What does the letter v on the forehead mean? Forehead and hairline according to siang min. Mark on the lower right side of the forehead

LOBACHEVSKY Nikolai Ivanovich, Russian mathematician, creator of non-Euclidean geometry.

Pedagogical activity

Born into a poor family of a small employee. Almost all of Lobachevsky's life is connected with Kazan University, which he entered after graduating from high school in 1807. After graduating from the university in 1811, he became a mathematician, in 1814 - an adjunct, in 1816 - an extraordinary and in 1822 - an ordinary professor. Twice (1820-22 and 1823-25) he was dean of the Faculty of Physics and Mathematics, and from 1827 to 1846 - rector of the university.

Under Lobachevsky, Kazan University flourished. Possessing a high sense of duty, Lobachevsky took on difficult tasks and each time fulfilled the mission entrusted to him with honor. Under his leadership, the university library was put in order in 1819. In 1825 Lobachevsky was elected librarian of the university and remained in this post until 1835, combining (from 1827) the duties of a librarian with the duties of a rector. When the construction of buildings began at the university, Lobachevsky became a member of the construction committee (1822), and from 1825 he headed the committee and worked in it until 1848 (with a break in 1827-33).

On the initiative of Lobachevsky, the Scientific Notes of Kazan University began to be published (1834), an astronomical observatory and a large physics laboratory were organized.

Lobachevsky's active university activities were stopped in 1846, when the Ministry of Education rejected the request of the university's academic council to retain Lobachevsky not only at the department, but also as rector. The undeserved blow was all the more noticeable because the Ministry granted the request of the Academic Council, requested in the same petition, to retain astronomer I. M. Simonov, a member of the expedition of F. F. Bellingshausen and M. P. Lazarev (1819-21) at the department. the shores of Antarctica.

Non-Euclidean geometry

The greatest scientific feat is considered to be his creation of the first non-Euclidean geometry, the history of which is usually counted from the meeting of the Department of Physical and Mathematical Sciences at Kazan University on February 11, 1826, at which Lobachevsky delivered a report “A concise presentation of the foundations of geometry with a rigorous proof of the parallel theorem.” In the minutes of the meeting about this great event there is the following entry: “The presentation of G. Ord. Professor Lobachevsky was heard on February 6 of this year with the attachment of his essay in French, about which he wants to know the opinion of the members of the Department and, if it is beneficial, he asks for the essay take into account scientific notes Faculty of Physics and Mathematics."

In 1835, Lobachevsky briefly formulated the motives that led him to the discovery of non-Euclidean geometry: “The futile efforts since the time of Euclid for two thousand years made me suspect that the concepts themselves do not yet contain the truth that they wanted to prove and which they wanted to verify, like others physical laws, can only be experiments, such as, for example, Astronomical observations. Having finally been convinced of the correctness of my guess and considering the difficult question completely resolved, I wrote a discussion about this in 1826.”

Lobachevsky proceeded from the assumption that through a point lying outside a given line, several lines pass through that do not intersect with a given line. Developing the consequences arising from this assumption, which contradicts the famous V postulate (in other versions the 11th axiom) of Euclid’s Elements, Lobachevsky was not afraid to take a daring step, which his predecessors stopped at for fear of contradictions: to construct a geometry that contradicts everyday experience and "common sense" - the quintessence of everyday experience.

Neither the commission consisting of professors I. M. Simonov, A. Ya. Kupfer and adjunct N. D. Brashman, appointed to consider " Concise presentation", nor Lobachevsky's other contemporaries, including outstanding mathematician M.V. Ostrogradsky, could not appreciate Lobachevsky’s discovery. Recognition came only 12 years after his death, when in 1868 E. Beltrami showed that Lobachevsky’s geometry can be realized on pseudospherical surfaces in Euclidean space, if geodesics are taken as straight lines.

Janos Bolyai also came to non-Euclidean geometry, but to a lesser extent. full form and 3 years later (1832).

Further development of Lobachevsky's ideas

Lobachevsky's discovery confronted science with at least two fundamental problems: important issues, which have not been raised since Euclid’s Elements: “What is geometry in general? What geometry describes geometry real world". Before the advent of Lobachevsky's geometry, there was only one geometry - Euclidean, and, accordingly, only it could be considered as a description of the geometry of the real world. The answers to both questions were given by the subsequent development of science: in 1872 Felix Klein defined geometry as the science of invariants of one or another groups of transformations (different geometries correspond to different groups of motions, i.e. transformations under which the distances between any two points are preserved; Lobachevsky geometry studies the invariants of the Lorentz group, and precision geodetic measurements have shown that in areas of the Earth’s surface that can be considered with sufficient accuracy flat, Euclidean geometry is fulfilled). As for Lobachevsky’s geometry, it operates in the space of relativistic (i.e., close to the speed of light) velocities. Lobachevsky entered the history of mathematics not only as a brilliant geometer, but also as the author of fundamental works in the field. algebra, theory of infinite series and approximate solution of equations.

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Biography of Nikolai Lobachevsky (1792-1856)

Short biography:

Education: Kazan University

Place of Birth: Nizhny Novgorod

A place of death: Kazan

– Russian mathematician: biography with photo, place and date of birth, discoveries in mathematics and geometry, contributions to science, non-Euclidean geometry.

One of the world's most eminent mathematicians, William Clifford, once called Nikolai Lobachevsky"Copernicus of Geometry". The Englishman knew what he was talking about - Lobachevsky created a whole new branch of this science - non-Euclidean geometry.

Nikolai Lobachevsky was born into the family of an official in 1792. When Nikolai was 8 years old, his father died. The mother of the future mathematician and three children were left practically in poverty. Fortunately, according to the laws of that time, all three brothers had the right to study at the expense of the treasury, and their mother sent them to the Kazan gymnasium. Nikolai finished it in 1806. An incredible success both for him and for all mathematics was that in 1805 a university was opened in Kazan, and many teachers of the gymnasium not only began to work in it, but also offered their students to take a course of study. The second time, Lobachevsky passed the exams and became a student.

At the university, despite some complaints about his behavior, Lobachevsky was in good standing. Having completed the course of study, he remained at the university and in 1814 became an adjunct (assistant professor) of mathematics. Two years later, with the personal help of rector M. Saltykov, he was elected extraordinary professor. In 1819, after the reorganization of the university, Lobachevsky became dean. After 7 years, his colleagues elected him rector of the university. He successfully solved both administrative and economic problems of the educational institution, not forgetting about teaching and scientific work.

A scientific work Nikolai Ivanovich began back in 1811 with the work “The Theory of the Elliptical Motion of Celestial Bodies.” Lobachevsky also wrote a paper on solution theory algebraic equations. But the main work of his scientific career was the creation of non-Euclidean geometry. In 1826 he read the first report about it. For that time, this bordered on a crime. Both colleagues and superiors sharply criticized the mathematician’s thoughts. Fortunately, since the time of Copernicus, morals have softened somewhat, and the support of the university caretaker M. Musin-Pushkin helped, so Lobachevsky could continue his work and was even awarded an order, and in 1938 he was elevated to the nobility.

Lobachevsky's works on non-Euclidean geometry were also published abroad. Karl Gauss praised Lobachevsky's work in his letters, but did not speak out loud, considering the thoughts of his colleague from Russia too bold. Gauss only recommended that Nikolai Ivanovich be elected a foreign member of the Gottingen Scientific Society.

Nevertheless, during his lifetime, Lobachevsky’s theories did not receive recognition. It was only towards the end of the 19th century that they began to be used when considering the relationship between space and time. But Lobachevsky received his share of recognition. His work at Kazan University made it possible to create a modern educational institution, which had an excellent scientific base. In addition, Lobachevsky’s decisive actions during the cholera epidemic in 1830 and a huge fire in 1842 not only saved the university, but also helped save the lives of townspeople.

Lobachevsky, who was blind by that time, dictated his last work, entitled “Pangeometry,” in 1855, and in February next year the great mathematician died exactly 30 years after his first report on non-Euclidean geometry.

Known as:

Nikolai Ivanovich Lobachevsky (20 November ( December 1) (17921201 ) , Nizhny Novgorod - February 12 (24) , Kazan), great Russian mathematician, creator Lobachevsky geometry, figure in university education and public education. Famous English mathematician William Clifford called Lobachevsky the “Copernicus of geometry.”

Biography

N. I. Lobachevsky was born in the Ardatovsky district Nizhny Novgorod province. His parents were Ivan Maksimovich Lobachevsky (an official in the geodetic department) and Praskovya Aleksandrovna Lobachevskaya. In 1800, after the death of her father, her mother and her family moved to Kazan. There Lobachevsky graduated from the gymnasium (-), and then (-) and the newly founded Kazan Imperial University, to whom he gave 40 years of his life.

While studying at the university, Lobachevsky was greatly influenced by Martin Fedorovich Bartels- friend and teacher of the great German mathematician Carl Friedrich Gauss. He took patronage over a poor but gifted student. In his senior year, Lobachevsky’s description included “dreamy self-conceit, perseverance, disobedience,” as well as “outrageous actions” and even “signs of godlessness.” The threat of expulsion loomed over him, but the intercession of Bartels and other teachers helped avert the danger.

After graduating from the university, Lobachevsky received a degree master's degree in physics and mathematics with honors () and was left at the university. IN 1814 became adjunct, after 2 years - extraordinary, and in 1822- ordinary professor. Students highly appreciated Lobachevsky's lectures.

The range of his duties was extensive - lecturing on mathematics, astronomy and physics, equipping and putting in order the library and museum, etc. The list of official duties even includes “monitoring the reliability” of all students in Kazan.

The 200th anniversary of Lobachevsky was celebrated in 1992. The Bank of Russia issued commemorative coin in the series " Prominent personalities of Russia ».

A crater is named in honor of Lobachevsky Moon. Streets in Moscow and Kazan also bear his name. science Library Kazan University. On March 20, 1956, a decree of the presidium was issued Supreme Council USSR about assignment to Gorky ( Nizhny Novgorod) University named after N.I. Lobachevsky.

Lobachevsky geometry

Main article: Lobachevsky geometry

Student notes of Lobachevsky's lectures have been preserved (from 1817), where they attempted to prove fifth postulate Euclid, but in the manuscript of the textbook “Geometry” () he already abandoned this attempt. IN " Reviews of teaching pure mathematics"For 1822/23 and 1824/25, Lobachevsky pointed out the “still invincible” difficulty of the problem of parallelism and the need to accept in geometry as initial concepts directly acquired from nature.

How can one think that Mr. Lobachevsky, an ordinary professor of mathematics, would write a book for some serious purpose that would bring a little honor to the latter? school teacher? If not scholarship, then at least common sense every teacher should have, and in the new geometry even this latter is often lacking.

Title page of Lobachevsky's book

But Lobachevsky does not give up. B - he publishes articles on “imaginary geometry” in “Scientific Notes”, and then the most complete of his works “ New principles of geometry with a complete theory of parallels».

Not finding understanding at home, he tries to find like-minded people abroad. IN 1840 Lobachevsky prints on German"Geometric Studies on the Theory of Parallels", which contains a clear statement of his main ideas. One copy receives Gauss, the “king of mathematicians” of that time.

As it turned out much later, Gauss himself secretly developed non-Euclidean geometry, but never decided to publish anything on this topic. Having familiarized himself with Lobachevsky's results, he expressed his sympathy for the ideas of the Russian scientist indirectly: he recommended electing Lobachevsky as a foreign corresponding member of the Royal Society of Göttingen. Gauss entrusted rave reviews about Lobachevsky only to his diaries and closest friends.

In popular culture

Proceedings

• N. I. Lobachevsky. Complete collection works in five volumes.

Volume 1, 1946.

• N. I. Lobachevsky. Geometric studies on the theory of parallel lines. On the principles of geometry. Volume 2, 1949.
• N. I. Lobachevsky. Geometry. New principles of geometry with a complete theory of parallels.
• N. I. Lobachevsky. Volume 3, 1951.
• Imaginary geometry.

Application of imaginary geometry to some integrals.

Pangeometry.

• Bell E.T. Creators of mathematics. M.: Education, 1979, 256 pp., chapter 15.
• Vasiliev A.V. Nikolai Ivanovich Lobachevsky. - M.: Science. 1992. - 229 p. (Scientific and biographical series).
• Glazer G.I. History of mathematics in school. - M.: Education, 1964. - P. 345-350.
• Historical and local history House-Museum of N. I. Lobachevsky in Kozlovka, Chuvashia.
• Kagan V.F. Lobachevsky. M.-L.: Publishing House of the USSR Academy of Sciences, 1948, 507 pp. + 17 inserts.

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