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Nikolai Ivanovich Lobachevsky
Nikolai Ivanovich Lobachevsky is a famous Russian mathematician who was born in 1792. He was the first to discover the internal consistency and stability of non-Euclidean geometry. He was born in a poor family engaged in government service. He developed the principles of physics using his revolutionary methods of Non Euclidean geometry. His method is also used more in the theory of relativity in physics. He was admitted to Kazan University in 1807 to study medicine. In the following year of Lobachevsky's admission to that university, a teacher of pure mathematics was called from Germany. Astronomer J. J. Litro also taught. Under their influence, Lobachevsky decided to study mathematics and science. He completed his master's degree in mathematics and physics from Kazan University in 1811.
In 1812, he completed a paper entitled "The theory of elliptical motion of heavenly bodies". Two years later, he became an associate professor at Kazan University, and in 1816, he was appointed a distinguished professor. He became a full professor in 1822 and was also the head of mathematical experts at Kazan University. His important contribution is to contribute to the development of new and modern methods in the field of geometry by disagreeing with Euclid's fifth postulate. The fifth postulate mentioned by Euclid in his element is mentioned in modern times as follows.
Through a point parallel to the given line only one line can be drawn parallel to the given line. This is the essence of Euclid's parallel postulate. Euclid's first book referred to as Euclid's elements nearly 2000 years ago and its contents were first reviewed by the Greek mathematician Proclus. In that review, Proclus disagreed with the fifth postulate. Proclus' disagreement with Euclid's fifth postulate was repeated by many geometers.
Gauss tried to influence this postulate from 1792, but he realized in 1813 that it would be wrong to prove this postulate mathematically, and after the proof seemed to contradict Sacher's proof, Gauss mentioned the possibility of developing a new geometry. This was received by Lobachevsky. Many mathematicians mentioned about Non-Euclidean geometry, but the basis of its systematic and systematic development was established by Lobachevsky. He published a new system of geometry. He realized that Euclid's fifth postulate was not true and named it "imaginary" to create a new system or Non-Euclidean geometry. But this work of his was not accepted by geometers during his lifetime. He mentioned something different from the fifth postulate in his geometry.
Through a given point lying outside the given line at least two straight lines can be drawn that do not intersect the given line. Based on this, his parallel postulate is mentioned as follows.
There exist two lines parallel to a given line through a given point not on the line.
The difference between the geometry developed by Lobachevsky and the Euclidean geometry is the parallel postulate which he mentioned in a new form in the fifth postulate. He accepted the remaining four. This is how he developed Non Euclidean geometry.
Overall, his contributions to the field of mathematics are mentioned in the following points:
• Started axiometic of Non Euclidean geometry.
• Started On the principles of geometry.
• Published Imaginary geometry and theory of parallel which helps in the development of Non Euclidean geometry.
• Introduced the new branch of geometry.
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