俗话说，几何是这个世界之美的原型。我们日常生活中，学习或工作中几乎所有事物都与数学有一定关联。这种关联是货真价实存在于我们身边的，只是我们中的一些人并不承认他们有发现和感知美的眼睛。就如上海宏润博源学校这次研究的主题，很多人会提出疑问：书法如何才能和数学取得关联?这听起来很荒谬，是因为人们几乎没有在这方面做过研究。你是否有点好奇?跟随我们的步伐一起来探究吧!

As the old saying goes, Mathematics rules of the beauty of the world. Almost everything in our daily life, study or work, is related to mathematics. The relationship really exists around us, while some of us do not perceive it or deny admitting having ever seen it. Just like our main topic, large numbers of people cannot believe their eyes and asked: How can calligraphy have association with Math? It is ridiculous because hardly any people do a research on it.If you have a desire to know how, come with us!

中国书法字形结构的三个规律。

Three rules in the structure of Chinese characters

1.横平Horizontal

2.竖直Vertical

3.字距不一The distance between characters is different

上述的三个要点都与数学知识相关联，毕竟数学知识的运用也算是书法发展中最重要的因素之一。

All the three points about calligraphy mentioned above are relevant to Math, since Math is one of the most important factors in the development of calligraphy.

书法文字的中心线

在书写练习中，每当你一寻到这个字的中心线，你就能大概率避免这个字的架构倾斜。然而随着你的书写速度逐步提升，这个字的字形也变得难以控制。但亘古不变的是，字的中心线依旧存在，即使它看起来不那么明显了。当然，在快速的书写之下，这也是一个字仍然能保持美观与合理的原因之一。

Once you find the location of the center line in a character, you can avoid letting it lean to either side. As the speed of writing increases, the shape of the character can hardly be controlled. However, there still exists the center line, though it is not that obvious. That is the reason why the character can still look beautiful and reasonable.

如上图所示，就是中心线在名家赵孟頫、文徵明笔下的字里的体现。

For example, the pictures above show the center line of the Chinese character written by Wen Zhengming and Zhao Mengfu.

书法文字的对称性

众所周知，对称是反射的一种类型。近期在我们的数学课上，我们学习了《图形转换》这一章节，其中内容也包括反射。让我们通过一张简单的图片来看看几何中是如何定义对称的。

It is universally known that symmetry is a kind of reflection. Recently, in our Geometry H course, we learnt the chapter Transformations, and it also including reflection. Let’s see how we define symmetry in geometry by a simple picture.

As the picture on the left shows, it is a picture of axial symmetry in geometry. It seems that the left and the right are completely the same.

However, in the field of calligraphy, it is not that simple to explain the use of symmetry. In calligraphy, the calligrapher must keep a dynamic balance of the characters. They are required to accurately control the strength they use when they are writing, and the final purpose is to make the viewers have a sense of visual balance.

然而在书法领域，对称的运用解释起来并不简单。在书写中，运笔者务必保持字形的动态平衡。他们要将控制书写时的笔力的方法熟稔于心，而最终目的是为了让观者有一种视觉上的平衡感。

书法文字中隐藏的几何学

书法文字的结构并不是一成不变的，但至少是稳定的。在汉字书写中找到一个或以上的几何图形并不是什么稀奇事儿。当然了，无论如何，总还是会有些微妙的变化于其中。几何原则在书法字形结构中至始至终都体现得淋漓尽致。如果你不能体会到字形中的几何妙处，也就不能将书法艺术会于心间了。

The structures of calligraphy are not consistent, but at least they are stable. It is easy to find one or more shapes in the writing of a calligraphy character. There are also numerous changes in them. On any account, the principle of geometry structure exists from the beginning to the end. If you cannot take control of the structure, you are not able to appreciate the real art of calligraphy.

运用于汉字书写中的比例

不管运笔者使用的是哪一种字体(楷书、行书、草书等)，每个字它本身的笔画距离都有相应的比例，这样才能使字看起来更加上眼，更加惟妙惟肖。通常情况下，这个比例一般是二分之一或者三分之一。另外，由于书写速度的提升，笔画间的距离比例也会相应地做出改变，但这也是因人而异。

Whatever font the calligrapher uses, every character has its own ratio in distance so as to make itself elegant and notable. Usually, the ratio will be 1/2 or 1/3. What’s more, on account of the increasing speed of writing, the ratio will accordingly be changed in terms of the calligrapher.

研究结论

正如一位古哲学家毕达哥拉斯(那位提出勾股定理的男人)所说：“万物皆数。”你甚至无法想象，我们日常生活中的方方面面都涉及了数学知识。在听完我们的展示以后，你可能会说：“天呐，数学真是令人叹服!”不错，甚至我们中华传统文化艺术——书法也能与数学相关联。如果你想练得一手好字，我会跟你说：先学好数学哦!此外，平日里你拍照时的构图或许不知不觉就运用了黄金分割比，甚至你能发现大自然的赠礼——彩虹，也是一条靓丽的抛物线……

大千世界充满着数学之美，让我们用明亮的双眼去探寻吧~

According to the ancient philosopher Pythagoras (the man who first came up with Pythagorean theorem.) , ‘Mathmatics rules everything.’ Math refers to multiple sides in our daily life that you can’t imagine them all. After listening to our presentation, you may say, ‘How amazing math is!’ That is, even our ancient Chinese calligraphy can be related to math. If you want to have a good handwriting, I will tell you: To begin with, you should learn math well! What’s more, you will apply ‘golden ratio’ unconsciously when you are taking a photo; you will find rainbow is also a parabola…

This is a world filled with the beauty of math…Let’s find them out with our bright eyes!

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