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Modelling and Data Analysis
2025. Vol. 15, no. 1, 210–251
https://doi.org/10.17759/mda.2025150111
ISSN: 2219-3758 / 2311-9454 (online)

Sets of points that are a certain distance apart

 
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Abstract

The article continues the cycle ([1] – [15]) of methodological developments by the authors. The article discusses problems related to sets of points whose distances are rational numbers (let's call these sets rational). The study of such sets is related to the solution of Diophantine equations. The relevant tasks can be used when choosing topics for students' research work. The authors draw on their work experience at the Faculty of Information Technology of the MSUPE.

General Information

Journal rubric: Method of Teaching

OpenAlex citations: 2

OpenAlex trends: Computational Geometry and Mesh Generation, Mathematics and Applications, Advanced Numerical Analysis Techniques

Information about the work in OpenAlex

Number of citations: 2

Topics

Computational Geometry and Mesh Generation

This cluster of papers focuses on advances in mesh generation algorithms, including Delaunay triangulations, Voronoi diagrams, and centroidal Voronoi tessellations. It also covers topics such as geometric optimization, quality meshing, computational geometry, hexahedral meshing, and approximation algorithms.

Number of works: 60583  |  Total number of citations: 730924

Topic detailsв OpenAlex

Mathematics and Applications

This cluster of papers covers a wide range of topics in geometric mathematics, including hyperbolic geometry, loops, billiards in ellipses, Poncelet's theorem, Moufang loops, trigonometry, algebraic structures, and their applications in relativity and inversive geometry.

Number of works: 159236  |  Total number of citations: 813807

Topic detailsв OpenAlex

Advanced Numerical Analysis Techniques

This cluster of papers focuses on the application of isogeometric analysis in computational engineering, particularly in the areas of structural analysis, fluid-structure interaction, shape optimization, and boundary element methods. The use of NURBS, finite elements, CAD, mesh refinement, T-splines, and their implementation in CNC machining are central to the research.

Number of works: 101582  |  Total number of citations: 1060909

Topic detailsв OpenAlex

Work details in OpenAlex

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2025150111

Received 31.01.2025

Accepted

Published

For citation: Kulanin, Y.D., Stepanov, M.E. (2025). Sets of points that are a certain distance apart. Modelling and Data Analysis, 15(1), 210–251. (In Russ.). https://doi.org/10.17759/mda.2025150111

© Kulanin Y.D., Stepanov M.E., 2025

License: CC BY-NC 4.0

References

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Information About the Authors

Yevgeny D. Kulanin, Candidate of Science (Physics and Matematics), Professor, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0001-6093-7012, e-mail: lucas03@mail.ru

Mikhail E. Stepanov, Candidate of Science (Education), Associate Professor, Department of Applied Mathematics, Faculty of Information Technologies, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0003-4803-8211, e-mail: mestepanov@yandex.ru

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