PPLICATION OF KINEMATIC APPROACHES IN GEOMETRIC PROBLEMS

This work is devoted to the use of kinematic methods in the process of solving geometric problems. The first part of the work is devoted to solving geometric problems by considering the movements of some image points. The minimum knowledge required to apply the kinematic method in elementary geometry is briefly outlined. Then a solution to a generalized version of a well-known geometric problem is presented. The importance of studying elements of operator calculus from an interdisciplinary perspective is also presented. The next part of the article examines problems selected according to the principle of gradual complication, from high school to bachelor’s degree. In these problems, the radius of curvature at various points is determined by kinematic way. Using the result of solving a kinematic problem about a body thrown in a horizontal direction, the expression for the radius of curvature of a parabola is determined. One physical method for determining the radius of curvature of a cycloid is presented. The problem of motion, which generates the equations of an ellipse and a hyperbola, is considered, and a kinematic version of determining the radii of curvature at the points of intersection of these curves and axes of symmetry is presented. The main methodological novelty of the work lies in the development, generalization and systematic presentation of kinematic problems that bring geometric results. Some methodological guidelines and arguments are also given to substantiate the importance of the discussed kinematic approaches to solving geometric problems.