Biography, legends, discoveries of the ancient Greek scientist Archimedes and his discoveries Archimedes is an ancient Greek mathematician, physicist, mechanic and engineer from Syracuse. Made many discoveries in geometry. He laid the foundations of mechanics and hydrostatics, and was the author of a number of important inventions. Forward > Biography of the scientist Archimedes was born in Syracuse (Sicily) and lived in this city during the era of the 1st and 2nd Punic Wars. It is believed that he was the son of the astronomer Phidias. He began his scientific career as a mechanic and technician. Archimedes traveled to Egypt and became close to Alexandrian scientists, including Conon and Eratosthenes. This was the impetus for the development of his outstanding abilities. Archimedes was close to the Syracusan king Hieron II. During the 2nd Punic War, Archimedes organized the engineering defense of Syracuse against Roman troops. His war machines forced the Romans to abandon their attempts to take the city by storm and force them to resort to a long siege. During the capture of the city by the troops of Marcellus, Archimedes was killed by a Roman soldier, whom, according to legend, he greeted with the words “don’t touch my drawings.” At the grave of Archimedes, a monument was erected with the image of a ball and a cylinder described around it. The epitaph indicated that the volumes of these bodies are related as 2: 3 - the discovery of Archimedes, which he especially appreciated.< Назад Вперед >About the work of Archimedes< Назад Вперед >The works of Archimedes show that he was well acquainted with the mathematics and astronomy of his time, and amaze with the depth of penetration into the essence of the problems under consideration. A number of works take the form of messages to friends and colleagues. Sometimes Archimedes first informed them of his discoveries without proof, adding with subtle irony a few incorrect sentences. In the IX - XI centuries. Archimedes' works were translated into Arabic from the 13th century. they appear in Western Europe in Latin translation. From the 16th century Printed editions of Archimedes begin to appear in the 17th - 19th centuries. they are translated into new languages. The first edition of individual works of Archimedes in Russian dates back to 1823. Some of Archimedes’ works have not reached us or are known only in fragments, and his “Message to Eratosthenes” was found only in 1906. Interests and first works< Назад Вперед >Mechanics was constantly in the circle of interests of Archimedes. In one of his first works, he studies the distribution of loads between the supports of a beam. Archimedes owns the definition of the concept of the center of gravity of a body. Using, in particular, integration methods, he found the position of the center of gravity of various figures and bodies. Archimedes gave a mathematical derivation of the laws of leverage. He is credited with the proud phrase: “Give me a place to stand, and I will move the Earth.” Archimedes laid the foundations of hydrostatics. He formulated the main principles of this discipline, including the famous law of Archimedes. Archimedes's last work was devoted to the study of the equilibrium of floating bodies. At the same time, he identifies stable equilibrium positions. Archimedes invented a water-lifting mechanism, the so-called. Archimedes propeller, which was the prototype of ship propellers, as well as aircraft propellers. They say that Archimedes found the solution to the problem of determining the amount of gold and silver in Hiero's sacrificial crown when he sat in the bath, and ran home naked shouting “Eureka!” ("found!"). Legends< Назад Вперед >Already during the life of Archimedes, legends were created around his name, the reason for which was his amazing inventions, which had a stunning effect on his contemporaries. There is a well-known story about how Archimedes was able to determine whether the crown of King Hiero was made of pure gold or whether the jeweler mixed a significant amount of silver into it. The specific gravity of gold was known, but the difficulty was to accurately determine the volume of the crown: after all, it had an irregular shape! Archimedes pondered this problem all the time. One day he was taking a bath, and then a brilliant idea came to his mind: by immersing the crown in water, you can determine its volume by measuring the volume of water displaced by it. According to legend, Archimedes ran naked into the street shouting “Eureka!” (εύρηκ α), that is, “Found!” At this point, the fundamental law of hydrostatics was discovered: Archimedes' law. Another legend says that the heavy multi-deck ship Syracuse, built by Hieron as a gift to the Egyptian king Ptolemy, could not be launched. Archimedes built a system of blocks (pulley hoist), with the help of which he was able to do this work with one movement of his hand. According to legend, Archimedes said at the same time: “If I had another Earth at my disposal to stand on, I would move ours” (in another version: “Give me a fulcrum, and I will turn the world upside down”). Archimedes turns over planet Earth Death of a great scientist< Назад Вперед >The story of the death of Archimedes at the hands of the Romans exists in several versions: The story of John Tzetz (Chiliad, book II): in the midst of the battle, 75-year-old Archimedes sat on the threshold of his house, pondering in depth over the drawings he made right on the road sand. At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman shouting: “Don’t touch my drawings!” The soldier stopped and coldly killed the old man with his sword. Plutarch's story: “A soldier approached Archimedes and announced that Marcellus was calling him. But Archimedes insistently asked him to wait one minute, so that the problem he was working on would not remain unsolved. The soldier, who did not care about his proof, became angry and pierced him with his sword.” The warrior burst into the house of Archimedes to rob, raised his sword at the owner, and he only managed to shout: “Stop, wait at least a little. I want to finish solving the problem, and then do whatever you want!” Archimedes himself went to Marcellus to take him his instruments for measuring the magnitude of the Sun. On the way, his burden attracted the attention of Roman soldiers. They decided that the scientist was carrying gold or jewelry in the casket, and, without thinking twice, cut his throat. The supposed tomb of Archimedes in Syracuse Plutarch claims that the consul Marcellus was angry at the death of Archimedes, whom he allegedly ordered not to be touched. Cicero, who was quaestor in Sicily in 75 BC. e., writes in Tusculan Conversations (Book V) that in 75 BC. e., 137 years after these events, it was possible to discover the dilapidated tomb of Archimedes; on it, as Archimedes bequeathed, there was an image of a ball inscribed in a cylinder. Death of Archimedes according to one version In memory of Archimedes< Назад Вперед >In memory of the great ancient Greek scientist, the following were named: The boat “Archimedes” The asteroid “Archimedes” And also in those days they began to mint coins with the face of Archimedes: Click to enlarge Presentation prepared< Назад Выйти >Kirzhaev Dmitry Information Electronic encyclopedia "Wikipedia" Electronic encyclopedia "BSU" Finish > End of slide show Click to exit< Уменьшить

Archimedes

This is an amazing man whose name

people have remembered for more than 2,000 years.

He was a talented mathematician

mechanic and engineer.

Every schoolchild is familiar with chi c lo π ,

lever balance rule

"golden" rule of mechanics,

law of floating bodies, etc.

The name of Archimedes lives in legends.

I was interested in learning something new about him.

WITH possession:

• Biography
• Mathematical works
• Archimedes screw
• Archimedean spiral
• Celestial Sphere by Archimedes
• Lever balance rule
• The golden rule of mechanics
• Block device
• Legends
• Conclusion

Biography

Archimedes born 287 BC in Syracuse on the island of Sicily. Archimedes' father, the astronomer and mathematician Phidias, was closely related to Hiero, the tyrant of Syracuse. The father instilled in his son a love of mathematics, mechanics and astronomy from childhood.

In Alexandria of Egypt - the scientific and cultural center of that time - Archimedes met famous Alexandrian scientists.

He corresponded with Eratosthenes until the end of his life.

It was here that Archimedes became acquainted with the works of Democritus, Eudoxus and other outstanding Greek geometers.

After leaving Alexandria, Archimedes returned to Sicily. In Syracuse he was surrounded by attention and did not need funds. Because of its long history, Archimedes' life is closely intertwined with legends.

Mathematical works

Archimedes was a remarkable practical mechanic and theorist, but the main work of his life was mathematics. According to Plutarch, Archimedes was simply obsessed with her. He forgot about food and did not take care of himself at all. His works related to almost all areas of mathematics of that time: he did remarkable research in geometry, arithmetic, and algebra.

He found all the semiregular polyhedra that now bear his name, significantly developed the doctrine of conic sections, and gave a geometric method for solving cubic equations, the roots of which he found using the intersection of a parabola and a hyperbola. Archimedes also carried out a complete study of these equations, that is, he found under what conditions they would have real positive different roots and under what conditions the roots would coincide.

Snub cube

Truncated tetrahedron

Cuboctahedron

13 treatises of Archimedes have reached us

• The treatise “On the Ball and the Cylinder” established that the ratio of their volumes is 2/3. The ball inscribed in the cylinder was carved on his grave.
• The essay “On the Equilibrium of Plane Figures” is devoted to the study of the center of gravity of various figures.
• In his treatise “On Conoids and Spheroids,” Archimedes examines the sphere, ellipsoid, paraboloid and hyperboloid of revolution and their segments and determines their volumes.
• In the essay “On Spirals” he explores the properties of the curve that received his name and the tangent to it.
• In his treatise “Measurement of the Circle,” Archimedes proposed a method for determining the number Pi, which was used until the end of the 17th century.
• In "Psammit" ("Calculus of grains of sand"), Archimedes proposes a number system that made it possible to write down extremely large numbers, which amazed the imagination of his contemporaries. “Counted” them up to 10 64.
• In "Squaring the Parabola" he determines the area of ​​a segment of a parabola first using a "mechanical" method, and then proves the results geometrically.
• Archimedes owns the “Book of Lemmas”, “Stomachion” and was discovered only in the 20th century. "Method" (or "Ephod") and "Regular Heptagon". In the Method, Archimedes describes the process of discovery in mathematics, making a clear distinction between his mechanical techniques and mathematical proof.

The surviving works of Archimedes can be divided into three groups:

First group - determination of the areas of curvilinear figures or, accordingly, the volumes of bodies.

Archimedes found a general method that allows one to find any area or volume. Using his method, he determined the areas and volumes of almost all bodies that were considered in ancient mathematics.

He considered his best achievement to be the determination of the surface area and volume of a sphere.

Archimedes' ideas formed the basis of integral calculus.

The second group consists of works By geometric analysis of statistical hydrostatic problems:

"On the equilibrium of plane figures."

Famous hydrostatic law ,

entered into science as Archimedes' law , formulated in the treatise "On Floating Bodies."

For every body

immersed in liquid

there is a buoyant force directed upward and

equal to the weight of the fluid displaced by it.

Archimedes' law is also true for gases.

F A = ρ and · g ∙ V T = P and

To the third group can be attributed various mathematical works: For example, as among cylinders, inscribed into a ball, find the cylinder with the largest volume?

In progress "On Measuring a Circle" Archimedes gave his famous approximation of the number π: « Archimedean number ».

He was able to assess the accuracy of this approximation:

To prove this, he constructed inscribed and circumscribed 96-gons for the circle and calculated the lengths of their sides.

Archimedes screw

Archimedes became famous for many mechanical designs. The endless screw he invented for scooping water moves water through the pipe to a height of up to 4 m.

It is still used in Egypt.

Archimedean spiral -

flat curve,

trajectory of point M,

moving from a point 0

at a constant speed along a beam rotating around pole 0

with constant angular velocity .

Equation in polar coordinates:

r = a∙f, where a is a constant.

"Celestial Sphere" by Archimedes

Archimedes built a planetarium or “celestial sphere”, during the movement of which one could observe the movement of the five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, the disappearance of both bodies beyond the horizon.

After the death of Archimedes

the planetarium was taken out

Marcellus to Rome,

where throughout

several centuries

was admired

In the treatise “On Leverages” Archimedes established

LEVER EQUILIBRIUM RULE

Opened "golden" mechanical rule : the number of times a mechanism gives a gain in strength, the same number of times it gives a loss in distance “Give me a foothold and I will change the whole world”

Archimedes was the first to invent

block device,

studied its mechanical properties

and put it into practice

Legend says that the luxurious ship Syrokosia, built by Hieron as a gift to the Egyptian king Ptolemy, could not be launched. Archimedes built a system of blocks (pulley hoist), with which he was able to do this work with the help of a few people.

Legend of the Crown

Exists the legend of how King Hiero ordered Archimedes to check whether the jeweler had mixed silver in his golden crown. The integrity of the product could not be compromised. Archimedes could not complete this task for a long time. The solution came by chance when he lay down in the bathtub and noticed the displacement of liquid. Archimedes shouted: “Eureka!” - “Found it!”, and ran naked into the street. He realized that the volume of a body immersed in water is equal to the volume of displaced water. Thus, Archimedes found out that silver was mixed into gold, exposed the deceiver and discovered the basic law of hydrostatics!

Siege of Syracuse

Engineering genius Archimedes showed particular strength during the siege of Syracuse by the Romans in 212 BC. e. But at that time he was already 75 years old! Powerful throwing machines built by Archimedes threw heavy stones at the Roman troops. Thinking that they would be safe at the very walls of the city, the Romans rushed there, but at that time light, short-range throwing machines pelted them with a hail of cannonballs. Powerful cranes grabbed ships with iron hooks, lifted them up, and then threw them down, so that the ships turned over and sank.

According to legend, during the siege, the Roman fleet was burned by the defenders of the city, who, using mirrors and shields polished to a shine, focused the sun's rays on them on the orders of Archimedes.

Legends of Death

According to the first, in the midst of the battle, he sat on the threshold of his house, thinking deeply about the drawings he made right on the road sand.

At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman shouting: “Don’t touch my drawings!”

This phrase cost Archimedes his life. The soldier stopped and coldly killed the old man with his sword.

Second version says that the Roman commander Marcellus specially sent a warrior to search for Archimedes.

The warrior found the scientist and said:

- Come with me, Marcellus is calling you.

- What kind of Marcellus?! I have to solve the problem!

The angry Roman drew his sword and killed Archimedes.

About Archimedes in verse

And many years before us, during a difficult year, the native Syracuse was defended by the scientist Archimedes.

Captivated by an unknown plan, He did not know that there were enemies in the city, And in thought, on the hot earth, He drew some circles.

He drew thoughtfully, not proudly, Forgetting current affairs, - And suddenly, with an incomprehensible chord, the Shadow of a spear crossed the drawing.

But frightening the killers with his calmness, He, without humiliating himself, without trembling, extended his hand, protecting not himself, but the signs of the drawing.

One of the large lunar craters (82 kilometers wide) was named after Archimedes

Used materials:

• http://class-fizika.spb.ru
• http://ru.wikipedia.org
• http://www.home-edu.ru
• http://www.chrono.ru
• http://www.krugosvet.ru
• http://tmn.fio.ru
• http://edu.nstu.ru
• http://www.mirf.ru/archive.php
• Physicon program

Life of Archimedes. Life of Archimedes. Archimedes received an excellent education from his father, the astronomer and mathematician Phidias, a relative of the Syracusan tyrant Hiero II, who patronized Archimedes. Archimedes received an excellent education from his father, the astronomer and mathematician Phidias, a relative of the Syracusan tyrant Hiero II, who patronized Archimedes.

Mechanics. Mechanics. The basic principles of statics are formulated in the essay “On the Equilibrium of Plane Figures.” The basic principles of statics are formulated in the essay “On the Equilibrium of Plane Figures.” The famous law of hydrostatics, which entered science with his name (see Archimedes' law), was formulated in the treatise “On Floating Bodies.” The famous law of hydrostatics, which entered science with his name (see Archimedes' law), was formulated in the treatise “On Floating Bodies.”

Death of Archimedes. Death of Archimedes. On the tombstone of Archimedes, as the scientist said, a cylinder with an inscribed sphere was depicted, and the epitaph spoke of Archimedes’ greatest discovery - that the volumes of these bodies are in the ratio 3:2. When the Roman orator and public figure Cicero, who lived in the 1st century. BC, was in Sicily, he also saw this monument with a ball and a cylinder overgrown with bushes and thorns.

And in conclusion... And in conclusion... We all know Archimedes as the greatest mathematician and physicist, who issued many laws that have survived to this day. A mechanic who made many discoveries that are used in mechanical engineering today. We all know Archimedes as the greatest mathematician and physicist, who issued many laws that have survived to this day. A mechanic who made many discoveries that are used in mechanical engineering today.

Slide 2

Biography of Archimedes

Archimedes (287 BC - 212 BC) - ancient Greek mathematician, mechanic and engineer from Syracuse. His father was the astronomer Phidias, who instilled in his son a love of mathematics, mechanics and astronomy from childhood. Already during the life of Archimedes, legends were created around his name, the reason for which was his amazing inventions, which had a stunning effect on his contemporaries. There is a well-known story about how Archimedes was able to determine whether the crown of King Hiero was made of pure gold or whether the jeweler mixed a significant amount of silver into it. The specific gravity of gold was known, but the difficulty was to accurately determine the volume of the crown: after all, it had an irregular shape! Archimedes pondered this problem all the time. One day he was taking a bath, and then a brilliant idea came to his mind: by immersing the crown in water, you can determine its volume by measuring the volume of water displaced by it. According to legend, Archimedes jumped naked into the street shouting “Eureka!”, i.e., “Found it!” And indeed, at that moment the fundamental law of hydrostatics was discovered.

Slide 3

Archimedes was a remarkable practical mechanic and theorist, but his main work in life was mathematics. According to Plutarch, Archimedes was simply obsessed with her. He forgot about food and did not take care of himself at all. His works related to almost all areas of mathematics of that time: he did remarkable research in geometry, arithmetic, and algebra. Thus, he found all the semiregular polyhedra that now bear his name, significantly developed the doctrine of conic sections, and gave a geometric method for solving cubic equations, the roots of which he found using the intersection of a parabola and a hyperbola. Archimedes conducted a complete study of these equations, that is, he found under what conditions they would have different roots and under what conditions the roots would coincide. Archimedes' ideas were almost two millennia ahead of their time. Only in the 17th century were scientists able to continue and develop the works of the great Greek mathematician. Only then was their true meaning revealed.

Slide 4

Archimedes' inventions

Archimedes became famous for other mechanical structures. The endless or Archimedean screw he invented for scooping up water is still used in Egypt. Archimedes built a planetarium or “celestial sphere”, during which one could observe the movement of the five planets, the rising of the Sun and the Moon, the phases and eclipses of the Moon, and the disappearance of both bodies beyond the horizon.

Slide 5

Legends of Death

According to the first, in the midst of the battle, Archimedes sat on the threshold of his house, pondering in depth over the drawings he made right on the road sand. At this time, a Roman soldier running past stepped on the drawing, and the indignant scientist rushed at the Roman shouting: “Don’t touch my drawings!” This phrase cost Archimedes his life. The soldier stopped and coldly killed the old man with his sword. The second version says that the Roman commander Marcellus specifically sent a warrior to search for Archimedes. The warrior found the scientist and said: “Come with me, Marcellus is calling you.” “What kind of Marcellus?!” I have to solve the problem! The angry Roman drew his sword and killed Archimedes. According to the third version, a warrior burst into the house of Archimedes for robbery, raised his sword at the owner, and he only managed to shout: “Stop, wait at least a little. I want to finish solving the problem, and then do what you want!” Finally, the fourth version is this: Archimedes himself went to Marcellus to take him his instruments for measuring the magnitude of the Sun. On the way, his burden attracted the attention of Roman soldiers. They decided that the scientist was carrying gold or jewelry in the casket, and, without thinking twice, cut his throat. Such are the legends. However, many historians believe that Archimedes was not killed by accident - after all, his mind was worth an entire army in those days.

Archimedes (BC) Archimedes devoted himself to mathematics and mechanics. The devices and machines he designed were perceived by his contemporaries as technological marvels. He discovered the law of specific gravity and studied the theory of lifting mechanisms. Archimedes devoted himself to mathematics and mechanics. The devices and machines he designed were perceived by his contemporaries as technological miracles. He discovered the law of specific gravity and studied the theory of lifting mechanisms. His inventions included the Archimedes screw, a device for raising water or bulk materials such as sand. Archimedes said of the lever, the theory of which he studied: “Give me a fulcrum, and I will turn the whole world.” Among his inventions is the Archimedes screw, a device for raising water or bulk materials such as sand. Archimedes said about the lever, the theory of which he was studying: “Give me a fulcrum, and I will turn the whole world over.”

Why does buoyant force occur? The liquid presses on the side walls with a force opposite in direction and equal in magnitude, therefore the forces acting on the side walls of the body are mutually balanced, their resultant is zero. But the forces acting on the upper and lower parts are not equal. A column of water h 1 presses on the upper part with a force F 1. And on the lower part a column of water h 2 presses with a force F 2. The value of the buoyant force is equal to the difference F 2 -F 1.

Archimedes' Law: "A body immersed in a liquid loses its weight as much as the weight of the displaced liquid." Archimedes' Law: "A body immersed in a liquid loses its weight as much as the weight of the displaced liquid." the buoyancy force depends: on V t, on the density of the liquid, but does not depend on the type of substance from which the body is made, the depth of immersion, on the shape of the object with equal volume, the buoyancy force depends: on V t, on the density of the liquid, but does not depend on the type of substance from of which the body is made, the depth of immersion, the shape of the object with equal volume