Author: Safarov, To’lqin Nazarovich

Annotation: Cyclic surfaces in the Galilean space were studied in this work and compared with the saddle-shaped surface in the Euclidean space. That is, it was shown that the saddle-shaped surfaces in the Euclidean space are divided into two types in the Galilean space. An example is that a hyperbolic paraboloid in Euclidean space is a saddle-shaped and cyclic surface in Galilean space. In it, the equation of the surface in the Galilean space in vector form, the first and second quadratic forms of the surface, and the full curvatures were derived. The family of cyclic surfaces in Galilean space is sufficiently illuminated. In order to develop the geometrical knowledge of students majoring in mathematics in higher education institutions, the distinction between saddle-shaped surfaces in Euclidean and Galilean spaces and their general aspects are revealed.

Keywords: Euclidean space, Galilean space, non-Euclidean geometry, saddle surfaces, cyclic surfaces, surface equations, first and second quadratic forms, full curvature.

Pages in journal: 605 - 614