浅析数学中的美

浅析数学中的美

刘志有

（咸阳师范学院 数学与信息科学学院，陕西 712000）

摘 要

数学是研究现实世界中的空间形式与数量关系的科学，是刻画自然规律和社会规律的科学语言和有效工具，数学对推动人类生产生活和改造自然起着重大的作用．数学美即是蕴藏于它所特有的抽象概念、公式符号、命题模型、结构系统、推理论证、思维方法等等之中的简单、和谐、严谨、奇异等形式，它是数学创造的自由形式，它揭示了规律性，是一种科学的真实美．本文将论述数学中的简洁美、对称美、和谐美、符号美、奇异美、意象美，这些美不但令人赏心悦目，能够陶冶人的性情，能够使人聪明，而且更能使人高尚. 研究数学中的美，使我们感受美的神韵，提高我们对数学的学习兴趣，培养良好的思维品质，提高我们的数学素养，使我们更加热爱数学，进而更加热爱科学．

关键词 :简洁美；对称美；和谐美；符号美；奇异美；意象美

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Simply Analyzing the Beauty in the Mathematics

Liu Zhi You

(Xian Yang Normal University Mathematics and Information Science

Department Shaanxi 712000)

Abstract

Mathematics, not only as a kind of science which research the relationship between the space form in the real world and the stichomythic but also as a scientific language and the effective tool which portrays natural laws and the social rules , plays a significant role in impelling the humanity to produce lives and transforming our mother nature. Mathematical beauty is one of science beauties, which is a form of simplexes, harmony, precision and singularity of it’s own abstract conception, the formula symbols, propositional model, structural systems, reasoning argument, mode of thinking and so on. It is a free-form in the mathematical creation it reveals the regular pattern. It is a real beauty science. The following paper will state the compact beauty, symmetry beauty, harmonious beauty, symbol beauty, singular beauty, image beauty in the mathematics. These beauties not only make us pleased, singular and wise, increasing our interest but also make us a noble person. In research of the beauty of mathematics, we can feel the spirit of the beauty, stimulate our interest in mathematics-learning and develop our good thinking quality which makes us love math more as well as loving science more.

Keywords: Compact beauty；Symmetry beauty；Harmonious beauty；Symbol

beauty；Singular beauty；Image Beauty

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目 录

摘 要.............................................................................................................................I ABSTRACT.................................................................................................................. II 前 言............................................................................................................................ 1 1

数学中的简洁美..................................................................................................... 2 1.1 数学语言的简洁性 ............................................................................................ 2 1.2 数学方法的简洁性 ............................................................................................ 4 2

数学中的对称美..................................................................................................... 5 2.1 2.2 2.3 3

对称性在几何中的应用.................................................................................. 5 对称性在积分中的应用.................................................................................. 7 对称性在方程中的应用.................................................................................. 8

数学中的和谐美..................................................................................................... 9 3.1 3.2

美丽的黄金分割.............................................................................................. 9 数学推理的和谐性........................................................................................ 10

4 数学中的符号美................................................................................................... 11 4.1 4.2 4.3

数学符号的方便性........................................................................................ 11 数学符号的简洁性........................................................................................ 12 数学符号的代表性........................................................................................ 12

5 数学中的奇异美................................................................................................... 12 5.1 5.2

数学方法的奇异性........................................................................................ 12 数学思维的奇异性........................................................................................ 13

6 数学中的意象美................................................................................................... 14 6.1 6.2

数字与诗歌.................................................................................................... 14 数学与诗歌.................................................................................................... 16

结束语.......................................................................................................................... 17 参考文献...................................................................................................................... 18 谢 辞.......................................................................................................................... 19

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