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

Article type: scientific article

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

Received: 07.11.2022

Accepted:

For citation: Kulanin Y.D., Stepanov M.E. On Visualization of Solutions to Some Extreme Problems. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2022. Vol. 12, no. 4, pp. 94–104. DOI: 10.17759/mda.2022120407. (In Russ., аbstr. in Engl.)

References

  1. Kulanin E.D., Nurkaeva I.M. On two geometric problems on extremums. Mathematics at school. 2019. No. 4. P. 35-40.
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  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, PhD in Physics and Matematics, Professor, Moscow State University of Psychology and Education, Moscow, Russia, ORCID: https://orcid.org/0000-0001-6093-7012, e-mail: lucas03@mail.ru

Mikhail E. Stepanov, PhD in Education, Associate Professor, Moscow State University of Psychology and Education, Moscow, Russia, ORCID: https://orcid.org/0000-0003-4803-8211, e-mail: mestepanov@yandex.ru

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