On asymptotic features of n-spheres
https://doi.org/10.21285/2227-2917-2025-1-64-72
EDN: XSVWXG
Abstract
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.
About the Authors
S. S. Bokov
Russian University of Transport (MIIT)
Russian Federation
Competing Interests:
Russian Federation
Sergei S. Bokov, Senior Lecturer of the Department of Buildings and Structures in Transport
9, 9 Bldg., Obraztsova St., Moscow 127994, GSP-4
AuthorID: 1051214
Competing Interests:
The authors declare no conflict of interests regarding the publication of this article
R. N. Shmatkov
Siberian Transport University
Russian Federation
Competing Interests:
Russian Federation
Ruslan N. Shmatkov, Candidate of Physico-Mathematical Sciences, Associate Professor, Associate Professor of the Department of Higher Mathematics
191 Dusy Kovalchuk St., 630049 Novosibirsk
AuthorID: 14998
Competing Interests:
The authors declare no conflict of interests regarding the publication of this article
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Review
For citations:
Bokov S.S., Shmatkov R.N. On asymptotic features of n-spheres. Izvestiya vuzov. Investitsii. Stroitelstvo. Nedvizhimost. 2025;15(1):64-72. (In Russ.) https://doi.org/10.21285/2227-2917-2025-1-64-72. EDN: XSVWXG
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