Synergetic Effects of Schwartz Cylinder’s Computer Design in Mathematics Education

In this paper, one of the "problem zones" in mathematics concerned with the surface area of three-dimensional bodies is presented by computer and mathematical modeling with synergetic effects. The main classroom activity of students concerns the learning problem with mastering by students understanding of "problem zones" essence. Students construct the multifaceted surfaces of Schwartz cylinder (or "boot") using computer and mathematical modeling and adapt the most important generalized constructions of surface area to the actual positions of mathematical knowledge and fractal parameters. The computer design and mathematical modeling of nonlinear dynamics of synergetic effects manifestation are developed step by step and dynamic invariants are revealed in the course of surface area mastering. Namely, the means of the QT Creator environment are used for computer design of non-linear dynamics of functional and fractal parameters and technological constructs. Students reveal the regularities and irregularities of lateral surface approximations of Schwartz cylinder in small group working. The study was carried out on the basis of lateral surface triangulations of the cylinder with regular and irregular limiting grinding by layered polyhedral complexes using computer and mathematical modeling tools. The integration stages of computer design and mathematical modeling of complex mathematical construct make the possibility of essence revealing and the students creativity development. It shows the novelty and breakthrough of our method compared to conventional methods.