On asymptotic features of n-spheres
S. S. Bokov, Ruslan Shmatkov · Izvestiya vuzov Investitsii Stroitelstvo Nedvizhimost · 2025
As an object of computer simulation, a three-dimensional sphere is used in many areas of contemporary science and technology due to its convenience, simplicity, and versatility. An increased number of parameters for contemporary models complicates the limiting area of simulation parameters to an n-dimensional sphere (n-sphere). For example, a four-dimensional sphere used in astronomy to simulate the movement of celestial bodies includes a fourth parameter of time in addition to the length, width, and height of material point movement. In other areas of science, the growing number of simulation parameters increases the dimensionality of the limiting sphere. This sets the problem of the limit number of simulation parameters for maintaining the relevance of the model. The article examines the asymptotic features of n-sphere parameters at an unlimited increase in the sphere dimensionality and number of simulation parameters. For providing an analytical solution to the problem and its numerical simulation, a hypothesis about the limited use of n-spheres for high-order models is put forward. The article may be of interest to researchers and students studying numerical simulation and infinite behavior of hyperspheres.