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ГЕОМЕТРІЯ МАС І БАРИЦЕНТРИЧНИЙ МЕТОД РОЗВ’ЯЗУВАННЯ ПЛАНІМЕТРИЧНИХ ЗАДАЧ

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Працьовитий М., Одинець Ю.
Педагогічні науки: теорія, історія, інноваційні технології
|
2016
|
issue 3(57)
327-340
EN
In the article we put some recommendations on the possibilities to provide to talented math students push out beyond the program material. We propose relatively closed system of educational material on the center of mass. In this paper we propose a relatively closed system of educational material about the center of mass points (centroid), the center of mass of material points (barycenter) and barycenteric geometric method for solving problems for students who are interested in geometry, its methods and connections with physics and for future mathematics teachers that are the students of pedagogical universities studying methods for solving problems of plane geometry and principles of their harmonization. This system includes the theorem of existence and uniqueness of the center of mass and its location and also proofs of basic properties of barycenter. The presentation of theoretical material is complete and strict accompanied by examples and counterexamples, the selection of problems of educational and research character is also available. We justify the expediency of pupils and students of pedagogical universities with barycenteric method of solving problems of plane geometry. Also we base efficiency of vector and coordinate geometry method of building mass, highlights the relationship of physical and metric approaches to key concepts topics including depending optimization and Lagrange and Jacobi identity. We propose order of introduction of concepts (including alternative definition, discusses the sequence of presentation of factual material, give succinct formulation essentially of barycenteric method for solving positional and metric problems and discussed motivational bases of learning etc. Finally we analyse some risk zones and propose some methodological and methodical caveats.
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