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Modelling and Data Analysis
2021. Vol. 11, no. 1, 40–60
doi:10.17759/mda.2021110104
ISSN: 2219-3758 / 2311-9454 (online)

On Different Approaches to Solving Extreme Problems

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Y.D. Kulanin, I.M. Nurkaeva, M.E. Stepanov

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Abstract

The article discusses the geometric and analytical methods for solving known extreme problems and identifies the logical relationships between these problems, the preference for using one or another method for solving extreme problems is shown by specific examples.

General Information

Keywords: Extreme problems, Lemoine point, Lhuillier point, isogonality, centroid, Lagrange multiplier method, triangle, tetrahedron

Journal rubric: Optimization Methods

DOI: https://doi.org/10.17759/mda.2021110104

For citation: Kulanin Y.D., Nurkaeva I.M., Stepanov M.E. On Different Approaches to Solving Extreme Problems. Modelirovanie i analiz dannikh = Modelling and Data Analysis, 2021. Vol. 11, no. 1, pp. 40–60. DOI: 10.17759/mda.2021110104. (In Russ., аbstr. in Engl.)

References

  1. Kulanin E.D., Nurkaeva I.M. On two geometric problems on the extremum // Mathematics in School. M., 2019. No. 4. – pp. 35–40.
  2. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. Propaedeutics of solving extreme problems in the school course of mathematics. // Data modeling and analysis. 2019. No. 4. – pp. 127–144.
  3. Kulanin E.D., Stepanov M.E., Nurkaeva I.M. The role of figurative thinking in scientific thinking. // Data modeling and analysis. 2020. – vol. 10. – No. 2, pp. 110–128.
  4. Ponarin Y.P. Elementary geometry: in 2 t. – T. 2: solid geometry, transform space. – M.: MCNMO, 2006.
  5. Prasolov V.V. Problems of plane geometry: a tutorial. – 6th ed. stereotype. – M.: MCNMO, 2007. – pp. 282–283.
  6. Stepanov M.E. The image of the force field as a heuristic model in mathematics”. Data modeling and analysis. Proceedings of the Faculty of Information Technologies of MSPPU. – 2007, Issue 3.
  7. Prasolov V.V., Tikhomirov V.M. Geometry. MCNMO, 1997.

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

Irina M. Nurkaeva, Candidate of Science (Education), Associate Professor of the Department of Applied Informatics and Multimedia Technologies, Moscow State University of Psychology and Education, Moscow, Russian Federation, ORCID: https://orcid.org/0000-0002-1949-6734, e-mail: nurkaevaim@yandex.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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