Danish physicist Bohr Niels: biography, discoveries. Brief biography of Niels Bohr Niels ole block biography

Why the son and grandson of Nobel laureates have no chance of winning the prize, did Niels Bohr actually measure the height of a building with a barometer, did he play for the Danish national football team and which Russian Nobel laureate can thank him for his prize, read in the section “How to get a Nobel Prize” "

Once, a fellow student of the author of the article, who became a famous hydrodynamic physicist, talked about his colleague: “You know, Thomas once complained to me that the fact that his father was given the Nobel Prize practically puts an end to his own chances for the Nobel Prize . And the fact that there is a famous grandfather in the family makes these chances strictly zero.” Indeed, both Thomas Bohr's father and grandfather became Nobel laureates. But, as we know now, his great-grandfather was nominated for the Nobel Prize in Physiology or Medicine. So, if fate had it its way, there would have been four generations of Nobel laureates in the Bohr family. Today our column has reached the first of the crowned Hogs.

Niels Hendrik David Bohr

Nobel Prize in Physics 1922. The formulation of the Nobel Committee: “For services to the study of the structure of atoms and the radiation emitted by them.”

Niels Bohr was born into the family of a very talented scientist Christian Harald Laurits Peter Emil Bohr, a prominent physiologist and specialist in respiratory chemistry. Christian discovered the so-called Bohr effect, the essence of which is that the curve of blood saturation with hemoglobin depends on the acidity of the blood. For his research, Nils' father was nominated three times for the Nobel Prize in Physiology or Medicine.

It must be said that the Borov family was generally exceptionally talented and gifted in everything. Take Nils' brother, Harald. Not only did he become a mathematician, but he was also a very strong Danish footballer. However, Nils was also a decent goalkeeper in his youth: at one time, Harald and Nils both played for the Danish football club Akademisk Boldklub Gladsaxe (this professional football club still plays in the second division of the Danish Football League). But the story that the future Nobel laureate played for the Danish national football team is not true. He did not play, unlike Harald, who reached the semi-finals with the Danish team at the 1908 Olympics in London.

Niels Bohr was an extraordinary child. Already at school, he was actively interested in physics, mathematics and philosophy: his father’s guests and friends were appropriate. For example, the famous Danish philosopher Harald Geffting or an expert on Scandinavian-Slavic relations, linguist Wilhelm Thomsen.

In 1903, he entered the University of Copenhagen, and his first major research work on measuring the surface tension of water by the oscillation of a water jet was awarded the Gold Medal of the Royal Danish Academy of Sciences (1905). This was purely theoretical work, but in the next two years Bohr occupied his father's physiological laboratory and supplemented the work with an experimental part.

Taking this opportunity, I would like to dispel the story that has long been circulating on the Internet about how a Bohr student replaced a professor of physics at the university (apparently Christian Christiansen, who confirmed the Stefan-Boltzmann law in 1884 - in those years he was the only professor of physics), and as he was supported by Rutherford, to whom Bohr and his professor turned to as an arbitrator.

The story tells how the student Bohr refused to solve the “boring” physical problem of how to measure the height of a tower using a barometer using the standard method (measure the pressure at the foot and at the top), but proposed another, “mocking” one - throw a barometer from the tower and measure the time of fall, measure the shadow cast by the barometer and the shadow cast by the tower, and the barometer itself - and by proportion find out the height of the tower, and even exchange the barometer for information about the height of the tower with the building caretaker.

Let us trust the words of Bohr himself - in 1953 he published an article in memory of a friend: “For the first time I was lucky enough to see and hear Rutherford in the fall of 1911, when, having graduated from the university in Copenhagen, I worked in Cambridge with J. J. Thomson, and Rutherford came from Manchester to speak at the annual Cavendish dinner." Moreover, even then Bohr and Rutherford did not meet, and they began to become “family friends” two years later.

In 1910, Bohr became a master. Simultaneously with receiving his last “educational” degree, another important event happened in the life of the future Nobel laureate: he met Margret Norlund, the sister of the mathematician Nils Norlund. In 1912 they registered their marriage.

Niels Bohr and Margret Norlund during their engagement

Public domain

In 1911, Bohr defended his doctoral dissertation - and again brilliantly, and again his work represented an independent and very powerful work, this time on the electronic theory of metals. Along the way, he proved a theorem of statistical mechanics, from which it followed that the total magnetic moment of any set of electric charges that move in an electric field according to the laws of classical mechanics is equal to zero (in 1919, this theorem would be proven independently of Bohr by a Danish woman physicist, Hendrika Johanna van Leuven, and the theorem will be called the Bohr–van Leuven theorem).

One important conclusion followed from the Borah-van Leeuwen theorem: within the framework of classical physics, it will not be possible to explain the magnetic properties of metals. So Bohr’s dissertation became the great physicist’s first step towards a “quantum revelation.”

Also in 1911, Bohr received a scholarship of 2,500 crowns for an internship abroad. And, naturally, he goes to the capital of world physics - Great Britain, to the Cavendish Laboratory. Work under the guidance of the teacher and mentor of many Nobel laureates, Sir Joseph John Thomson. And he receives a cruel blow - upon arriving, the young scientist “from the wheels” finds an error in his mentor’s calculations, informs him and...

“I was disappointed that Thomson was not interested because his calculations were wrong. This was also my fault. I didn’t know English well enough and therefore couldn’t explain myself... Thomson was a genius who, in fact, showed the way to everyone... In general, working at Cambridge was very interesting, but it was an absolutely useless activity,” writes Bohr about his boss .

It became clear to the scientist that the most interesting things are now happening in Manchester, where another of Thomson’s students, Rutherford, is working. It must be said that two years before Bohr’s arrival in England, Rutherford, already a Nobel laureate, made his famous discovery - the structure of the atomic nucleus. In the laboratory, all they talked about was what consequences this discovery would entail for physics.

Actually, the first consequences happened already in the same year, significant for Bohr, 1911: Rutherford published an article about his planetary model of the atom, according to which electrons revolved around a tiny nucleus, like planets around the Sun. But since the nucleus in Rutherford’s model is positively charged and the electrons are negatively charged, the question arose: how do electrons not fall on it? According to all the rules of classical mechanics and the laws of electromagnetic interaction, this is exactly what should have happened.

Working with Rutherford in Manchester forced Bohr to work on resolving the existing contradiction. In general, the mentorship of “Crocodile” (as the New Zealander was nicknamed by physicists) became a very important impetus for development for Bohr. Subsequently, Bohr even wrote that Rutherford became a second father to him.

After working with Rutherford, Bohr returned to Copenhagen to teach at the university and get married. During their honeymoon, the young family came to visit the Rutherfords, and since then, scientific cooperation has been complemented by family friendship.

Bohr made his brilliant guess in 1913, when he became acquainted with Balmer's formula, which describes a series of spectral lines of the hydrogen atom. Bohr realized: there are orbits in which electrons do not lose energy. And there is a strictly defined number of such orbits; moving from orbit to orbit, the electron emits or absorbs energy equal to the difference in the energies of the orbits, that is, quantized.

In 1913, three parts of Bohr's article “On the structure of atoms and molecules” were published, which described the unified quantum model of the Bohr-Rutherford atom. What’s interesting is that the article was published in a philosophical magazine, Philosophical Magazine. From then on, Bohr's triumphal march through the world of physics began. It is enough to recall two quotes about his theory that have become classic.

“I consider the original quantum theory of spectra put forward by Bohr to be one of the most revolutionary ever created in science; and I don’t know of any other theory that would be more successful.”

Ernest Rutherford

Nobel laureate in physics 1908, teacher and co-author of Niels Bohr

“All my attempts to adapt the theoretical foundations of physics to these results [that is, the consequences of Planck's law for black body radiation] have been a complete failure. It was as if the earth had disappeared from under our feet and there was nowhere to be seen solid soil on which to build. It has always seemed to me a miracle that this wavering and contradictory basis was sufficient to allow Bohr, a man with brilliant intuition and subtle instincts, to find the main laws of spectral lines and electron shells of atoms, including their significance for chemistry. This still seems like a miracle to me. This is the highest musicality in the field of thought."

Bohr Niels Hendrik David (October 7 1885 , Copenhagen - November 18 1962 , Copenhagen), Danish scientist, one of the founders of modern physics. Author of fundamental works on quantum mechanics, the theory of the atom, the atomic nucleus, and nuclear reactions.

Childhood and youth

Niels Bohr was born into the family of Christian Bohr, a professor of physiology at the University of Copenhagen, and Ellen Bohr, who came from a wealthy and influential Jewish family. The parents of Nils and his younger, beloved brother Harald (a future major mathematician) managed to make their sons' childhood happy and meaningful. The beneficial influence of the family, especially the mother, played a decisive role in the formation of their spiritual qualities.

Nils received his primary education at Gammelholm Grammar School, which he graduated from 1903 . During his school years he was an avid football player; later he became interested in skiing and sailing. At the age of twenty-three he graduated from the University of Copenhagen, where he acquired a reputation as an unusually gifted research physicist. His graduation project on determining the surface tension of water from the vibrations of a water jet was awarded a gold medal by the Royal Danish Academy of Sciences. IN 1908-11 Bohr continued to work at the university, where he carried out a number of important studies, in particular on the classical electronic theory of metals, which formed the basis of his doctoral dissertation.

Work in England

Three years after graduating from university, Bohr came to work in England. After a year in Cambridge with J. J. Thomson, Bohr moved to Manchester to work with Rutherford, whose laboratory at that time occupied a leading position. Here, by the time of Bohr's appearance, experiments were taking place that led Rutherford to the planetary model of the atom. More precisely, the model was still in its infancy. Experiments on the passage of alpha particles through pieces of foil led Rutherford to the belief that at the center of the atom there is a small charged nucleus in which almost the entire mass of the atom is concentrated, and much lighter electrons are located around the nucleus. Since the atom as a whole is electrically neutral, the total charge of all electrons must be equal in magnitude to the charge of the nucleus, but differ in sign from it. The conclusion that the charge of the nucleus must be a multiple of the charge of the electron was important, but there was still a lot of uncertainty. Thus, “isotopes” were discovered - substances with the same chemical properties, but with different atomic weights.

The problem of the atomic number of elements. Displacement law

Bohr's first important achievement in Rutherford's laboratory was his understanding that chemical properties are determined by the number of electrons in an atom, and therefore by the charge of the nucleus, and not by its mass, and this explains the existence of isotopes. Since an alpha particle is a helium nucleus with a charge of +2, then during alpha decay, when this particle flies out of the nucleus, the “daughter” element should be located in the periodic table two cells to the left of the “parent”, and during beta decay, when an electron flies out of the nucleus, one cell to the right. This is how the “law of radioactive displacements” was discovered. But this discovery was followed by others, much more important. They concerned the atomic model itself.

Rutherford-Bohr model

This model is often called "planetary" - in it, just as the planets revolve around the Sun, electrons move around the nucleus. But such an atom cannot be stable: under the influence of the Coulomb attraction of the nucleus, each electron moves with acceleration, and an accelerating charge, according to the laws of classical electrodynamics, must emit electromagnetic waves, losing energy. Quantitative calculations show that such “radiation instability” of the atom is catastrophic: in about a hundred-millionth of a second, all electrons would have to lose energy and fall onto the nucleus. But in reality nothing like this happens, and many atoms are quite stable. A problem arose that might seem insoluble. And it really could not be resolved without the involvement of radical new ideas. It was these ideas that were put forward by Bohr.

He postulated that (contrary to the laws of mechanics and electrodynamics) there are orbits in atoms in which electrons do not emit when moving. According to Bohr, an orbit is stable if the angular momentum of the electron located on it is a multiple of h/2p, where h is Planck’s constant. Radiation occurs only when an electron moves from one stable orbit to another, and all the energy released in this case is carried away by one radiation quantum. The energy of such a quantum, equal to the product of frequency n by h, in accordance with the law of conservation of energy, is equal to the difference between the initial and final energies of the electron (“Frequency Rule”). Thus, Bohr proposed to combine Rutherford's model ideas with the idea of ​​quanta, first expressed by Planck in 1900 . Such a connection was fundamentally contrary to all the provisions and traditions of classical theory. But, at the same time, this classical theory was not completely rejected: the electron was considered as a material point moving according to the laws of classical mechanics, but of all the orbits, only those that met the “quantization conditions” were declared “allowed.”

The electron energies in such orbits are inversely proportional to the squares of integers - orbit numbers. Using the “frequency rule,” Bohr came to the conclusion that radiation frequencies must be proportional to the difference between the inverse squares of integers. This pattern had indeed already been established by spectroscopists, but until then it had not found its explanation.

Bohr explained not only the spectrum of the simplest atom - hydrogen, but also helium, including ionized helium, showed how to take into account the influence of nuclear motion, predicted the structure of filling electron shells, which made it possible to understand the physical nature of the periodicity of the chemical properties of elements - the periodic table of Mendeleev. For these works Bohr 1922 was awarded the Nobel Prize.

Bohr Institute in Copenhagen

After completing his work with Rutherford, Bohr returned to Denmark, where he 1916 was invited as a professor at the University of Copenhagen. A year later he was elected a member of the Royal Danish Society (in 1939 he became its president).

IN 1920 Bohr creates the Institute of Theoretical Physics and becomes its director. In recognition of his services, the city provides Bor with the historic "Brewer's House" for the institute. This institute was destined to play an outstanding role in the development of quantum physics. Undoubtedly, the exceptional personal qualities of its director were of decisive importance here. He was constantly surrounded by collaborators and students (in reality there was no line between the first and second), who came to Bor from everywhere. F. Bloch, O. Bohr, W. Weiskopf, H. Casimir, O. Klein, H. Kramers, L. D. Landau, K. Meller, U. Nishika, A. Pais, L. belonged to his large international school. Rosenfeld, J. Wheeler and many others. "The Brewer's House" became the center of attraction for all theorists. W. Heisenberg came to Bohr more than once, just at the time when the “uncertainty principle” was being created, and E. Schrödinger had painful discussions with Bohr there, trying to defend the pure wave point of view. It was at the Bohr Institute that what determined the qualitatively new face of physics of the 20th century was formed.

The Rutherford-Bohr model was obviously inconsistent. It combined both the provisions of classical theory and what clearly contradicted them. To eliminate these contradictions, a radical revision of many of the basic provisions of the theory was required. Here, Bohr’s direct merits, and the role of his scientific authority, and simply his personal influence, were very great. It was Bohr who realized that to create a physical picture of the processes of the microworld, a different approach is needed than for the “world of big things” and he was one of the main creators of this approach. He introduced the concept of the uncontrolled influence of measurement procedures, of “additional” quantities - such that the more accurately one of them is determined, the greater the uncertainty of the other. The name of Bohr is associated with the probabilistic (so-called Copenhagen) interpretation of quantum theory and the consideration of many of its “paradoxes”. Of considerable importance here were discussions between Bohr and Einstein, who never came to terms with the probabilistic interpretation of quantum mechanics. To understand the laws of the microworld and their relationship with the laws of classical (i.e., non-quantum) physics, the principle of correspondence formulated by Bohr is of no small importance.

Nuclear topics

Bohr, starting from Rutherford with nuclear physics, constantly paid great attention to nuclear topics. IN 1936 he proposed the theory of a compound nucleus, and soon the droplet model, which played a significant role in the study of the problem of nuclear fission. Bohr predicted the spontaneous fission of uranium nuclei.

After the actual capture of Denmark by the Nazis, Bohr secretly left his homeland and was taken first to England (he almost died on the plane), and then to America, where he and his son Aage worked for the Manhattan Project in Los Alamos. In the post-war years, he paid great attention to the problem of nuclear arms control, the peaceful use of the atom, even addressed messages to the UN, and participated in the creation of the European Center for Nuclear Research. Judging by the fact that he did not refuse to discuss some aspects of the “atomic project” with the Soviet physicist, he found monopoly ownership of atomic weapons dangerous.

Bohr paid much attention to issues related to physics, including biology. He was invariably occupied with philosophical problems of natural science.

Bohr's moral and scientific authority was exceptionally high. Any, even fleeting, communication with him made an indelible impression. He spoke and wrote in such a way that it was clear: he was intensely looking for words that would express feelings and thoughts with the utmost precision and truth. V. L. Ginzburg was deeply right when he called Bohr uniquely delicate and wise.

Bohr was an honorary member of more than 20 academies of sciences in various countries and a laureate of many national and international prizes.

Date of birth: October 7, 1885
Place of birth: Copenhagen, Denmark
Date of death: November 18, 1962
Place of Death: Copenhagen, Denmark

Niels Henrik David Bohr- Danish physicist. Niels Bohr was born on October 7, 1885 in Copenhagen. His father was also a physicist and was twice nominated for the Nobel Prize.

Already at school, Nils became interested in physics, mathematics and philosophy, as well as football, where he played as a goalkeeper for the Akademisk club along with his brother.

In 1903, Bohr began studying at the University of Copenhagen, studying physics, chemistry, astronomy and mathematics. Again, with my brother, I created a circle among students to study philosophy.

In 1906, he conducted a study to determine the surface tension of water using jet oscillations, for which he was awarded a gold medal from the Royal Danish Society. Over the next year, he refined his work and presented it to a higher audience.

In 1910, Bohr became a master, and a year later a doctor of science, defending his dissertation on the classical theory of metals and their electronic structure. In his dissertation, he proved a theorem of classical mechanics, which was discovered in 1919 by another physicist van Leeuwen, and therefore was named after the surnames of Bohr and this scientist.

In 1911, Bohr was awarded a scholarship for an internship at Cambridge with Thomson, but due to the stardom of his mentor, Bohr did not get along with him and went to Manchester, where he began to work together with Rutherford, who at that time created a model of the atom according to the type of arrangement of planets in the Solar System.

Bohr also took part in the development of this model, and after that he studied alpha and beta rays. In 1912 he returned to Denmark and soon married his friend's sister.

Soon Bohr wrote an article on the deceleration of charged particles when passing through any substance and passed it on to Rutherford, who published it in 1913.

Bohr continued to work at the university, worked as a teacher and studied the theory of atomic structure through the prism of quantum mechanics.

In 1913, he discovered the laws of the arrangement of lines for the structure inside the atom and the principle of its radiation. He sent a draft version of the article to his friend Rutherford, and soon published his article in the Philosophical Magazine. According to Bohr's theory, there are certain lines in an atom through which electrons and other particles inside it pass, which releases energy.

His theory substantiated the emission of hydrogen, and he also obtained a constant value for the Rydberg quantity.

In 1914, he met Einstein, and after that he worked as a lecturer in mathematical physics at the University of Manchester, where he worked until 1916. In parallel with his work as a teacher, he worked on his theory of applying it to many-electron atoms, but there was no success.

In 1914 he explained the splitting of spectral lines, but only half, and in 1916, after bringing quantum conditions to a unified state and introducing quantum numbers into circulation, he again began to intensively approach his theory from a new angle.

In 1916, he became head of the department of theoretical physics at the University of Copenhagen, and a year later he petitioned the Danish authorities to build a new educational institution, which opened in March 1921 and was named Niels Bohr Institute for Theoretical Physics.

In 1918, he wrote an article on the interaction of quantum theory and physics in its classical manifestation, and soon formulated the correspondence principle, on the basis of which Heisenberg created mathematical mechanics in 1925.

In 1921, Bohr, based on the periodic system of Mendeleev, gave a scheme for filling the space of an atom with electrons, and in 1922 he received the Nobel Prize for his discovery of this scheme.

In 1927, he worked on changes to the principles of quantum mechanics and presented his concept of complementarity based on dualism.

This principle became the basis for Bohr's creation of the Copenhagen interpretation of quantum mechanics, which became a stumbling block between him and the rest of the scientific world, including Einstein.

In the 1930s, Bohr became interested in nuclear research and in 1936 he formulated a formulation for the occurrence of nuclear reactions. He developed his idea and in 1953 created an optical model of the nucleus, explained the principle of its fission and the theory of half-life.

In 1933 he created a Committee to help scientists who fled Nazi Germany, and in 1940 Denmark was completely occupied by the Germans. Bohr, because of his half-Jewish origin, feared for his fate, but in 1941 he met with the head of the German atomic project about the possibility of using nuclear weapons.

Bohr pretended that he did not understand Heisenerg and refused to cooperate, and in 1943 he fled to England and then to the USA, where he worked under a different name and created an atomic bomb. Gradually learning all its terrifying consequences, he called on Roosevelt and Churchill to abandon the use of such weapons and establish a ban.

In 1950, he wrote a letter to the UN to ban the use of nuclear weapons.

At the end of his life he wrote articles, gave lectures and studied elementary particles.

Achievements of Niels Bohr:

Discoveries in the field of atomic structure, the principle of complementarity, nuclear theory and quantum theory
Nobel Prize
Numerous medals and academic degrees

Dates from the biography of Niels Bohr:

October 7, 1885 – born in Copenhagen
1903-1910 – studies at the University of Copenhagen
1906 - first scientific work
1911 – Doctor of Science, meeting Rutherford
1922 – Nobel Prize
1941 - work on the atomic bomb begins
November 18, 1962 - death

Interesting Niels Bohr Facts:

Had 6 children, one of whom died at a young age, and one became a physicist and received a Nobel Prize
Member of the USSR Academy of Sciences as a foreign member
An element of the periodic table and a crater on the Moon bear his name.
Established a medal in his name and awarded himself its first copy

Hello! Let's assume this is an equilateral triangle. And I want to create another shape from this equilateral triangle. I want to do this by dividing each side of the triangle into three equal parts... Three equal parts... This equilateral triangle may not be drawn perfectly, but I think you'll understand. And in each middle part I want to build one more equilateral triangle. So in the middle part, right here, I'm going to make another equilateral triangle... Here too... And here's another equilateral triangle. And from an equilateral triangle it turned out something like a Star of David. And I want to do this again, i.e. I will divide each side into three equal parts, and in each middle part I will draw another equilateral triangle. An equilateral triangle in each middle part... I'll do this for each side. Here and here... I think you get the idea... Here, here, here... I'm almost done with this step... This is what the figure will look like now. And I can do this again - once again divide each segment into three equal parts and in each middle part draw one equilateral triangle: here, here, here, here, and so on. I think you understand where this is going... And I could continue to do this forever. In this lesson I want to think about what will happen to this figure. What I'm drawing now, i.e. if we continue to do this indefinitely, at each step we will divide each side of the figure into three equal parts, and then add one equilateral triangle to each middle part - this figure presented here is called a Koch snowflake. Koch's snowflake... It was first described by this gentleman, a Swedish mathematician whose name was Niels Fabian Helge von Koch. And this snowflake is one of the earliest examples of fractals. Those. this is a fractal. Why is it considered a fractal? Because it looks very much like itself at any scale at which you view it. For example, if you look at it on this scale, then in this part you see a bunch of triangles, but if you enlarge, for example, this part, then you will still see something like this figure. And if you enlarge it again, you will see the same figure. Those. A fractal is a figure made up of several parts that, at any scale, look similar to the entire figure. What’s especially interesting (and why I included such a lesson in the geometry playlist) is that the perimeter of this figure is equal to infinity. Those. If you build a figure like the Koch snowflake, you will have to add another small equilateral triangle to each small triangle an infinite number of times. And to show that the perimeter of such a figure is equal to infinity, let's look at one of its sides here... Here is one of its sides. If we started with the original triangle, this is where this side would be. And suppose its length is equal to S. If we divide this side into three equal parts, then the length of this part will be equal to S/3, the length of this part will also be S/3... Actually, I’d better write below: S/3, S/ 3, S/3. Then we draw an equilateral triangle to the middle part. Like this. Those. the length of each side is now S/3. And the length of this entire new part... It can no longer be called just a line, because there is now a triangle on it... The length of this part, this side, is now equal not to S, but [(S/3)*4 ]. Previously, the length was equal to [(S/3)*3], but now we have one, two, three, four segments of length S/3. Now, after we have added one triangle to the original side, the length of our new side will be equal to 4 times S/3, i.e. (4/3)*S. So, if the original perimeter (i.e. if there was only one triangle) was P₀, then after adding one set of triangles, the perimeter of P1 would be 4/3 times the original perimeter. Because the length of each side of the figure will now be 4/3 times greater than originally. Those. the original perimeter Р₀ consisted of three sides, then each of their sides began to have a length 4/3 times greater, which means that the new perimeter Р₁ will be equal to 4/3 times Р₀. And after adding the second set of triangles, the perimeter of P₂ will be equal to 4/3 times P₁. Those. after each addition of new triangles, the perimeter of the figure becomes 4/3 times larger than the previous perimeter. And if you add new triangles an infinite number of times, then it turns out that when calculating the perimeter, you multiply some number by 4/3 an infinite number of times - therefore, you get an infinite perimeter value. This means that the perimeter with the index “infinity” P∞ (the perimeter of the figure if you add triangles to it an infinite number of times) is equal to infinity. Well, it's interesting, of course, to imagine a figure that has an infinite perimeter, but what's more interesting is that this figure actually has a finite area. When I say finite area, I mean a limited amount of space. I can draw some shape around and this Koch snowflake will never go beyond its boundaries. And to think... Well, I won't give a formal proof. Let's just think about what happens on either side of the figure. So, for the first time, at the first separation step, this triangle appears... At the second step, these two triangles appear, and also these two. And then triangles appear here, here, here, here, etc. But notice that you can keep adding more and more triangles, essentially an infinite number of them, but you will never get beyond this point. The same restriction will be observed for this side, also for this side, and for this, for this, and also for this. Those. even if you add triangles an infinite number of times, the area of ​​this figure, this Koch snowflake, will never be greater than the area of ​​this bounding hexagon... Well, or greater than the area of ​​this figure... I draw an arbitrary figure that extends beyond the hexagon. You could draw a circle that extends beyond it... So, this figure drawn in blue or this hexagon drawn in purple, of course, have a certain area. And the area of ​​this Koch snowflake will always be limited, even if you add triangles to it an infinite number of times. So there's a lot of interesting stuff here. The first is that it is a fractal. You can increase it in size and at the same time we will see the same figure. The second is an infinite perimeter. And the third is the final area. Now you may say: “But these are too abstract things, they don’t exist in the real world!” But there's this fun fractal experiment that people talk about. This is a calculation of the perimeter of England (well, actually, this can be done for any country). The outline of England looks something like this... So the first way you could approximate the perimeter is to measure this distance, plus this distance, plus this distance, plus this distance, plus this distance and this distance . Then you might think, well, this shape has a finite perimeter. It is clear that its area is finite. But it is still clear that this is not the best way to calculate the perimeter; you can use a better method. Instead of this approximate calculation, you can draw smaller lines around the border, and this will be more accurate. Then you'll think, okay, this is a much better approximation. But, suppose, if you enlarge this figure... If you enlarge it well, then the border will look something like this. .. It will have curves like this... And, in fact, when you calculated the perimeter here, you simply calculated its height, like this. Of course, this will not be a perimeter, and you will need to divide the border into many parts, approximately like this, to get an accurate perimeter. But even in this case, we can say that this is not an entirely accurate calculation of the perimeter, because If you enlarge this part of the line, it will turn out that in the enlarged version it looks different - for example, like this. Accordingly, the division lines will look different - like this. Then you will say: “Eh, no, we need to be more precise!” And you will divide this line into parts even more. And this can be done endlessly, with millimeter precision. The real border of an island or continent (or anything else) is actually a fractal, i.e. a figure with an infinite perimeter, the calculation of which can reach, so to speak, the atomic level. But still the perimeter will not be accurate. But this is almost the same phenomenon as Koch's snowflake, and it can be interesting to think about it. That's all for today. See you in the next lesson!

Soviet film actress Tatyana Andreevna Bozhok was born into the family of a railway worker and a housewife in 1957 in Moscow. In the family she was the youngest daughter and the sixth child. Since childhood, Tanya not only studied well, but was also interested in theatrical art: she went to the drama club of the Palace of Pioneers on Shabolovka.

At the age of 15, the assistant director of the film “Every Day of Doctor Kalinnikova” noticed her in the studio and invited Tatyana to film. This film became the debut in the film career of the young actress.

Movies

In Viktor Titov’s drama, dedicated to the work and scientific discoveries of Dr. G. Ilizarov, Tatyana Bozhok played the role of patient Tanechka. Famous artists became her partners in the workshop.

Romantics

Photos of young Tatyana ended up in the Mosfilm file, and immediately after the first work, the young artist received an offer from Sergei Bondarchuk himself, who was selecting the cast for his film “They Fought for the Motherland.” A short girl with large, sensitive eyes and a thin voice was cast in the role of a nurse in the epic drama of the master.

After a successfully performed role, he invites Tatyana Bozhok to study in his workshop at VGIK, which he runs together with his wife. Since his students have already completed 1 year of study, the girl is taken straight into the 2nd year without exams.

Cinema hall

Thanks to her youthful appearance, even the matured and already married actress often got the roles of young ladies. These are young teachers who have barely graduated from college (“The Adventures of Petrov and Vasechkin”, “Citizens of the Universe”, “Beware, Cornflower!”), and pioneer leaders (“Yeralash”, “Everything is the other way around”), and young secretaries or telephone operators (“Wick” ). Each role played by Tatyana Bozhok was quickly remembered by the audience thanks to her gift of transformation.

After graduating from the institute, the actress manages to star in the comedy “Ladies Invite Gentlemen,” where she played the main role. Her partners on the stage were actors who were venerable by that time and.

Cinema

The 23-year-old inexperienced graduate of VGIK was somewhat complex at first, but her partner supported the girl and often gave wise advice on working on her image. And Leonid Kuravlev treated the young artist very tenderly and fatherly. It happened that while filming in another city, he even fed her tasty supplies. Tatiana Bozhok still has a good relationship with him.

Another significant work of the early period was her role as Masha from the film “The Singles Are Provided with a Hostel.” And again Tatyana Bozhok finds herself in the company of famous stars of Soviet cinema:,. The actress also played the main role in Arnold Agababov’s film “There, Beyond the Seven Mountains,” about the love of a Russian girl from the Siberian wilderness and a native Caucasian Armenian from Yerevan.

Particularly memorable roles of the actress were her work in films for children and in the almanac “Jumble,” in which she starred for 30 years, starting in 1973. Many fans often thought that Tatyana Bozhok was the mother of Fedya Stukov, the actor who played Tom Sawyer. But in real life, the actress is not a relative of Fedor.

Even the episodic appearance of Tatyana Bozhok in the frame was remembered by the audience. And her phrase “me too, James Bond has been found!” from the epic film “Guest from the Future,” where she played Kolya’s mother, became a catchphrase.

Cinema

One of the popular roles of the actress is the role of teachers. These are often naive, eccentric people who may suffer from their absent-mindedness and indecisiveness. Such teachers, performed by Tatyana Bozhok, can be found in children's films “The Adventures of Petrov and Vasechkin”, “Beware, Cornflower!”. And for her role as a teacher in the film “Citizens of the Universe,” Tatyana Bozhok even received an award for best actress at the Moscow Festival of Young Filmmakers in 1984.

Voice acting

During the period of stagnation in Russian cinema, Tatyana Bozhok switched to working on scoring cartoons and foreign films. At first, she used more of her voice, which was given to her by nature. A high, almost childish timbre allowed her to voice funny cartoon characters, as well as children. But for adult roles, Tatyana Andreevna needed to change her voice, making it lower.

Tatiana Bozhok |