Application of Equilibrium Conditions as an Alternative Means of Proving Geometric Statements

Abstract

Key words: mechanics, mathematics, interdisciplinary connections, axiom, theorem, problem, learning The article is devoted to mechanical approaches towards proving geometric statements. In this paper, in order to illustrate the deep connections between physics and geometry, the justifications for geometric statements, using the ideas of statics, is presented. Classifications of physical justifications for geometric statements are given, which is the main scientific and methodological novelty of the paper. The first part of the work represents interdisciplinary connections between physics and geometry along with their features. In the process of their formation and development, the mutual influence of these sciences is shown. The next section presents examples of demonstrative applications of physics in geometry and their classification. The toolkit of physical justifications belonging to the first type, in a sense, already contains a geometric statement that needs to be justified. The second class includes geometric statements supported by the intuitive physical reasoning. The third class includes reasoning that, instead of geometric axiomatics, is based on the application of physical laws and hypotheses. Among the three types mentioned, the evidence, based on the latter, is the most rigorous and independent. The last section of the article discusses the proof of geometric statements based on the application of equilibrium conditions for bodies. The possibilities of applying the discussed approaches in the context of STEM education are presented.