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Modelling and Data Analysis
2022. Vol. 12, no. 4, 94–104
https://doi.org/10.17759/mda.2022120407
ISSN: 2219-3758 / 2311-9454 (online)

On Visualization of Solutions to Some Extreme Problems

 
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Abstract

The article discusses the problem of finding a straight line on a plane, the sum of the squares of the distances to which from n given points of this plane will be the smallest. It is shown how to reduce this problem to solving a similar problem for three points, the solution of which is a straight line containing the major axis of the Steiner ellipse of a triangle with vertices at these points. There is also a hypothesis about the connection of the subject under consideration with the problem of the fields of attraction in the theory of fractals.

General Information

Keywords: visualization, extreme problems, sum of squared distances, complex plane, polynomial, derivative of polynomial, arithmetic mean of roots, center of gravity of roots, Steiner ellipse, minimum straight line, principal component, fractal

Journal rubric: Method of Teaching

OpenAlex citations: 8

OpenAlex trends: Advanced Theoretical and Applied Studies in Material Sciences and Geometry, Aerospace, Electronics, Mathematical Modeling, Advanced Computational Techniques in Science and Engineering

Information about the work in OpenAlex

Number of citations: 8

Topics

Advanced Theoretical and Applied Studies in Material Sciences and Geometry

This cluster of papers focuses on the application of nanomaterials, geometric modeling, and mathematical simulation in engineering. It covers topics such as nanomaterial-based polymer nanocomposites, technological equipment with electrohydraulic drives, vortex chamber pumps, and sustainable energy development. Additionally, it explores the use of descriptive geometry in modeling and design processes.

Number of works: 57200  |  Total number of citations: 226408

Topic detailsв OpenAlex

Aerospace, Electronics, Mathematical Modeling

This cluster of papers covers topics related to forest reforestation, including methods for direct seeding, noise reduction in manufacturing and repair workshops, chip design verification, hydraulic systems management, and seed grading optimization. It also explores environmental impact assessment, vibroacoustic characteristics research, and quality management systems in the context of urban environmental planning.

Number of works: 16661  |  Total number of citations: 17318

Topic detailsв OpenAlex

Advanced Computational Techniques in Science and Engineering

This cluster of papers focuses on the intersection of Internet of Things (IoT) and healthcare systems, including topics such as remote monitoring, algorithmic modeling, wireless sensor networks, telemedicine, biomedical signal processing, and digital information management. The papers also touch upon the application of IoT in smart city healthcare systems and the use of corpus analysis in technical writing classrooms.

Number of works: 19217  |  Total number of citations: 82460

Topic detailsв OpenAlex

Work details in OpenAlex

Article type: scientific article

DOI: https://doi.org/10.17759/mda.2022120407

Received 07.11.2022

Accepted

Published

For citation: Kulanin, Y.D., Stepanov, M.E. (2022). On Visualization of Solutions to Some Extreme Problems. Modelling and Data Analysis, 12(4), 94–104. (In Russ.). https://doi.org/10.17759/mda.2022120407

© Kulanin Y.D., Stepanov M.E., 2022

License: CC BY-NC 4.0

References

  1. Kulanin E.D., Nurkaeva I.M. On two geometric problems on extremums. Mathematics at school. 2019. No. 4. P. 35-40.
  2. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. Propaedeutics of solving extremal problems in the school course of mathematics. Modeling and data analysis. 2019. No. 4. P.127-144.
  3. Kulanin E.D., Nurkaeva I.M. Once again about the Mavlo problem. Mathematics at school. 2020. No. 2. S. 76-79.
  4. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. About different approaches to solving extreme problems. Modeling and data analysis. 2020.     T.11. No. 1. P.40 - 60. 
  5. Cesaro E. Elementary textbook of algebraic analysis and infinitesimal calculus. Part one. ONTI, L-M: 1936. 
  6. Pearson K. On lines and planes of closest fit to systems of points in space,  Philosophical Magazine, (1901) 2, 559—572; http://pca.narod.ru/ 
  7. Zinoviev A. Yu. Visualization of multidimensional data, Krasnoyarsk, KSTU Publishing House, 2000.
  8. (Electronic resource) URL: https://dic.academic.ru/dic.nsf/ruwiki/1105612?ysclid=la3pdtnhsn961871750
  9. Paytgen H.-O., Richter P.H. The beauty of fractals. Images of complex dynamic systems. Moscow: Mir, 1993.
  10. Kulanin Y.D., Stepanov M.E. Comprehensive Consideration of Mathematical Concepts as a Methodical Technique. Modelirovanie  i  analiz  dannykh  =  Modelling  and  Data Analysis, 2022. Vol. 12, no. 4

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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