Question

кто из российских математиков начала 19 века совершил переворот в развитии геометрии? в чем состоял этот переворот?

Answer 1

Лобачевский, ввел свою геометрию.

Answer 2

#### Russian Mathematicians in the 19th Century One of the Russian mathematicians who made a significant impact on the development of geometry in the early 19th century was **Nikolai Ivanovich Lobachevsky**. Lobachevsky is known for his groundbreaking work in non-Euclidean geometry, which challenged the traditional Euclidean geometry that had been widely accepted for centuries. #### The Revolution in Geometry Lobachevsky's revolution in geometry consisted of introducing a new system of geometry that did not adhere to Euclid's parallel postulate. Euclid's parallel postulate states that through a point not on a given line, only one line can be drawn parallel to the given line. Lobachevsky proposed an alternative postulate, known as the "Lobachevskian parallel postulate," which states that through a point not on a given line, multiple lines can be drawn parallel to the given line. This seemingly small change had profound implications for the field of geometry. It led to the development of non-Euclidean geometry, which explored geometrical systems where the parallel postulate did not hold. Lobachevsky's work laid the foundation for the study of hyperbolic geometry, which is one of the non-Euclidean geometries. Lobachevsky's ideas were initially met with skepticism and resistance from the mathematical community. However, his work eventually gained recognition and had a significant impact on the development of mathematics and physics. Lobachevsky's non-Euclidean geometry opened up new possibilities and challenged the long-held assumptions about the nature of space. #### Conclusion In summary, Nikolai Ivanovich Lobachevsky, a Russian mathematician of the early 19th century, is credited with revolutionizing the field of geometry. His introduction of non-Euclidean geometry, which challenged the traditional Euclidean geometry, marked a significant turning point in the development of the subject. Lobachevsky's work paved the way for the study of hyperbolic geometry and had a lasting impact on mathematics and physics.