.

A few minutes - and the neighboring galley also took up fire. The Roman naval commander came out of his stupor and ordered to weigh anchor in order to move away from the walls of the accursed city with its main defender Archimedes.

Weighing anchors, putting rowers on the oars, turning huge ships around and taking them out to sea to a safe distance is not a quick thing. While the Romans frantically ran around the decks, choking on suffocating smoke, the young Syracusans were transferring mirrors to new ships. In the confusion, the galleys approached each other so close that the fire was thrown from one ship to another. Hurrying to sail, some ships unfolded their sails, which, as it turned out, burned no worse than the resin sides.

The battle was soon over. In the raid, many Roman ships burned out, and the remnants of the fleet retreated from the walls of the city. There were no casualties among the young army of Archimedes.

Glory to the great Archimedes! shouted the delighted inhabitants of Syracuse and thanked and hugged their children. A mighty warrior in shining armor firmly shook hands with the curly-haired boy. His small palm was covered in bloody calluses and abrasions from polishing the copper sheet, but he didn't even wince at the handshake.

Well done! - the warrior said respectfully. The Syracusans will remember this day for a long time.

Two millennia have passed, and this day has remained in history, and not only Syracusans remembered it. Inhabitants different countries know amazing story about the burning of the Roman galleys by Archimedes, but he alone would not have done anything without his young assistants. By the way, quite recently, already in the twentieth century AD, scientists conducted experiments that confirmed the full performance of the ancient "superweapon" invented by Archimedes to protect Syracuse from invaders. Although there are historians who consider this a legend ...

Oh, sorry, I wasn't there! - exclaimed Galatea, attentively listening with her brother to the evening fairy tale, which was told to them by their mother, Princess Dzintara. She continued to read the book.

Having lost hope of capturing the city with the help of weapons, the Roman commander resorted to the old tried and tested method - bribery. He found traitors in the city, and Syracuse fell. The Romans broke into the city.

Find me Archimedes! - ordered the commander. But the soldiers, drunk with victory, did not understand well what he wanted from them. They broke into houses, robbed and killed. One of the soldiers ran out to the square where Archimedes worked, drawing a complex geometric figure in the sand. The soldiers' boots trampled on the fragile design.

Don't touch my blueprints! said Archimedes sternly.

The Roman did not recognize the scientist and in anger struck him with a sword. This is how the great man died.

The fame of Archimedes was so great that his books were often rewritten, thanks to which a number of works have survived to our time, despite the fires and wars of two millennia. The history of the books of Archimedes that have come down to us has often been dramatic. It is known that in the 13th century, some ignorant monk took the book of Archimedes, written on durable parchment, and washed away the formulas of the great scholar in order to get clean pages for writing down prayers. Centuries passed, and this prayer book fell into the hands of other scientists. Using a strong magnifying glass, they examined its pages and distinguished traces of the erased precious text of Archimedes. The book of the brilliant scientist was restored and printed in large numbers. Now it will never disappear.

Archimedes was a real genius who made many discoveries and inventions. He was ahead of his contemporaries not even for centuries - for millennia.

In the book "Psammit, or Calculus of grains of sand" Archimedes retold the bold theory of Aristarchus of Samos, according to which in the center of the world is located big sun. Archimedes wrote: "The Aristarchus of Samos ... believes that the fixed stars and the Sun do not change their place in space, that the Earth moves in a circle around the Sun, which is in its center ..." Archimedes considered the heliocentric theory of Samos to be convincing and used it to estimate the size spheres of fixed stars. The scientist even built a planetarium, or "celestial sphere", where one could observe the movement of the five planets, the rising of the sun and moon, its phases and eclipses.

The lever rule, discovered by Archimedes, became the basis of all mechanics. And although the lever was known before Archimedes, he outlined his complete theory and successfully applied it in practice. In Syracuse, he single-handedly launched the new multi-deck ship of the king of Syracuse, using an ingenious system of blocks and levers. It was then, having appreciated the full power of his invention, Archimedes exclaimed: "Give me a fulcrum, and I will turn the world upside down."

The achievements of Archimedes in the field of mathematics, which, according to Plutarch, he was simply obsessed with, are invaluable. His main mathematical discoveries relate to mathematical analysis, where the ideas of the scientist formed the basis of integral and differential calculus. Of great importance for the development of mathematics was the ratio of circumference to diameter calculated by Archimedes. Archimedes gave an approximation for the number π (the Archimedean number):

The scientist considered his highest achievement to be works in the field of geometry and, above all, the calculation of a ball inscribed in a cylinder.

What is a cylinder and a sphere? Galatea asked. Why was he so proud of them?

Archimedes was able to show that the area and volume of a sphere are related to the area and volume of the circumscribed cylinder as 2:3.

Dzintara got up and removed from the shelf a model of the globe, which was soldered inside a transparent cylinder so that it was in contact with it at the poles and at the equator.

I have loved this geometric toy since childhood. Look, the area of ​​the ball is equal to the area of ​​four circles of the same radius or the area of ​​the side of the transparent cylinder. If we add the areas of the base and top of the cylinder, it turns out that the area of ​​the cylinder is one and a half times more area ball inside it. The same relation holds for the volumes of a cylinder and a sphere.

Archimedes was delighted with the result. He knew how to appreciate the beauty of geometric figures and mathematical formulas - that is why it is not a catapult or a burning galley that decorates his grave, but the image of a ball inscribed in a cylinder. That was the wish of the great scientist.

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

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

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

Engineering

The scientist actively developed mechanical structures. He laid out a detailed theory of the 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 the work of the port. And the “Archimedean screw”, designed to scoop up water, is still used in Egypt.

Great importance have the theoretical research of a scientist in the field of mechanics. Based on the proof of the law of the lever, he began to write the work "On the equilibrium of plane figures." The proof is based on the axiom that on equal arms, equal bodies will necessarily balance. The same principle of building a book - starting with the proof of his own law - Archimedes observed when writing the work "On the Float of Bodies". This book begins with a description of the well-known law of Archimedes.

Mathematics and physics

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

Even before Archimedes, formulas were invented for calculating the areas of a circle and polygons, the volumes of a pyramid, cone and prism. But the experience of the scientist allowed him to develop general tricks 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 later became the basis for this theory.

The mathematician also laid the foundations of differential calculus. From a geometric point of view, he studied the possibilities of determining the tangent to a curved line, from a physical point of view, the speed of a body at any time. The scientist explored a flat curve known as the Archimedean spiral. He found the first generalized way to find tangents to a hyperbola, a parabola, and an ellipse. It was only in the seventeenth century that scientists were able to fully comprehend and reveal all the ideas of Archimedes that had come down to those times in his surviving writings. The scientist often refused to describe inventions in books, which is why not every formula he wrote has survived to this day.

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 of the cases described, Archimedes finalized 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 the 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 discovery of a scientist in the field of physics was a statement that is known as the law of Archimedes. He determined that any body immersed in a liquid is subjected to pressure by a buoyant force. It is directed upwards, and in magnitude is equal to the weight of the liquid that was displaced when the body was placed in the liquid, regardless of what the density of this liquid is.

There is a legend associated with this discovery. Once Hieron II allegedly turned to the scientist, 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. Then he placed these ingots in turn in a vessel of water and noted how much its level increased. Then the scientist put a crown in the vessel and found that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus it was discovered that the master had kept some of the gold for himself.

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

Astronomy

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

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

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

Personal life

Much less is known about the scientist's personal life than about his science. Even his contemporaries composed numerous legends about a gifted mathematician, physicist and engineer. The legend tells that one day Hieron II decided to present a multi-deck ship as a gift to Ptolemy, the king of Egypt. It was decided to name the water vessel "Syracusia", but it could not be launched in any way.

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

"Give me a point of support and I will move 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 win. So, he designed throwing machines, with the help of which the soldiers of Syracuse threw heavy stones at their opponents. When the Romans rushed to the walls of the city, hoping that there they would not come under fire, another invention of Archimedes - light close-range throwing devices - helped the Greeks to bombard them with cannonballs.

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, the 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 performance of such devices by reconstructing them from surviving descriptions.

Thanks to the efforts of Archimedes, the hope of the Romans to storm the city failed. Then they decided to go to the siege. In the autumn 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 argue that the place of death of Archimedes was his laboratory. The scientist was allegedly so carried away by research that he refused to immediately follow the Roman soldier, who was ordered to take Archimedes to the commander. He pierced the old man with his sword in anger.

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

Compositions

• Parabola squaring
• About the ball and cylinder
• About spirals
• About conoids and spheroids
• On the equilibrium of plane figures
• Epistle to Eratosthenes about the method
• About floating bodies
• Circle measurement
• psummit
• Stomachion
• Archimedes' bull problem
• Treatise on the construction of a bodily figure with fourteen bases near a ball
• Book of Lemmas
• A book about building a circle divided into seven equal parts
• The Book of Touching Circles

A well-known cliche says that many educated people were ahead of their time by making discoveries that benefited all of humanity. Among them, the figure of the scientist Archimedes of Syracuse stands apart. Numerous of his ideas found successors only after hundreds and even thousands of years, not counting those that were immediately implemented.

This ancient ascetic, having absolutely no prerequisites, made the greatest revolutions in the field of geometry, laid the foundations of hydrostatics, and developed mechanics. His developments really influenced the development of physics, astronomy and many other sciences. Let's find out together what kind of person he was, how his earthly path developed and how he entered his name in historical documents forever.

Who is Archimedes of Syracuse: a biography of an absent-minded inventor

Since ancient times, Sicily has been a disputed territory. The Siculians lived on one side of the island, and the Phoenicians on the other. They could not divide the space between them. The Greeks and Carthaginians dreamed of capturing the fertile land, and later they were replaced by the Chalkids, who were forced out by the Romans. After the death of the tyrant (invader, occupying ruler) Agathocles of Syracuse, the troubled times. Crime grew, the government was deeply corrupt. If a new strong ruler Pyrrhus had not arisen, Sicily could completely go to Carthage. In Syracuse, a new tyrant, Hieron II, was brought to power. It was in such an environment that the future great mathematician and astronomer Archimedes was born and grew up.

Hieron II had the honorary title of king, he became tyrant of Syracuse in the year 270 BC, and reigned until the year 215 or twelfth. The famous ancient Greek philosopher, public figure and historian Plutarch claims that the ruler was closely related to the physicist Archimedes.

Activities and discoveries of Archimedes

Understanding what Archimedes is known for, many people remember funny stories about a lever and a container of water. But this is only a small fraction of what this active person, who cannot sit still, independently invented, developed and even made. One of the main inventions of the geometer is considered to be a helical screw or an endless screw (Archimedes' worm), without which there would be no bulk modern mechanisms.

A similar design is located inside an ordinary household meat grinder, and in the Crimea you can still find water-lifting machines based on this principle. The military inventions of the scientist helped to defend the besieged Syracuse from the attacks of the Roman troops, more numerous and well-armed than the local army. Archimedes not only invented military machines, but also made them with his own hands, tested them and taught people how to use them.

With the help of the lever invented by him, humanity got the opportunity to move and lift colossal loads. The most “advanced” invention, really ahead of its time, can be called a planetarium with a heavenly vault, which Archimedes also built himself. True, there was a small problem - at the heart of his theory was a system of the world, the center of which was the Earth. But other planets (Mars, Mercury and Venus) he, as expected, revolved around the Sun.

The birth and childhood of the future scientist

A variety of information about the birth and life of the famous Syracusan mathematician Archimedes can easily be found in the works of the ancient Romans: the famous architect Mark Vitruvius Pollio, the historian Titus Levi and the great orator Cicero. Greek scientists referred to it more than once and mentioned it in their works: the military leader and historian Polybius, the outstanding philosopher Plutarch and even the famous mythographer Diodorus Siculus. They often lived many years after the scientist himself departed to another world, therefore it will not be possible to verify the accuracy of the information. However, we have no other sources at our disposal.

The future genius was born in the family of a mathematician and astronomer. Researchers often point out that his father was the ancient Greek scientist Phidias (Φειδίας ), a well-known and respected, but not rich person. Some ancient texts state that he had a position at the court of Hiero II, which his son later inherited. Moreover, they say that Archimedes was a cousin (grandchild?) of the tyrant's nephews. The king of Syracuse himself was poor, like a church mouse, and therefore his subjects could not boast of special savings.

Approximately around 287 BC, a replenishment took place in the family of Phidias - he had a boy, whom it was decided to name Archimedes. No information about whether the guy had brothers or sisters could be found in historical papers. The father himself taught his son to read, write, taught the basics of mathematics and astronomy, but this was not enough. The baby absorbed his father's talents, and he was a really knowledgeable astronomer.

Becoming an inventor

The scientific and cultural center of the IV-III centuries BC was a glorious city located in the Nile Delta - Alexandria of Egypt, founded about a hundred years before the birth of Archimedes. Scientists, researchers, artists from all over the world flocked there. It was there that our hero went to continue his studies. His first teacher was the most famous astronomer of our time, Konon of Samos, who not only wrote works on this science in seven volumes, as Virgil testifies, but even compiled a calendar with sunrises and sunsets, as well as estimated weather forecasts.

Interesting

The late Hellenistic mathematician, philosopher, and mechanic Pappus of Alexandria wrote that Conon actually discovered the spiral of Archimedes some ten or fifteen years before him. Apollonius of Perga said that he studied conic sections, but his works contained unfortunate errors, which is why practical experimental developments did not want to work. Archimedes allegedly took the already finished developments and simply completed them, correcting the inaccuracies. It was not possible to find out the true state of things.

At that time, the city had the most complete library in the world. More than seven hundred thousand original manuscripts were collected there. The young man studied the works of Eudoxus of Cnidus and Democritus of Abdera. He was especially interested in geometry, because he studied all the available ancient works tirelessly. It was impossible to get a better and more universal education at that time. Before understanding what Archimedes did, it does not hurt to know about his friendship with Eratosthenes of Cyrene, who was about the same age as him.

There is evidence that despite the fact that fate divorced the guys after studying in Alexandria, they never stopped talking. The young scientist, full of hopes, dreams and ideas, returned to the fertile Sicily in Syracuse. A brilliant education opened many doors for him, and a sharp mind allowed him to get a job as a court astronomer to the usurper and tyrant of Syracuse, where his father used to work. According to scattered and often later information, he was a well-known, deeply respected person with a good income, due to his outstanding mental abilities.

The heyday of the scientific thought of Archimedes

Little is known about his human qualities. Many believed that he was a somewhat absent-minded, slightly eccentric person, because of which he subsequently suffered. He was kind, sympathetic, often helped acquaintances and friends, but he constantly hovered in the clouds, as they say - a little "out of this world." But the time has come to find out what Archimedes discovered and invented, otherwise the “picture” will remain incomplete.

Mathematics of Archimedes: Algebra, Analysis, Geometry

Plutarch believed that Archimedes was literally obsessed with this exact science, in which many did not understand anything at all, and did not even look beyond the summation of hundreds. Having sat up for his treatises, he could completely forget to have breakfast or dinner, wash himself or do other necessary household chores. The ideas that the scientist expressed, his developments and calculations were continued only after many thousands of years. At the end of the seventeenth century, it became clear to mathematicians what this “man from the future”, who managed to get ahead of his time, had in mind.

Archimedes studied conic sections, developed the concept of semi-regular polyhedra, found a geometric method for solving cubic equations, being able to connect them with curves (hyperbola and parabola). He perfected general method calculating the area of ​​three-dimensional figures, introduced the concept of extremums, managed to calculate the volumes of balls, ellipsoids, hyperboloids and other figures. In his work "On Spheres and Cylinders" he derived an axiom, later named after him.

Eureka - what Archimedes found: mechanics

Archimedes invented many real devices that, to the surprise of his contemporaries, also worked. In mechanics, he reached incredible heights. For example, a lever was already well known to a person before, he had used it for a long time, but it was this scientist who was the first to describe in detail how and why it greatly facilitates efforts. Plutarch wrote that cranes and hoists, systems of blocks and levers, developed by Archimedes, were arranged in the port of Syracuse. They greatly facilitated the loading and unloading operations when transporting heavy objects.

Archimedes' auger, "worm" or screw, which is basically the same thing, is used to scoop up water today in Egypt and other countries. It is installed in many modern mechanisms, in particular, in the meat grinder already mentioned above. The scientist is the author of numerous works on mechanics: "On the balance of plane figures", "On floating bodies" and many others.

Astronomy - the science of the celestial spheres

To show exactly how the stars move in the sky, the great inventor personally built a planetarium with a moving celestial sphere. In this room one could see how the Sun and the Moon walk across the sky, how they disappear behind the horizon and reappear, how various eclipses occur and how the stars move. Archimedes proved that Mars, Mercury and Venus revolve precisely around the star, and not around the Earth.

In the work "Psammit" ("Calculation of grains of sand"), written in the form of a letter to the king of Syracuse, he firmly relies on heliocentric system world order, which was described by Aristarchus of Samos. The treatise contains reflections on the correct measurement of distances between planets, as well as the calculation of the volume of these celestial bodies. These were very accurate calculations, which were confirmed by later studies.

Warfare: Saving Syracuse

During the Second Punic War, Archimedes also showed himself as a military tactician and strategist, capable of providing the army with advanced mechanical inventions. These mechanisms were capable of much, despite the fact that the elderly scientist was then already more than seventy-five years old. He designed and built powerful catapults that could throw boulders up to two or three hundred meters away. "Archimedes' claw" (large cranes with hooks) picked up Roman ships, lifted them into the air, and then "slapped" them on the water or shore with a swing.

After such an action, the Romans were shocked, they stopped the frontal attack and decided to besiege Syracuse. According to legend, at that moment it dawned on Archimedes: he ordered all the soldiers to polish the concave shields to a shine. Focusing the sun's glare on the enemy ships, the inhabitants of the city set them on fire. Historians believe that this is a beautiful myth, and it is impossible to burn ships in this way. Be that as it may, Syracuse was still defeated, but the brilliant scientist did not recognize this.

Incidents from the legendary life of a genius: the death of a hero and his memory

The life of a great man was full of various events. He did not fit into his age so much that various legends were regularly composed about him, which were passed off at face value. Knowing how powerful the mind of this man was, everyone could admit the veracity of such legends.

Worth knowing

There is a well-known story about how Archimedes discovered the laws of hydrostatics. Allegedly, his distant relative, and part-time employer and tyrant of Syracuse, Hieron, ordered a crown from a Jewish jeweler. It should have been made of the purest gold, but the ruler had no confidence in the loyalty of the performer. Therefore, he brought the finished little thing to the scientist so that he could find out if there were any impurities of silver in it. Archimedes pondered and went to the bathhouse, where in the warmth his thoughts became purer and clearer. It was only when he plunged into a bath filled to the brim with water that he understood how to correctly measure the volume of an object. Then he ran out into the street shouting "Eureka!" (Found from Greek), and ran home to make calculations, forgetting to put on a towel. So it was opened main law Archimedes: a body immersed in a liquid is subjected to a buoyant force numerically equal to the weight of the liquid, the volume of which is equal to the volume of the part of the body below the liquid level. What happened next with the crown and the tyrant is unknown.

There are other legendary cases that have come down to us, the veracity of which cannot be proved. Once Hieron decided to strengthen friendly relations with the Egyptian king Ptolemy. To do this, he ordered to build the largest and most beautiful ship in the world and present it as a gift. They called the ship "Syracusia", but it was so huge that it was impossible to launch it.

No matter how hard people fought, they could not move it even a centimeter. Archimedes was urgently called, who immediately, from improvised means, hastily built a chain hoist (a system of blocks and levers), and with a slight movement lowered the ship into the waters of the Nile. Since then, he has been credited with the words: "Give me a foothold, and I will move the Earth."

Death is one, but there are many versions

It is believed that Archimedes died at an advanced age (more than seventy-five years) during the siege of Syracuse, but there is no reliable version of what happened. But there are several assumptions that would not hurt to know.

• According to the story of the Byzantine philologist John Tsets, who lived more than a thousand years later, Archimedes was sitting at his house and drawing something in the sand when a passing Roman stepped on his calculations. The enraged scientist rushed at him with his fists and immediately fell from the sword.
• Diodorus Siculus, who lived a hundred years after Archimedes, has his own view on the version of his death. In it, the old man, carried away by his diagrams, did not notice how a Roman soldier began to drag him in order to shackle him in chains. When he saw what was happening, he cried out that they brought him a terrifying car. The soldier was frightened and killed the scientist, for which he later paid with his head.
• Another version says that Archimedes was heading to the consul Marcus Claudius Marcellus with a casket containing his tools for measuring the distance to the Sun and planets, fearing that they could be spoiled in the confusion. The soldiers thought that the old man was carrying gold in the box and stabbed him to death.
• Plutarch believed that a Roman soldier killed Archimedes for disobedience. He came to call him to the consul, but he was busy and did not pay any attention to him. Then the guy hit the scientist with a sword, for which he was executed on the orders of Marcellus.

It is believed that the consul himself severely repented that he did not think in advance to give a strict order to save Archimedes' life. Titus Livy in his treatise "Roman History from the Foundation of the City" wrote that he found the relatives of the scientist and buried him with all the honors that were possible. Arriving on the island one hundred and forty years after the above events, the quaestor (master) of Sicily Mark Tullius Cicero found the grave of a mathematician and astronomer. As the elder had bequeathed, there was a picture on it - a circle inscribed in a cylinder.

In memory of mathematics

The inventions of Archimedes will forever remain the greatest achievements of mankind. Therefore, the memory of him will not disappear as long as we use them in everyday life. On the Moon, one of the craters bears the name of Archimedes, and an asteroid, also having the same name, rushes through outer space. There are streets, avenues and squares named after him in Amsterdam, Donetsk, Syracuse and Nizhny Novgorod

The Czech prose writer and playwright Karel Capek published a story called The Death of Archimedes, and Sergei Zhitomirsky wrote the story The Scientist from Syracuse: Archimedes, which was published in the early eighties of the last century. Enrico Gemelli played the mathematician in the 1914 silent feature film Cabiria. There is even a domestic Soviet cartoon "Kolya, Olya and Archimedes", describing the life of Syracuse at the time of the capture by the Romans.

Archimedes is the greatest ancient Greek mathematician, physicist, astronomer and military engineer. He miraculously combined the qualities of a theoretical scientist and a practitioner, successfully applying his knowledge and inventions to protect his native city.

Archimedes was born in Sicily, in the wealthy city-state of Syracuse, a former Greek colony. His father, the mathematician and astronomer Phidias, was friends with the Syracusan tyrant Hieron II and may even have been his relative. The craving for knowledge led Archimedes to Alexandria, the main scientific center of that time, where he met and became friends with many prominent scientists, such as Conon and Eratosthenes of Cyrene. After living in Alexandria for several years, Archimedes returned to Syracuse and remained there for the rest of his life.

One of the most famous statements attributed to Archimedes is: “If I had another Earth at my disposal, on which I could stand, I would move ours.” According to Plutarch's story, when Hieron II heard these words, he asked to translate such a bold idea into action and show some kind of heaviness moved by a small effort. In response, Archimedes ordered the royal three-masted cargo ship "Syracuse" to be filled with luggage, recently pulled ashore by a whole crowd of people with great difficulty, put a large team of sailors on it, and he sat down at a distance and, without any tension, stretching the end of the rope passed through compound block, pulled the ship closer to him - so slowly and evenly, as if he was sailing on the sea.

In addition to the system of blocks, Archimedes invented a water-lifting screw, which was used in ancient times to irrigate fields and pump water from mines.

Another amazing invention of Archimedes is a small planetarium, during the movement of which one could observe the movement of the planets, as well as the phases and eclipses of the moon.

Fearing a Roman attack, Hiero II asked Archimedes to create a defensive system for Syracuse. On the advice of Archimedes, the city walls were rebuilt so that they could accommodate catapults and winches that lifted heavy stones and threw them over long distances, while the scientist himself began to develop new machines. The defense of Syracuse became a battle between the Romans and Archimedes.

One of the most terrible weapons used by the inhabitants of Syracuse were the "beaks of Archimedes." They descended on any ship that came into range, grabbed it tightly and lifted it or turned it over. No one knows how these "beaks" work, perhaps they were a huge hook lowered with a winch.

Some ancient historians of the siege of Syracuse mention focusing mirrors, with which the besieged set fire to the sails and hulls of ships that approached the city wall within an arrow's flight distance. Archimedes could have come up with such "burning" mirrors, however there is no evidence that he actually did it.

The name of Archimedes is associated not only with many legends, but also with real discoveries. He determined the value of the number i with amazing accuracy, 2000 years before the advent of integral calculus described a method for calculating the volume and surface area of ​​curved bodies, invented a way to express very large numbers, demonstrating it by counting the number of grains of sand that exist in the Universe.

In 212 BC. e. The Romans still captured Syracuse. Bursting into the house of Archimedes, one of the soldiers saw an old man, thoughtfully drawing on the sand geometric figures. The inventor asked not to interfere with his thinking about solving the problem, which made the warrior very angry, and he, drawing his sword, killed Archimedes.

By using various machines, invented by Archimedes, Syracuse withstood the siege of Roman ships for about three years.