Archimedes and his discoveries. Archimedes - biography, information, personal life What Archimedes created

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

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

Biography of Archimedes

So, an outstanding resident of Magna Graecia was born in 287 BC. e., and died in 212 BC. e. His father was an astronomer named Phidias, about whom nothing is known. Family ties with the tyrant of Syracuse, Hieron II, are also suggested. The most detailed biography of Archimedes was written by his friend Heraclides. But this work was lost, and therefore the details of the life of the mathematician and inventor remained unclear. Nothing is known about his wife and children, but there is no doubt about his studies in Alexandria, where the famous Library of Alexandria was located.

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

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

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

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

Archimedes is killed by a Roman soldier

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

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

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

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

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

Archimedes' claw lifts a Roman ship

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

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

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

A focused sunbeam sets a ship on fire

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

Legacy of Archimedes

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

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

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

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

The ancient Greek physicist, mathematician and engineer Archimedes made many geometric discoveries, laid the foundations of hydrostatics and mechanics, and created inventions that served as the starting point for 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 scientific figures of his time.

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

Archimedes probably spent his childhood 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. The scientist presumably received his primary education from his father. After living for several years in Alexandria, Archimedes returned to Syracuse and lived there until the end of his life.

Engineering

The scientist actively developed mechanical structures. He outlined 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 port operations. And the “Archimedean screw”, designed for scooping up water, is still used in Egypt.

Archimedes' inventions: Archimedes' screw

The theoretical research of a scientist in the field of mechanics is of great importance. Based on the proof of the law of leverage, he began to write the work “On the Equilibrium of Plane Figures.” The proof is based on the axiom that equal bodies on equal shoulders will necessarily balance. Archimedes followed the same principle of constructing a book - starting with the proof of his own law - when writing the work “On the Floating of Bodies”. This book begins with a description of Archimedes' well-known law.

Mathematics and physics

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

Even before Archimedes, formulas were invented to calculate the areas of circles and polygons, the volumes of pyramids, cones and prisms. But the scientist’s experience allowed him to develop general techniques for calculating volumes and areas. To this end, he improved the method of exhaustion, invented by Eudoxus of Cnidus, and brought the ability to apply it to a virtuoso level. Archimedes did not become the creator of the theory of integral calculus, but his work subsequently became the basis for this theory.

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

Archimedes' inventions: "solar" mirrors

The scientist considered the invention of formulas for calculating the surface area and volume of a ball to be a worthy discovery. If in the previous cases described, Archimedes refined and improved other people’s theories, or created quick calculation methods as an alternative to existing formulas, then in the case of determining the volume and surface of a ball, he was the first. Before him, no scientist had coped with this task. Therefore, the mathematician asked to knock out a ball inscribed in a cylinder on his gravestone.

The scientist's discovery in the field of physics was a statement that is known as Archimedes' law. He determined that any body immersed in a liquid is subject to pressure by a buoyant force. It is directed upward, and in magnitude is equal to the weight of the liquid that was displaced when the body was placed in the liquid, regardless of the density of this liquid.

There is a legend associated with this discovery. One day, the scientist was allegedly approached by Hiero II, who doubted that the weight of the crown made for him corresponded to the weight of the gold that was provided for its creation. Archimedes made two ingots of the same weight as the crown: silver and gold. Next, he placed these ingots in turn in a vessel with water and noted how much its level increased. The scientist then placed the crown in the vessel and discovered that the water did not rise to the level to which it rose when each of the ingots was placed in the vessel. Thus it was discovered that the master had kept part of the gold for himself.

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

Astronomy

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

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

Archimedes' inventions: planetarium

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

Personal life

Much less is known about the scientist’s personal life than about his science. His contemporaries also composed numerous legends about the gifted mathematician, physicist and engineer. Legend says that one day Hiero II decided to present Ptolemy, the king of Egypt, with a multi-deck ship as a gift. It was decided to name the watercraft "Syracuse", but it could not be launched.

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

“Give me a foothold and I will change the world.”

Death

In 212 BC, during the Second Punic War, Syracuse was besieged by the Romans. Archimedes actively used engineering knowledge to help his people achieve victory. Thus, he designed throwing machines, with the help of which the warriors of Syracuse threw heavy stones at their opponents. When the Romans rushed to the walls of the city, hoping that they would not come under fire, another invention of Archimedes - light throwing devices with close action - helped the Greeks pelt them with cannonballs.

Archimedes' inventions: catapult

The scientist helped his compatriots in naval battles. The cranes he developed grabbed enemy ships with iron hooks, lifted them slightly, and then abruptly threw them back. Because of this, ships turned over and crashed. For a long time, these cranes were considered something of a legend, but in 2005 a group of researchers proved the functionality of such devices by reconstructing them from surviving descriptions.

Archimedes' inventions: lifting machine

Thanks to the efforts of Archimedes, the Romans' hope of storming the city failed. Then they decided to go on a siege. In the fall of 212 BC, the colony was taken by the Romans as a result of treason. Archimedes was killed during this incident. According to one version, he was hacked to death by a Roman soldier, whom the scientist attacked for stepping on his drawing.

Other researchers claim that the place where Archimedes died was his laboratory. The scientist was allegedly so carried away by his research that he refused to immediately follow the Roman soldier who was ordered to take Archimedes to the military leader. He, in anger, pierced the old man with his sword.

There are also 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 both the citizens of Syracuse and his own subjects, gave Archimedes a magnificent funeral. Cicero, who discovered the scientist’s destroyed grave 137 years after his death, saw on it a ball inscribed in a cylinder.

Essays

• Quadrature of a parabola
• About the ball and cylinder
• About spirals
• About conoids and spheroids
• On the equilibrium of plane figures
• Epistle to Eratosthenes on Method
• About floating bodies
• Circle measurement
• Psammit
• Stomachion
• Archimedes' Bull Problem
• Treatise on the construction of a corporeal figure with fourteen bases around a ball
• Book of Lemmas
• A book about constructing a circle divided into seven equal parts
• Book about touching circles

😉 Greetings to regular readers and guests of the site! The article “Archimedes: biography, discoveries, interesting facts” is about the life of the ancient Greek mathematician, physicist and engineer. Years of life 287-212 BC. At the end of the article there is an interesting and informative video about the life of a scientist.

Biography of Archimedes

The famous ancient scientist Archimedes was the son of the astronomer Fidius and received a good education in Alexandria, where he became acquainted with the works of Democritus.

During the siege of Syracuse, Archimedes developed siege engines (flamethrowers), which destroyed a significant part of the enemy army. Archimedes was killed by a Roman soldier, despite the orders of General Marcus Marcellus.

Edouard Vimont (1846-1930). Death of Archimedes

A legend spread by the Greeks says that the great mathematician was stabbed to death while he was writing an equation in the sand, thereby wanting to contrast his superiority with Roman incompetence. It is possible that his death was also revenge for the damage his inventions caused to the Roman fleet.

"Eureka!"

The most famous anecdote about Archimedes tells how he invented a method for determining the volume of an irregularly shaped object. Hieron II ordered the golden crown to be donated to the temple.

Archimedes had to determine whether the jeweler had replaced some of the material with silver. He had to accomplish this task without damaging the crown, so he couldn't melt it in a simple mold to calculate its density.

While bathing, the scientist noticed that the water level in the bath increased when he entered it. He realizes that this effect can be used to determine the volume of the crown.

From the point of view of this experiment, water has an almost constant volume. The crown will displace the amount of water with its own volume. Dividing the mass of the crown by the volume of displaced water gives its density. This density would be lower than gold if less expensive and lighter metals were added to it.

Archimedes, jumping out of the bath, runs naked down the street. He is so excited about his discovery that he forgets to get dressed. He loudly shouts “Eureka!” ("I found"). The experiment was successful and proved that silver had indeed been added to the crown.

The story of the golden crown is not present in any of the known works of Archimedes. In addition, the practical applicability of the described method is questionable due to the need for extreme accuracy in measuring changes in water level.

The sage most likely used the principle known in hydrostat as Archimedes' law, and later described in his treatise on floating bodies.

According to him, a body immersed in a liquid is subjected to a force equal to the weight of the liquid displaced by it. Using this principle, the density of a gold crown can be compared to the density of gold.

Heat ray

Archimedes may have used a group of mirrors acting together as a parabolic mirror to set fire to ships attacking Syracuse. Lucian, a writer of the 2nd century, writes that Archimedes destroyed ships with fire.

In the 6th century, Antimius of Thrall called the weapon of Archimedes “burning glass.” The device, also called the "Thermim Beam Archimedes", was used to focus sunlight onto ships, thereby illuminating them.

This supposed weapon became the subject of controversy during the Renaissance regarding its actual existence. rejected it as impossible. Modern scientists are trying to recreate the described effects using only the tools available in Archimedes' time.

It has been suggested that large numbers of highly polished bronze screens, acting as mirrors, could be used to focus the sun's rays on a ship using the principle of a parabolic mirror.

Experiments of Archimedes in the modern world

In 1973, scientist Ioannis Sakas from Greece conducted an Archimedes heat ray experiment at the naval base in Scaramaga. He used 70 copper-coated mirrors measuring 1.5 by 1 m. They were aimed at a plywood model of the ship at a distance of 50 m.

When the mirrors are focused, the mock-up of the ship ignites in a few seconds. Previously, ships were coated with resinous paint, which likely contributed to the fire.

In October 2005, a group of MIT students conducted an experiment with 127 square mirrors measuring 30 x 30 cm, focusing on a wooden model of a ship at a distance of about 30 meters.

The flame appears on part of the ship in clear weather with a cloudless sky and if the ship remains motionless for about 10 minutes.

The same group is repeating the "MythBusters" television experiment using a wooden fishing boat in San Francisco. Some ignition occurs again. The Myth Hunters define the experience as a failure due to the long time and ideal weather conditions required for ignition.

If Syracuse is in the east, then the Roman fleet attacks in the morning for optimal light focusing. At the same time, conventional weapons such as flaming arrows or catapult-launched projectiles can be used much easier to sink a ship at such a short distance.

Many scientists consider the ancient Greek scientist one of the greatest mathematicians in history, along with Gauss and Euler. His contribution to geometry and mechanics is enormous; he is considered one of the pioneers of mathematical analysis.

He systematically applies mathematics to natural sciences, technological discoveries and inventions. His scientific contributions have been studied and described by Eratosthenes, Conon and Dosithedes.

Works of Archimedes

• the mathematician calculated the surface of a parabolic segment and the volumes of various mathematical bodies;
• he examined several curves and spirals, one of which bears his name: Archimedes spiral;
• gave a definition of semi-regular multistats called Archimedes;
• presented a proof that the array of natural numbers is infinite (also known as Archimedes' axiom).

Archimedes (287 BC - 212 BC) - Greek mathematician, engineer and physicist who laid the foundations of mechanics and hydrostatics. He gained worldwide fame thanks to his discoveries in geometry.

Information about Archimedes was left by Titus Livius, Plutarch, Polybius, Cicero, Vitruvius and other ancient authors. But they all lived after the events described. Archimedes was born in Syracuse (a Greek colony in Sicily). The father of the future scientist was the astronomer and mathematician Phidias, who was closely related to the tyrant of Syracuse. The Greek inventor studied in Alexandria of Egypt - the scientific center of that time. Here he met the astronomer Conon and the philosopher Eratosthenes. Archimedes then returned to Syracuse. Here he was always surrounded by attention and never lacked funds. But real events from his life are difficult to distinguish from the legends that were inspired by his inventions.

Legends

They say that the scientist discovered the famous law of Archimedes while taking a bath. According to legend, he shouted “Eureka!” (“Found it!”) jumped out naked into the street.

According to another legend, Archimedes helped launch a heavy multi-deck ship, built using a special block system. At the same time, he stated: “Give me a foothold, and I can turn the world upside down.”

The scientist's engineering genius manifested itself during the siege of Syracuse during the 2nd Punic War. According to legend, Archimedes was 75 years old at this time. However, the powerful throwing machines designed by the engineer were abandoned by the Roman troops. Special cranes grabbed Roman ships with iron hooks, lifted them up and threw them down so that the ships sank. Additionally, during the Siege of Syracuse, the Roman fleet was burned using mirrors and polished shields that focused the sun's rays onto the ships. Note that the veracity of the latest stories has been confirmed by experiments.

Death of Archimedes

There are several versions of the death of Archimedes. According to the story of John Tsets, at the height of the battle, the mathematician sat near his house and reflected on the drawings that he had made on the road sand. A Roman soldier running past stepped on the drawing, after which the scientist rushed at him with the words: “Don’t touch the drawings!” As a result, the soldier killed the old man in cold blood.

But Plutarch says that a soldier came to Archimedes and said that Marcellus was calling him. But the scientist asked the legionnaire to wait until he solved the problem. The warrior got angry and pierced the inventor with a sword. According to the third version, Archimedes personally went to Marcellus, intending to take him instruments for measuring the Sun. But his burden attracted the attention of the Romans. The latter decided that the scientist was carrying gold or jewelry and killed him.

Diodorus Siculus claims that Archimedes died while sketching a diagram. At this time, the Roman soldier began to drag him, but, absorbed in the diagram, the scientist said: “Get away from my diagram!” Someone give me my car!” The Roman got scared and killed the old man. Nevertheless, Marcellus gave the scientist a magnificent funeral, and the murderer was beheaded. Plutarch also claims that Marcellus was very angry at the death of the inventor, whom he ordered not to be touched.

Scientific activity

Plutarch notes that Archimedes was obsessed with mathematics. While doing science, he even forgot about food. The Greek scientist carried out research on arithmetic, geometry and algebra. In particular, it was Archimedes who found all semiregular polyhedra, developed the doctrine of conic sections and discovered a geometric method for solving cubic equations. He found a general method for calculating volumes and areas. Archimedes' ideas became the basis of integral calculus. But he considered his best achievement to be the determination of the volume and surface of a sphere. Even at his grave, Archimedes asked to knock out a ball inscribed in a cylinder.

The inventor calculated the surface area for a sphere segment and a turn of the so-called “Archimedes spiral”, determined the volumes of the ellipsoid, sphere and paraboloid segments. Archimedes calculated the ratio of the circumference of a circle to its diameter. Archimedes' ideas were significantly ahead of their time. Only in the 17th century. scientists continued and developed the works of the great mathematician.

Archimedes was the first to successfully apply the lever in practice. For example, he built quite a lot of block-lever mechanisms that made it easier to lift and transport heavy loads. The great engineer invented the Archimedes screw (auger), designed to scoop out water. This mechanism is still used in Egypt today. Archimedes became the first theorist of mechanics.

In addition, the Greek scientist built a planetarium, during the movement of which it was possible to observe some planets, sunrise, phases and eclipses of the Moon. He believed that the world system is heliocentric (the planets revolve around the Sun).

The following works of Archimedes have survived to this day:

• "About Spirals";
• “Squaring a parabola”;
• “About floating bodies”;
• “On the ball and the cylinder”;
• "Circle Measurement";
• "Psammit";
• "Stomachion";
• "Book of Lemmas".

Archimedes created more than 40 inventions. Most of them relate to the field of military equipment. For example, the throwing machines invented by Archimedes launched stones weighing 250 kg. Some modern researchers even claim that Archimedes invented cannons.

Named in honor of the brilliant scientist:

• Archimedes crater;
• asteroid 3600 Archimedes;
• streets in Amsterdam, Dnepropetrovsk, Donetsk, Nizhny Novgorod and a square in Syracuse.

Leibniz once said that if you carefully read the works of Archimedes, then the discoveries of geometers will no longer be surprising. And indeed, some of the calculations of the Greek scientist were repeated only 1.5 thousand years later by the same Leibniz and Newton.

Karel Capek wrote the story "The Death of Archimedes". Non-canonical versions of the scientist’s death are given in the stories of Russian writers A. Bashkuev “Kill Archimedes” and O. Voron “War and the Geometer”.

In 1972, the cartoon “Kolya, Olya and Archimedes” was filmed about the great scientist.

Name: Archimedes

Years of life: 287 BC e. - 212 BC e.

State: Ancient Greece

Field of activity: Mathematics, geometry, physics, mechanics

Greatest Achievement: Archimedes is responsible for a number of inventions and discoveries that are important and widely used to this day.

The most famous ancient Greek mathematician, Archimedes, was born in the city of Syracuse in Sicily in 287 BC. His father, whose name was Phidias, gave his son a good education. It was he who introduced him to the sciences and instilled a love for them. Perhaps at a young age Archimedes lived for some time in Egypt. He continued his education in Alexandria. The future mathematician studied the works of scientists and became acquainted with the science of geometry. But he spent most of his life in the city of Syracuse, where he was patronized by the ruler Hiero the second. Archimedes corresponded a lot with other mathematicians who lived at that time. These were the Alexandrian scientists Eratosthenes of Cyrene and Conon of Samos.

Archimedes' throwing machines

Archimedes was the defender of Syracuse during the siege of Syracuse in 213 BC. He invented throwing machines that were used to defend the city. He was greatly frightened by the Romans; they threw fire over a long distance; the stones could weigh up to 250 kilograms. But Syracuse was still captured by the Roman general Marcus Claudius Marcellus in the fall of 212 or spring of 211 BC. Archimedes was killed when Roman invaders sacked the city.

Archimedes' inventions

We know more about Archimedes than about other ancient scientists. But all the known facts of his life are more like funny fiction than the truth. His ingenious inventions make a great impression on people's imagination. Thanks to his inventions, mechanics became a science. He also became famous for his military inventions. He proved many theorems. Archimedes derived the number Pi, which is needed to calculate the areas and volumes of figures with many sides. Many people who lived at that time considered him the son of the gods, while others considered him crazy.

Archimedes spiral

All over the world it is believed that he invented a screw, with the help of which water was raised upward from lakes and rivers located at a lower level than the city. The canals filled faster with water rising in a spiral, and this happened without interruption. The inhabitants of Syracuse no longer suffered from lack of moisture. Their fields bore fruit well and the city prospered. The Archimedean screw is still used by residents of developing countries in Asia and Africa.

The meat grinder we all know in its design also contains a screw (auger) that moves the meat to the knives. Even the most ordinary screws are a brilliant invention of Archimedes. Augers are widely used in factories, in various mechanisms and machines. It is impossible to imagine an airplane or a modern ship without a propeller.

Archimedes' bath, Archimedes' force and Archimedes' law

Archimedes formulated the method of the hydrostatic principle. An interesting story is how he determined the ratio of silver and gold in Hiero's wreath by immersing it in water. An anecdotal version is when a naked Archimedes jumps out of the bath and shouts: “Eureka!” - runs around the city. Of course, this is greatly embellished.

Thus, the scientist found out that if an object is lowered into water, it will either drown or end up on the surface. Archimedes found out that this happens under the pressure of a lifting force (or buoyancy). The water that the object displaces has the same volume as the object being lowered. This means that the buoyant force is equal to the weight of the displaced fluid. It was this force that was called Archimedes.

Heat ray

No less mythical are the stories about the large mirrors that Archimedes used to destroy Roman ships by setting them on fire. Archimedes collected many mirrors and directed the rays they reflected to one point. The ships were built of wood and painted with resin, so they quickly caught fire. He studied catoptrics, that is, the reflection of light rays from mirrors.

But perhaps the ships caught fire from fiery arrows or from “fiery projectiles” fired by throwing machines. Later, some researchers tried to repeat this experiment. Some experimenters succeeded. The Romans, who captured Syracuse, demanded that manuscripts with formulas be given to them, and when Archimedes wrote the formulas on the sand with a stick, and then wiped the sand with his foot, refusing to give them up, they killed him.

Archimedes lever

The story is also interesting when he exclaimed: “Give me a fulcrum, and I will turn the whole Earth over!” Archimedes loved his city of Syracuse very much. He equipped the port with a whole system of levers. With their help it was much easier to lift or move loads. And when the Roman ships got very close to the city, its lever cranes easily lifted and overturned the Roman ships.

His invention is considered to be a mechanical device that demonstrates the movement of the Sun, Moon and other planets. It was a planetarium. It was possible to observe the movements of the Sun and planets. But, unfortunately, it was not preserved. He was taken to Rome by the conqueror of Syracuse, Marcellus. Only a few details have survived from this device.

All his work was theoretical in nature, but his interest in mechanics influenced his mathematical thinking. He derived a formula for calculating the area of ​​any sphere, as well as a formula for its volume. This was his pride. According to these records, they found his tomb; it was all covered with moss, grass, and dirt. When they cleared it, they saw that it depicted a sphere inscribed in a cylinder. This happened a century and a half after his death. Found the grave. Archimedes wrote many works on hydrostatics and theoretical mechanics. He used mechanical theories as a means to solve new mathematical theorems.

There are nine surviving treatises of Archimedes in Greek. A great mathematician and inventor, he was centuries ahead of his time. His theorems are included in the school curriculum in geometry to this day. His “simple” inventions advanced the development of human civilization far forward. He will forever remain in people's memory as a brilliant inventor, mechanic and designer, geometer.