Domenico Fetti. Archimedes ponders. 1620 year. Picture from the Old Masters Gallery, Dresden.
Edward Wimon. Death of Archimedes. 1820-s.
Archimedes Tomb in Syracuse.
Ortigia Island, historical center of Syracuse, the hometown of Archimedes. At these shores, Archimedes burned and sank Roman galleys.
Greek theater in Syracuse.
Archimedes overturns the earth with a lever. Old engraving. 1824 year.
The ball inscribed in the cylinder. The author of the illustration is Andre Karvas.
Archimedes' image on the Fields gold medal - the highest award among mathematicians. The inscription in Latin: "Transire suum pectus mundoque potiri" - "Surpass your human limitations and conquer the universe."
Each new tale of the writer and astrophysicist, doctor of physical and mathematical sciences Nikolai Nikolaevich Gorkavoy (Nick. Gorkavoy) is a story about how important discoveries were made in a particular field of science. And it is no coincidence that the princesses of 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 want to “know everything”. The stories told by Dzintara to the children are included in the Star Vitamin collection. It turned out to be so interesting that readers demanded a continuation. We suggest that you familiarize yourself with some of the tales from the future collection "Creators of the 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 of the Mediterranean, Sicily. The ancient Greeks, the creators of European culture, settled there almost three thousand years ago - in the VIII century BC, and by the time Archimedes was born, Syracuse was a thriving cultural city where its philosophers and scientists, poets and orators lived.
The stone houses of the townspeople surrounded the palace of Tsar 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 didn’t just wash, but relax and exchange the news.
That day in the baths on the main square of the city was noisy - laughter, screams, splash of water. Young people swam in a large pool, and people of respectable age, holding silver goblets of wine in their hands, led a leisurely conversation in comfortable boxes. The sun peered into the courtyard of the baths, illuminating the opening of the door leading to a separate room. In it, in a small pool, similar to a bath, a man sat alone, who behaved quite differently from the others. Archimedes - and it was he who - closed his eyes, but for some elusive signs it was obvious that this man was not sleeping, but was thinking intensely. In recent weeks, the scientist was so deep in his thoughts that he often forgot even about food and had to keep his family home so that he would not go hungry.
It began with the fact that Tsar Hieron II invited Archimedes to his palace, poured him the best wine, asked about health, and then showed the gold crown made for the ruler by the court jeweler.
“I don't 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 the exact same bar, and he made a crown of it.” The weight of the crown and the ingot is the same, my servant checked it. But I do not leave doubts, is not silver mixed into the crown? You, Archimedes, the greatest scientist of Syracuse, and I ask you to check it out, because if the king puts on a fake crown, even street boys will laugh at him ...
The ruler extended 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 your debtor.
Archimedes took the crown and an ingot of gold, left the royal palace and since then has lost peace and sleep. Well, if he can not solve this problem, then no one can. Indeed, Archimedes was the most famous scientist of Syracuse, he studied in Alexandria, was friends with the head of the Library of Alexandria, the mathematician, astronomer and geographer Eratosthenes and other great thinkers of Greece. Archimedes was famous for his many discoveries in mathematics and geometry, laid the foundations of mechanics, on his account several outstanding inventions.
The puzzled scientist came home, put the crown and ingot on the scales, lifted them in the middle and made sure that the weight of both objects was the same: the bowls swayed at the same level. The density of pure gold was known to Archimedes, the density of the crown (weight divided by volume) was to be known. If there is silver in the crown, its density should be less than the density of gold. And since the weights of the crown and the ingot coincide, then the volume of the fake crown must be greater than the volume of the gold ingot. The volume of the ingot can be measured, but how to determine the volume of the crown, in which so many complicated teeth and petals? This problem tormented the scientist. He was an excellent geometer, for example, he solved a difficult task - determining the area and volume of the ball and the cylinder described around it, but how to find the volume of a complex-shaped body? We need a fundamentally new solution.
Archimedes came to the bath to wash off the dust of the hot day and refresh his head tired of thinking. Ordinary people, bathing in a bath, could chat and chew figs, while Archimedes did not leave the thoughts about the unsolved task day or night. His brain was looking for a solution, clinging to any clue.
Archimedes took off his tunic, put it on the bench and went to the small pool. The water splashed in it three fingers below the edge. When the scientist plunged into the water, her level rose markedly, and the first wave even splashed out onto the marble floor. The scientist closed his eyes, enjoying the pleasant coolness. Thoughts about the volume of the crown habitually spin in your head.
Suddenly Archimedes felt that something important had happened, but he could not understand what. He opened his eyes in annoyance. From the side of the large pool came the voices and someone's heated debate - it seems about the last law of the ruler of Syracuse. Archimedes froze, trying to realize what did happen? He looked around: the water in the pool did not reach the edge with just one finger, and when he entered the water, its level was lower.
Archimedes got up and left the pool. When the water calmed down, she was again three fingers below the edge. The scientist climbed into the pool again - the water obediently rose. Archimedes quickly estimated the size of the basin, calculated its area, then multiplied 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 scientist’s weight. But when immersed, the body of Archimedes lost weight and swam in the water. Somehow, in a mysterious way, the water displaced by the body took the weight from him ...
Archimedes realized that he was on the right track - and the 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 the 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 opened, and it is not every day that you can see a naked person running through the central square of Syracuse.
The next day, the king reported on the arrival of Archimedes.
“I solved the problem,” said the scientist. - The crown is really a lot of silver.
“How did you know that?” - the ruler asked.
- Yesterday, in the baths, I guessed that the body, which is immersed in a pool of water, displaces a volume of fluid equal to the volume of the body itself, and at the same time loses weight. After returning home, I conducted many experiments with the scales, immersed in water, and proved that the body loses in weight as much as the liquid it displaces. Therefore, a person can swim, and a gold bar - no, but still in the water, it weighs less.
“And how does this prove the presence of silver in my crown?” - asked the king.
“They brought a vat of water,” Archimedes asked and took out the scales. While the servants dragged the vat to the royal chambers, Archimedes put a crown and an ingot on the scales. They balanced each other.
- If there is silver in the crown, then the volume of the crown is larger than the volume of the ingot. So, when immersed in water, the crown will lose more weight and the scales will change their position, ”said Archimedes and carefully placed both scales in the water. The cup with the crown immediately rose up.
- You are truly a great scientist! Cried 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 revealed by him the day before was much more valuable than a thousand gold crowns.
Archimedes' law 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 rests on the surface of the water thanks to the strength discovered by Archimedes.
When Archimedes grew old, his measured studies in science ended unexpectedly, however, as well as the quiet life of citizens, the rapidly growing Roman Empire decided to conquer the fertile island of Sicily.
In 212 BC a huge fleet of galleys packed with Roman warriors approached the island. The advantage in the power of the Romans was obvious, and the commander fleet I had no doubt that Syracuse would be captured very quickly. But there it was: as soon as the galleys approached the city, powerful catapults hit the walls. They threw heavy stones so precisely that the galleys of the invaders scattered into chips.
The Roman commander did not lose his head and commanded the captains of his fleet:
- Go to the very walls of the city! At close range, the catapult will not be terrible to us, and archers will be able to shoot precisely.
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 nuclei at them. The descended hooks of powerful cranes hitched Roman galleys with their noses and lifted them into the air. Galleys turned, fell down and sank.
The famous historian of antiquity, Polybius, wrote about the storming of Syracuse: "The Romans could have quickly taken possession of the city if someone had withdrawn one elder from the ranks of the Syracusans." This old man was Archimedes, who designed throwing machines and powerful cranes to protect the city.
Rapid capture of Syracuse did not work, and the Roman commander gave the command to retreat. The heavily thinned fleet moved to a safe distance. The city steadfastly held on thanks to the engineering genius of Archimedes and the courage of the townspeople. The scouts told the Roman commander the name of the scientist who created such an unapproachable defense. The commander decided that after victory, Archimedes should be acquired as the most valuable military trophy, because he alone was worth the whole army!
Day after day, month after month, the men were on duty on the walls, shot from bows, and charged the catapult 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 are still small!
Archimedes was old, he, like children, could not shoot a bow as far as young and strong men, but he had a powerful brain. Archimedes gathered the boys and asked them, pointing at the enemy galleys:
- Want to destroy the Roman fleet?
- We are ready, tell what to do!
The wise old man explained that he would have to work hard. He told each boy to take a large brass plate from the already prepared foot and place it on flat stone slabs.
- Each of you should polish the sheet so that it shines in the sun like gold. And then tomorrow I will 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.
- And we ourselves will fight? - asked the little curly little boy.
“Yes,” Archimedes said firmly, “tomorrow you will all be on the battlefield on a par with the warriors.” Each of you will be able to accomplish the feat, and then legends and songs will be added about you.
It is difficult to describe the enthusiasm that swept the boys after the speech of Archimedes, and they energetically set about cracking their brass plates.
The next day, at noon, the sun burned hot in the sky, and the Roman fleet stood still anchored in the outer roadstead. The wooden sides of the enemy galleys warmed up in the sun and oozed with resin, which was used to protect ships from leakage.
On the 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 brass plate. The shield supports were made so that the sheet of copper could be easily turned and tilted.
“We will check now how well you polished the copper,” Archimedes said to them. - I hope everyone knows how to let the sunbeams?
Archimedes approached the little curly little boy and said:
- Catch the sun with your mirror and direct the sunbeam into the middle of the large black galleys, just below the mast.
The boy rushed to follow the instructions, and the warriors who crowded on the walls looked at each other in surprise: what else did the sly Archimedes do?
The scientist was satisfied with the result - a light spot appeared on the side of the black galley. Then he turned to the rest of the teenagers:
- Place your mirrors in the same place!
Wooden poles creaked, copper sheets rattled - a flock of sunbeams ran to the black gallery, and her side began to fill with bright light. The Romans poured onto the galleys' decks - what is happening? The commander-in-chief came out and also stared at the glittering mirrors on the walls of the besieged city. The gods of Olympus, what else did these stubborn Syracusans come up with?
Archimedes instructed his army:
- Keep your eyes on the sunbeams - let them be sent to one place all the time.
Less than a minute later, as from a glowing spot on the side of a black galley, smoke poured down.
- Water, water! - shouted the Romans. Someone rushed to scoop outboard water, but the smoke quickly gave way to flame. Dry, tarred wood burned beautifully!
- Move the mirror to the next gallera on the right! - Archimedes commanded.
Minutes - and the next galley also took fire. The Roman naval commander came out of his stupor and ordered him to anchor in order to move away from the walls of the accursed city with his main defender Archimedes.
Losing anchors, landing paddlers on oars, deploying huge ships and taking them to sea to a safe distance is not a quick deal. While the Romans bustled about the decks, choking on the suffocating smoke, the young Syracusans were transferring mirrors to new ships. In the confusion, the galleys approached each other so closely that the fire spread from one ship to another. Hurrying to sail, some ships deployed the sails, which, as it turned out, were burning no worse than the tar walls.
Soon the battle was over. In the roadstead, many Roman ships were burning down, and the remains of the fleet retreated from the walls of the city. There was no loss among the young army of Archimedes.
- Glory to the great Archimedes! Shouted the enraptured inhabitants of Syracuse and thanked and hugged their children. The mighty warrior in brilliant armor shook the curly boy's hand tightly. His small palm was covered with bloody blisters and abrasions from polishing the copper sheet, but he didn’t even wince at the handshake.
- Well done! Said the warrior respectfully. - The Syracusans will remember this day for a long time.
Two thousand years have passed, and this day remains in history, and not only the Syracusans remembered it. Residents of different countries know an amazing story about the burning of Roman galleys by Archimedes, but he alone would not have done anything without his young assistants. By the way, most recently, already in the twentieth century of our era, scientists conducted experiments that confirmed the full working capacity of the ancient "super-weapon" invented by Archimedes to protect Syracuse from invaders. Although there are historians who consider it a legend ...
- Eh, sorry, I was not there! - exclaimed Galatea, attentively listening with her brother to the evening tale, which her mother, Princess Dzintar, told them. She continued to read the book:
- Having lost hope to seize the city with weapons, the Roman commander resorted to the old proven method - bribing. He found traitors in the city, and Syracuse fell. The Romans broke into the city.
- Find me Archimedes! - commanded the commander. But the soldiers, intoxicated with victory, did not understand well what he wanted from them. They broke into houses, robbed and killed. One of the warriors ran to the square where Archimedes worked, drawing a complex geometric figure on the sand. Soldiers shoes trampled fragile pattern.
- Do not touch my drawings! Said Archimedes menacingly.
The Roman did not recognize the scientist and in anger struck him with a sword. So this great man died.
Archimedes' fame was so great that his books were often rewritten, thanks to which a number of works survived to our time, despite the fires and wars of two millennia. The history of Archimedes' books that have come down to us was often dramatic. It is known that in the XIII century, some ignorant monk took the book of Archimedes, written on durable parchment, and washed away the formulas of the great scientist to get blank pages for recording prayers. Centuries passed, and this prayer book fell into the hands of other scholars. With the help of a strong magnifying glass they explored its pages and distinguished traces of the erased precious text of Archimedes. The book of the brilliant scientist was restored and printed in large quantities. Now she will never disappear.
Archimedes was a real genius who made many discoveries and inventions. He has outstripped his companions not even by centuries - by millennia.
In the book “Psammitus, or Calculus of Sand Grains,” Archimedes recounted the bold theory of Aristarchus of Samos, according to which the great Sun is located in the center of the world. Archimedes wrote: “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 located in its center ...” Archimedes considered Samioi’s heliocentric theory convincing and used it to estimate the size sphere of fixed stars. The scientist even built a planetarium, or “celestial sphere”, where one could observe the movement of five planets, the sunrise and the moon, its phases and eclipses.
The rule of lever, which Archimedes discovered, became the basis of all mechanics. And although the lever was known before Archimedes, he expounded his complete theory and successfully applied it in practice. In Syracuse, he single-handedly launched the new king-of-deck ship of the king of Syracuse, using an ingenious system of blocks and levers. It was then, appreciating the full power of his invention, Archimedes exclaimed: "Give me a fulcrum, and I will turn the world around."
Archimedes' achievements in the field of mathematics, which, according to Plutarch, was simply obsessed, are invaluable. His main mathematical discoveries relate to mathematical analysis, where the scientist's ideas formed the basis of integral and differential calculus. Of great importance for the development of mathematics was the ratio of the circumference of a circle to its diameter calculated by Archimedes. Archimedes gave an approximation for the number π (Archimedean number):
The scientist considered his work in the field of geometry to be his highest achievement, and, above all, the calculation of a ball inscribed in a cylinder.
- What kind of cylinder and ball? Asked Galatea. “Why was he so proud of them?”
- Archimedes was able to show that the area and volume of the sphere refer to the area and volume of the described cylinder as 2: 3.
Dzintar rose and removed from the shelf a model of the globe, which was sealed inside a transparent cylinder so that it touched 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 side area of a transparent cylinder. If you add the area of the base and the top of the cylinder, then it turns out that the area of the cylinder is one and a half times the area of the ball inside it. The same relationship holds for cylinder and ball volumes.
Archimedes was delighted with the result. He knew how to appreciate the beauty of geometric shapes and mathematical formulas - that is why it is not a catapult and a burning galley that decorates his grave, but an image of a ball inscribed in a cylinder. Such was the desire of the great scientist.