Abstract:
When studying metric spaces, students of higher education often have difficulties
with understanding the basic concepts and properties of these spaces. This, to a large extent,
is a consequence of the significant level of formalization of such concepts on the one hand, and
the preservation of the corresponding formulations and names familiar to students from a school
mathematics course. To overcome these difficulties, it is advisable to use methods of geometric
interpretation and visualization of these properties. At the same time, it is appropriate to use
elements of metric geometry. Its methods make it possible to interpret the geometric features of
the mutual placement of points of metric space in Cartesian (rectangular) coordinate systems,
which are familiar to students of higher education. Moreover, it becomes possible to visualize
these features with the help of graphic editors, since they, as a rule, use numerical values of the
coordinates of points to visualize them. Based on the definition of an angle as an ordered trio
of points of an arbitrary metric space, and the angular characteristic of this angle, the fact of
the flat placement of four points of a non-Euclidean metric space is established, and examples
of digital visualization of this arrangement using the dynamic geometric environment GeoGebra
3D are given.
Description:
Kuzmich, V. I. Analytical and geometric interpretation of the flat arrangement of points by means of metric geometry in the study of metric spaces / V. I. Kuzmich, L. V. Kuzmich, A. G. Savchenko, K. V. Valko // Journal of Physics : Conference Series, XVI International Conference on Mathematics, Science and Technology Education (ICon-MaSTEd 2024) (Kryvyi Rih, Ukraine 15/05/2024 - 17/05/2024). - 2024. - Volume 2871, Issue 1.
