THE TRINITY FORMULA AS A RESULT OF EMOTIONAL SEARCH FOR NEW GEOMETRY FORMULAS - Hetmanenko, Lyudmyla (Physical and Mathematical Education, 2023)
This article explores the importance of studying elements of formulaic geometry in the process of mathematical education and proposes original methods for solving classical and authorial problems based on new, previously unknown dependencies. The author introduces the author's triple formula.Formulation of the problem. The modern school curriculum for middle and high school geometry lacks information about elements of formulaic geometry. Some mathematicians, who lacked teaching experience, mistakenly believed that the number of formulas in classical geometry should be minimal, and elementary trigonometric functions were completely discarded. Analysis of current research and personal experience convincingly prove the unreliability of such a position.Materials and methods. A systematic analysis of scientific sources regarding the available information on theoretical concepts and practical applications of formulaic geometry was conducted. The following research methods and tools were used in preparing the article: comparative analysis of theoretical positions disclosed in scientific and educational literature, mathematical analysis and mathematical logic, observations of the educational process of general secondary education students.Results. The research resulted in the systematization of approaches to solving geometric problems using formulas. The peculiarities of applying the formulaic method to solve a large number of classical and authorial geometric problems of varying complexity were revealed. The main research results were obtained using the methods of formulaic geometry. The findings were tested in the scientific school of I.A. Kushnir's "Best Authorial Problem in Geometry" at Borys Grinchenko Kyiv University and are also recommended to students preparing for mathematics Olympiads.Conclusions. Solving geometric problems using the formulaic approach significantly reduces the size of the proof. The use of formulas, properties of geometric figures, and algorithms helps focus on the main ideas of the problem and perform calculations faster and more efficiently. Solving geometric problems using the formulaic approach also has an important emotional component for students studying mathematics. This approach contributes to building confidence in their knowledge. Rational use of formulas and algorithms in solving geometric problems encourages students' logical thinking and understanding of the connections between different geometric objects. Additionally, successful problem solving stimulates positive emotions such as joy in achieving results and satisfaction from one's own competence.
Keywords: formulaic geometry; trinity formula; equisize; geometric Olympiad problems; algebra in geometry