The Study of Geometry as the Most Important Way to Develop Heuristic Thinking

Abstract

Geometry by its nature is the most visual science of all that takes place in the life of mankind, and therefore the most visual for those who study at school or university – any book, even the most non-technical, contains drawings, and drawings, in turn, are directly related to geometry in general and descriptive geometry in general in particular. After all, geometry studies points, lines and surfaces, but if you look closely, any drawing consists of points, lines and surfaces. It is not difficult to notice, so it is difficult to refute. The clarity of the drawings for beginners to learn something is the most important help for understanding the text. From the clarity of the school with its drawings in textbooks, the first step is taken to abstraction: the study of exclusively points and flat geometric shapes that are included in planimetry. After studying the names of geometric shapes, the student begins to study the laws of construction, to study various theorems, to prove them, to apply these proofs to other, more complex theorems. Here comes into play a phenomenon that can be called heuristic thinking based on logical constructions. The article also shows the use of Olympiads – urban and All-Russian – to further improve the development of heuristic thinking among students in order to replenish the departments of geometric profiles of universities as a result, as well as replenish our country with scientists in the direction 2.5.1 — "Descriptive geometry and computer graphics. Digital product lifecycle support." And in other areas, too.