In 1914 he made his debut in the eccentric comedy "Making A Living".

Gloomy mountains sway, In paths the way clears, Meet the living – Ibarruri! And the dead rise to battle!

Among other poetic techniques, the use of visible and precise landscape detail often attracts attention. The baby "sees" the edge where the events depicted by him take place. This land is harsh, the land of "black fields and ravines" of the "steep slopes of Guadarrama" where even "the roads lay sternly to the clear dawn" are "gray paths" "tears flooded the earth".

"Spanish ballads" The baby is stern and tender, angry and touching. The poet is able to find simple and sincere words in which the tragedy of situations, events, human destinies does not leave the reader indifferent, makes him relive the heroic everyday struggles of the Spanish people for freedom and independence.

07.09.2011

Prominent Arab mathematician Muhammad Ben-Musa al-Khorezmi. Abstract

The abstract provides information about Muhammad Ben-Mus al-Khwarizmi (about 780-850 pp.). He is one of the most prominent Arab mathematicians of the first half of the IX century.

About the life of Muhammad bin Mus al-Khwarizmi, no certain information has survived. But, deciphering his full name, we can conclude that the place of his birth was Khorezm (centered in Khiva in Central Asia), that among his ancestors were magicians, sorcerers, who according to religious beliefs were able to influence the world and foretell the fate of man.

Al-Khwarizmi worked in Baghdad, in a group of prominent scholars invited by Caliph al-Mamun to the House of Wisdom. During this period he wrote five scientific papers – on arithmetic, algebra, astronomy, geography and the calendar. In 820, al-Khwarizmi wrote a large treatise entitled "Kitab al-Jabr al-Mukabala" for practical use.

In his introduction, al-Khwarizmi wrote that it is limited to the most accessible and useful in arithmetic, what people use the most in everyday life. As well as those related to land measurement and geometric calculations. Translated, the title of the treatise means: "A book on the operations of jebr (restoration) and mukabala (compilation)". Khorezm does not explain these terms: apparently, they were known before. It is clear from the text that the operation from the name of which the name "algebra" comes is to transfer the members of the equation from one part to another. The second operation is the compilation of similar members of the equation.

Al-Khwarizmi’s treatise consists of two parts – theoretical and practical. The first part contains the rules of multiplication, addition and subtraction of algebraic expressions, as well as the extraction of square roots.

The author pays a lot of attention to solving equations. He gives six types of equations. If we write them by formulas in the modern form, we have the equation: x2 = ax, x2 = a, ax = b, xz + ax = b, x2 + a = bx, ax + b = x2. Al-Khwarizmi provides both algebraic and geometric solutions to these equations. He does not use formulas. Performs all actions and calculations verbally, and then gives a geometric construction. The unknown is called the root, or thing, the square of the unknown – the square. This is how al-Khwarizmi solves the quadratic equation x2 + 21 = 10x.

He writes the condition as follows: "Squares and numbers are equal to the roots, for example, one square and the number 21 are equal to 10 roots of the same square, that is, ask what will become a square, which after adding 21 will be equal to 10 roots of the same square? " To solve, divide the number of roots in half; half of them are 5, multiply this number by itself, we will have the product of 25. Then we should subtract the number 21 from it, get the remainder of 4, and get the square root from it; it is equal to 2. This root must be subtracted from half the number of roots, which is equal to 5; we will have a remainder of 3. This will be the root of the required square, which is 9. Or you can add this root to half the number of roots, the sum will be 7. This will be the root of the required square , and the square itself will be 49.

Consider another geometric solution of the equation x2 + ax = b, which al-Khorezmi gives for the case: x2 + 10x = 39. He does it like this (see figure): to each of the sides of the square ABCD is a rectangle AVRM; complementing the figure with four small squares AMEN, we get a large square GHFE. Assuming that the square ABCD is x2, and the four rectangles AVRM are 10l:, we see that the heights of these rectangles will be determined by 10/4 = 5/2, and the sum of the areas of four small squares AMEN will be equal to 4 * (5/2) 2 = 25. Therefore, the larger square of GHFE is expressed in terms of x2 + 10x + 25. Remembering that x2 +10 x = 39, we find that it is equal to 64.

It turns out that the side of the larger square will be (64) 1/2 = 8, but this same side is expressed by x + 10/2, and therefore x = 8-5 = 3. (Negative root – 13 was not considered).

The next section of the treatise is devoted to questions of geometry. It’s called "Measurement." Here Muhammad ben-Musa al-Khwarizmi shows how to find the area of ​​a square, quadrilateral, triangle, then the length of a circle and the area of ​​a circle.

Al-Khwarizmi found the length of the circle in three ways, namely: multiplied the diameter by (3) 1/7; multiplied the diameter by itself, and then by 10 and extracted the square root of the product, and finally by the method of astronomers – multiplied the diameter by 62832 and divided the product by 20,000. He also found the area of ​​the circle in several ways, and then told how to find the area of ​​the circle. After that, al-Khwarizmi proceeded to find the volumes of parallelepipeds and pyramids. To the pyramids, he attributed the cone. The scientist wrote that the volume of the pyramids of triangular, quadrangular, round and in general any are found by multiplying one third of the area of ​​the base by the height. He also referred to a cylinder as a parallelepiped. Muhammad ben-Musa does not mention the volume of the bullet.

Al-Khwarizmi’s work is the first work in the history of mathematics where algebra is considered an independent science.

The second work of Muhammad bin Musa is called "Arithmetic". In this work, he first talks about the methods used to represent numbers. He rightly attributes the number system, in which nine signs are used, to the Indians. Al-Khwarizmi then gives some rules by which arithmetic operations are performed. When adding, he pays special attention to those cases when the sum of terms exceeds 9. According to this rule, tens should be added to the next name, and under these terms write only what is left of tens. If there is nothing left, then al-Khwarizmi offers to put a circle. It is clear that he knew zero. When adding and subtracting, he advises to start performing actions from higher digits, ie from left to right. The author performs multiplication in the same way as the Indians, writing the numbers in the cells.

Next, the author shows how to perform the action of division, as well as explains the actions with hexadecimal fractions.

According to some researchers, "Arithmetic" by Muhammad bin Musa al-Khorezmi was one of the first Arabic works in which Indian arithmetic is set forth. Later, al-Khwarizmi arithmetic narrative story ideas numbers called "Indian" moved to Western Europe, but later became known as Arabic.

Muhammad bin Musa al-Khwarizmi made excerpts from the astronomical tables of the Indians, known as the "Little Sidginta" and corrected the tables of the chords of Ptolemy, conducting systematic observations in Baghdad and Damascus. Al-Khwarizmi also includes works on astrolabe, sundial and works on geography. There is no exact information about the last years of Muhammad bin Mus al-Khwarizmi’s life. He died about 850

06.09.2011

Charles Chaplin: life and creative path. Abstract

The abstract provides information about Sir Charles Spencer Chaplin (April 16, 1889 – December 25, 1977). This is a famous American actor, director, screenwriter, producer, composer

Born in London, in a family of actors variety show. From 1897 he performed in the music hall, in 1907-1912 – at the F. Carnot Theater, where he mastered the art of pantomime, sculpture, expressive movements. The gift of improvisation and accurate household sketches determined Chaplin’s success in England and during the American tour of 1910-1912.

In December 1913 he signed a contract with the American film company "Keystone" where he began to act in M. Sennett. In 1914 he made his debut in the eccentric comedy "Making A Living". Acting as scurvy villains in films starring F. Sterling, C. Conklin, M. Norman and Fatty, he looked closely at the work of Sennett directors, analyzing the characteristics of the American comic school and the system of comedy masks based on the mismatch between the character’s life role and appearance.

Appearing in 12 films directed by M. Sennett or Sennett and Mabel Norman, Chaplin made his own comedy "Caught In The Rain" (1914), but until the end of the year remained in "Keystone" working alone, then with M. Norman … He still plays Chase’s scum, and even his best work in Sennett’s comedy Tillie’s Punctured Romance (1914) doesn’t suit the actor.

In 1915 he went to the company "Essene" where in the films directed by him on his own scripts gradually appears the image of a burlaka Charlie.

Having gained unprecedented popularity in Sennett’s comedies, Chaplin did not immediately overcome the inertia of thoughtless eccentricity. Still, the material of his tapes is close to real life, and conditional characters acquire the features of real people who experience real joys and sorrows. In the films "Burlak" (The Tramp, 1915), "Recruited" (His New Job, 1915), "Bank" (The Bank, 1915), the new appearance of the hero-shabby corresponds to his human nature and social status – a lonely and defenseless outsider rejected by the world.

In 1916, Chaplin signed a contract with Muchwell, securing creative control and the right to make no more than 12 films a year. In the best films of "Muchwell" such as "Silent Street" (Easy Street, 1917), "The Immigrant" (The Immigrant, 1917) and the new firm "First National" "Dog’s Life" (A Dog’s Life, 1918) , "On the Shoulder" "(Shoulder Arms, 1918) completes the evolution of the image of the little man, who embodies the disenfranchised world of the underprivileged, which is opposed by the wealth, violence and hypocrisy of modern civilization.

With each new work by Chaplin, the demands of the comedy of provisions were brought more and more into line with the demands of the dramatic conflict of good and evil, poverty and wealth, justice and "public order" – drama balanced eccentricity, laughter accompanied by tears, such as "The Kid" 1921), The Pilgrim (1923).