学习几何是培养启发式思维的最重要途径

N. Sal'kov
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摘要

几何学就其本质而言,是人类生活中最直观的一门科学,因此对于在学校或大学学习的人来说,也是最直观的一门科学--任何书籍,即使是最非技术性的书籍,都包含图画,而图画又与几何学,特别是描述性几何学直接相关。毕竟,几何学研究的是点、线和面,但如果仔细观察,任何图画都是由点、线和面组成的。这一点不难察觉,所以也很难反驳。对于初学者来说,图纸的清晰度是理解课文最重要的帮助。从学校教科书中图画的清晰度开始,第一步是抽象化:研究平面几何中的专有点和平面几何图形。在学习了几何图形的名称之后,学生开始研究构造规律,研究各种定理,证明这些定理,并将这些证明应用于其他更复杂的定理。这就是所谓的基于逻辑构造的启发式思维现象。文章还介绍了如何利用奥林匹克竞赛--城市奥林匹克竞赛和全俄奥林匹克竞赛--来进一步提高学生的启发式思维能力,从而为大学的几何图形系补充人才,并为我国补充 2.5.1--"描述性几何和计算机制图 "方向的科学家。数字产品生命周期支持"。在其他领域也是如此。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
The Study of Geometry as the Most Important Way to Develop Heuristic Thinking
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.
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