探讨了不定积分教学中一些方法，以及如何体现数学美。
In this paper, some methods of how to teach indefinite integral and how to embody mathematical beauty are approached.
数学美是科学美的一种，它既具有美的共性，更具有独特的个性。
The Math beauty is a scientific beauty. It's both beautiful common characteristic and special individuality.
本文从抽象性，统一性(兼简洁性)、精巧性三个方面系统地论述数学美。
The article describes the beauty of mathematics from three aspects; abstractness, unity (annex terseness) and ingenuity.
文章分析了数学和美的内在联系，阐述了数学美是科学美的内核及其代表。
It shows that maths beauty is the intension and representitive of science beauty.
本文简述了数学美的主要内容、具体体现以及数学的“以美启真”教学原则。
This paper gives a brief account about the main contents and specific embodiment of maths beauty and the maths teaching principle of "Enlightening the truth through the beauty".
由于这些原因，所以研究在数学教学中渗透数学美是具有重要的实际意义的。
This research will take mathematics as the host, examples as the background and deal with problems according to students'practical situation.
称美是数学美的重要组成部分，它普遍存在于初等数学与高等数学的各个分支。
Symmetrical beauty is one of the most important parts of mathematical aesthetics, which widely exists in every branch of elementary mathematics and higher mathematics.
文章在论述数学美的三种功能的同时，启发人们去发现、追求、运用其中的美。
At the same time of discussing on three functions of mathematical beauty, this paper enlightens people to discover, pursue and use the beauty in mathematics.
对称美是数学美的重要组成部分，它普遍存在于初等数学和高等数学的各个分支。
Symmetrical beauty is one of the most important parts of mathematical aesthetics, which widely exists in every branch of elementary mathematics and highermathematics.
数学美与数学教学整合的根本目的就是要实现数学学习过程与数学审美过程的统一。
The ultimate aim of conformity of mathematic beauty and mathematic teaching is the realization of unity of mathematic learning process and mathematic aesthetic process.
那么，我们所谓的数学美和优雅，并且可以引起我们的美的情感的主体究竟是什么？
Now, what are the mathematic entities to which we attribute this character of beauty and elegance, and which are capable of developing in us a sort of esthetic emotion?
数学美是一种科学美。本文简述了数学美的主要内容、具体体现以及数学的“以美启真”教学原则。
This paper gives a brief account about the main contents and specific embodiment of math's beauty and the math's teaching principle of "Enlightening the truth through the beauty".
数学是美学四大构件之一。数学的美学价值目前倍受关注。我们应该了解数学美，感受数学美，运用数学美。
Mathematics is one of the four major beauty piece of pats. Mathematic beauty currently is being paid attention to. We should understand, feel and apply mathematics beauty.
从审美评价的角度提出数学美包括数学的结构美、方法美和应用美三个方面，每个方面都包含了异常丰富的内容。
In addition, the author clearly shows from the point of view of aesthetic appraisal that, mathematical beauty displays in three part, i. e. mathematical structure, …
教师在教学中必须融入数学史、揭示数学美、建立融洽和谐的师生关系，这既是教高等数学的需要，也是高等数学教学的重要任务。
A teacher must incorporate mathematics history, reveal mathematical aesthetic and establish harmony between teachers and students, which is not only a must, but also an important task in the teaching.
所有的读者都有机会参与数学体验，欣赏数学之美，熟悉其具有逻辑而又出于直觉的思维方式。
All readers will have the chance to participate in a mathematical experience, to appreciate the beauty of mathematics, and to become familiar with its logical, yet intuitive, style of thinking.
现在我们已经知道科学无法尽善尽美，我们无需（像波兰尼那样）那么艰难的斗争以保留逻辑和数学无力施为的概念空间。
Now we know science is not perfectible we do not have to fight so hard to retain a conceptual space for that which cannot be done by logic and mathematics.
有一次，女儿在一次数学竞赛中落后于一个韩国小孩获得第二名，蔡美儿竟让这个女孩一晚上做2000道数学题直到她重新领先。
Once, one of her daughters came in second to a Korean kid in a math competition, so Chua made the girl do 2, 000 math problems a night until she regained her supremacy.
哥德尔不完备性定理抽走了数学家的逻辑美信仰，数学界出现了信仰危机。
Godel theorem made mathematicians lose their belief of logic beauty, the crisis of belief appeared in mathematical field.
数学不仅拥有真理，而且拥有至上的美——一种冷静而严肃、犹如雕塑那样的美。
Mathematics possesses not only truth, but supreme beauty-a beauty cold and austere. like that of sculpture.
数学的美可以转换成图形的美，换言之，美的图形也可以通过数学规律来构建。
Mathematics aesthetics can be converted into graphic aesthetics, in other words, the aesthetic graphics can be construct by mathematical laws.
在数学教学中，数学之美感能使人们达到以美启智，进而提高学生理解问题的能力。
In math teaching, math beauty can stimulate the students intelligence and increase their ability to comprehend problems.
文章通过论述数学的美，启发教育工作者学会运用数学的美去进行教学。
The charm of mathematics is discussed, inspiring people to learn to teach mathematics with the help of its charm.
大多数学者重视狭义的声音美而忽视了另一种声音美——广义的声音美，即声音的文化内涵美。
The broad sense, which is neglected by most scholars, means the internal beauty of its cultural meaning.
大多数学者重视狭义的声音美而忽视了另一种声音美——广义的声音美，即声音的文化内涵美。
The broad sense, which is neglected by most scholars, means the internal beauty of its cultural meaning.
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