Modelling and Data Analysis

2022. Vol. 12, no. 4, 94–104

doi:10.17759/mda.2022120407

ISSN: 2219-3758 / 2311-9454 (online)

# On Visualization of Solutions to Some Extreme Problems

## 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

- Kulanin E.D., Nurkaeva I.M. On two geometric problems on extremums. Mathematics at school. 2019. No. 4. P. 35-40.
- 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.
- Kulanin E.D., Nurkaeva I.M. Once again about the Mavlo problem. Mathematics at school. 2020. No. 2. S. 76-79.
- 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.
- Cesaro E. Elementary textbook of algebraic analysis and infinitesimal calculus. Part one. ONTI, L-M: 1936.
- 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/
- Zinoviev A. Yu. Visualization of multidimensional data, Krasnoyarsk, KSTU Publishing House, 2000.
- (Electronic resource) URL: https://dic.academic.ru/dic.nsf/ruwiki/1105612?ysclid=la3pdtnhsn961871750
- Paytgen H.-O., Richter P.H. The beauty of fractals. Images of complex dynamic systems. Moscow: Mir, 1993.
- 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

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