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Verbal counting

Painting, 1895, 107×79 cm

Description of the artwork «Verbal counting»

Painting by artist Bogdanov-Belsky "Oral counting" has almost greater fame than its author. Thanks to the intricate puzzle depicted on it, the work has become a textbook example of a mathematical puzzle. Many of those to whom she came across in the process of learning arithmetic calculations or among the numerous humorous versions of the canvas, of which there are plenty on the network, sometimes have not even heard of its creator.

In addition to the above example, there is another remarkable moment in the picture: the figure of a school teacher. An intellectual in a bow tie and a black tailcoat among ordinary rural boys looks like a foreign body. And this is no accident: "Oral Account" is dedicated to the guardian angel of the artist Bogdanov-Belsky, who gave him and other barefoot village tomboys a start in life in the form of a decent education - a university professor and hereditary nobleman Sergei Aleksandrovich Rachinsky.

Teaching is light


And the school depicted on the canvas is also not easy. Built with funds from Rachinsky in his ancestral village of Tatevo, it became the first Russian educational institution with full board for children of peasants. Bogdanov-Belsky himself was fortunate enough to study there.

The years spent at the Rachinsky school left an indelible mark on the artist's soul. Almost throughout his life, he will return with gratitude and warmth to this era, devoting more and more new canvases as teaching profession, and the process of schooling (1, 2, 3). And no wonder: the educational methods, and the personality of Rachinsky himself, were very outstanding.

The professor's interests were extremely versatile, and to some extent, mutually exclusive. Mathematician and botanist, he was the first to translate into Russian the famous work of Chalz Darwin on the origin of species. At the same time, Rachinsky believed that "The first of the practical needs of the Russian people ... is communication with the Divine"; "The peasant is not drawn to the theater in search of art, but to the church, not to the newspaper, but to the Divine Book".

He also believed that Dante and Shakespeare would be available for understanding to those who mastered Church Slavonic writing, while Beethoven and Bach would become closer to a person familiar with church chants. Moreover, Rachinsky developed a method for treating stuttering by reading Old Church Slavonic texts and church singing.

Therefore, in his school, the compulsory program included the study of the law of God, the interpretation of the Psalter, as well as participation in church services. In the painting Oral Counting, this feature is reflected in the image of the Mother of God with the Child, placed next to the slate board.

Mathematics is the queen of sciences


But Rachinsky relied not only on the church letter. The progressive teacher, developing the author's teaching methods, corresponded with his German colleague Karl Volkmar Stoy and Leo Tolstoy. He personally taught drawing, painting and painting at school.

But Rachinsky's main passion was mathematics, and the emphasis was placed on it in teaching. He created the textbook "1001 Problems for Oral Counting", and the puzzle in the picture of Bogdanov-Belsky from among them. By the way, such a task could not be included in the standard curriculum of public schools, since it did not provide for the study of degrees in primary school. But not in the Rachinsky educational institution.

This example can be solved by knowing about the regularities of adding squares of some two-digit numbers named after the famous Russian teacher. So, according to Rachinsky's sequences, the sum of the squares of the first three numbers on the board will be equal to the sum of the next two. And since in the first and second cases this number is 365, the answer to this already classical problem is extremely simple - 2.

The author: Natalia Azarenko
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About the artwork

Art form: Painting

Subject and objects: Genre scene, Interior

Style of art: Realism

Technique: Oil

Materials: Canvas

Date of creation: 1895

Size: 107×79 cm

Artwork in selections: 36 selections