Synergy of Computer Modeling of Lateral Surface ”Area” of Schwartz’s Cylinder

摘要

In this article problems of students' development by means of computer and mathematical modeling of surface area concept are discussed. The difficult mathematical concept is investigated on the example of lateral surface "area" of Schwartz's cylinder or Schwartz's "boot" with use of the Qt Creator environment. The directions and basic constructs of computer and mathematical modeling in the conditions of triangulations crushing of the cylinder lateral surface and the identification of dynamics growth of the areas of the corresponding manysided complexes in research activity of students setting in small groups are revealed. Logistic mapping is reviewed as the basic instrument of triangulations crushing of lateral surface of the cylinder, which based on ideas of T. Malthus and generating compliance to the scenario of P. Verhulst of chaotic dynamics of nontrivial growth of many-sided complexes of the areas. Some of the new regularities similar to expansion of a tree of M. Feigenbaum via the cascade of bifurcation transitions of doubling of the period are received. It is concern of the synergy research of growth of the areas of many-sided complexes, search of bifurcation points, pools of an attraction and fluctuations of the operating parameters of the area's growth. The connection of research activity of students with increase of mathematical competence and creative activity processes of self-organization and educational motivation is established.