ON THE PHYSICAL APPROACH TO SOLVING SOME PROBLEMS OF BYPASSING AREAS

This paper is devoted to the presentation of one physical approach to solving some problems of traversing regions encountered in combinatorics. The paper presents a new approach based on the direct application of formulas for determining the coordinates of the center of gravity of a group of bodies. The paper preliminarily presents the concept of the center of gravity of a set of material points, formulas for determining its coordinates, as well as two main properties/theorems possessed by the center of gravity of an arbitrary set of a finite number of bodies/material points, namely, the theorem of uniqueness of the center of gravity of a system composed of material points, and the theorem of the possibility of grouping material points. After that, the main traditional mathematical approaches used to solve some problems of traversing regions encountered in combinatorics are discussed in detail and summarized in the form of methodological guidelines. Next, a new approach to solving such problems is proposed, based on physical tools, in particular, by directly applying the formulas for determining the coordinates of the center of mass of material points. Some methodological guidelines are given for solving problems of traversing regions using the proposed physical approach. Two problems are examined, in the solution of which both well-known traditional mathematical approaches used in solving similar problems and a proposed new approach utilizing physical tools were presented.