However, in the concepts of non-Euclidean geometry and Riemannian space, parallel lines can intersect at infinity, and the intersection of parallel lines has greatly inspired Einstein. The person who laid the theory of non-Euclidean geometry and Riemannian space was also the first person to put forward the intersection of parallel lines. Ivanovic? Lobachevsky.
Lobachevsky 1856 was born in Russia, and his father also has deep research in the field of mathematics. Before his death, he had been studying the fifth postulate left by Euclid. After several generations of research, geometric problems were finally summed up by Euclid in the third century BC, and it was written as Geometry Elements, and geometry was officially named European Geometry.
Euclid gave five axioms and five postulates at the beginning of the Elements of Geometry. These five axioms can be applied to almost any science, and the five postulates can only be used in geometry. Euclid was very satisfied with the first four postulates, except the last postulate that studied parallel lines.
According to his idea, if a straight line intersects with two straight lines and the sum of two internal angles on the same side is less than two angles, then under infinite extension, the two internal angles must intersect, but Euclid can't give any proof. As a pioneer of geometric concepts and a mathematical researcher, he wants to solve his problems to surpass him.
However, from the third century to the19th century, countless researchers did not take this step. Lobachevsky began to study the fifth postulate from 18 15. At first, he tried to give his own proof in the thoughts of his predecessors, but after successive failures, he summed up a truth.
Since so many researchers have failed to prove it for so many years, it is impossible to succeed even if he continues to prove it? Lobachevsky changed his mind? Completely deny the fifth postulate? , that is, parallel lines do not intersect.
Generally speaking, denying the postulate put forward by Euclid, the pioneer of geometry, or even denying the research of dozens of generations, I'm afraid I can only say that he is bold. However, after a series of calculations and studies, he has established a new geometry, which consists of a new axiomatic system without any contradiction.
However, because the prototype and analogy of the new geometry were not found in reality, Lobachevsky defined this clock geometry as? Imagine geometry? 1826, Lobachevsky first proposed it at the academic conference of the Department of Physical Mathematics of Kazan University? Non-Euclidean geometry? Shortly after the opening, the audience reacted indifferently.
The academic committee of the department entrusted simonov, Gupfer and Bolesman to form a three-person appraisal team, but it was undoubtedly negative and even the papers were lost. Unwilling to fail, Lobachevsky devoted himself to his research, but the mathematical circles kept laughing at and questioning him.
Three years later, he wrote Principles of Geometry. Although he made a supplement in his paper, this paper even aroused the anger of academic authorities. A man named La Bucek made a personal attack on him in the newspaper Son of the Motherland, although he refuted it.
But Sons of the Motherland caught his article, and even Gauss, the enlightenment mathematician of non-European geometry, admired him very much. However, in the face of some arguments, he held a negative attitude towards Lobachevsky and non-European geometry, which plunged Lobachevsky into the whirlpool of public opinion.
The society even removed him from his post as a professor, but he didn't give up. Just before his death, he wrote his last book, On Geometry, but 1856 when he died, no one recognized him. Until 12, an Italian mathematician wrote An Attempt to Explain Non-European Geometry.
Is non-Euclidean geometry hotly debated again, and people call it Lobachevsky? Copernicus in geometry? .