Zu Chongzhi and Pi 祖冲之与圆周率

Zu Chongzhi

Zu Chongzhi (zǔ chōng zhī 祖冲之) was a famous mathematician and scientist in ancient China. He lived in Southern and Northern dynasties (nán běi cháo 南北朝). When he was young, he had a broad range of interests, such as natural science and philosophy. And he was interested in mathematics, astronomy and machinery.

 

Circle Cutting MethodThe achievement Zu Chongzhi had made in the calculation of the value of pi (yuán zhōu lǜ 圆周率) has been internationally acknowledged. Liu Hui (liú huī 刘徽), a mathematic in Three Kingdoms period (sān guó shí qī 三国时期), proposed a way to calculate the value of pi—Cutting Circle Method (gē yuán shù 割圆术). based on the earlier research, he resorted to the “Cutting Circle Method” and concluded that the value of pi falls among 3.1415926 to 3.1415927 after more than 1000 times of calculation. He also put forward the viewpoint that the approximate value of pi was 355/133, which was called “milü”(mì lǜ 密率), which had boosted the calculation of pi to a new phase.

Zu ChongzhiThe value of pi Zu Chongzhi had calculated is more than 1000 years ahead of the western mathematics. Thus the value of pi is also called “Zu Lü”(zǔ lǜ 祖率) so as to commemorate him.
Besides the accomplishment in mathematics, Zu Chongzhi had solved the calculation of sphere volume. The method he had adopted is called Cavalieri Principle (kǎ wǎ liè lì yuán lǐ 卡瓦列利原理) in the west, which is created by an Italian mathematic Cavalieri 1000 years later. Cavalier Principle is also called “Zu Principle”(zǔ lǜ 祖率).

He compiled the book Zhui Shu (zhuì shù 缀术) which has gathered his accomplishment in mathematics and was taken as a teaching material during Tang Dynasty (táng cháo 唐朝). Besides the achievements in mathematics, he also made great contribution to the astronomy and machinery. He calculated that a tropical year is 365. 365.24281481 days. He made compass cart which was lost for many years in the world.

祖冲之与圆周率
Zu Chongzhi      祖冲之（公元429年─公元500年），字文远，南北朝时期人，汉族人，是中国杰出的数学家，科学家。生于未文帝元嘉六年，卒于齐昏侯永元二年，祖籍范阳郡遒县（今河北涞水县）。祖冲之对于自然科学和文学、哲学都有广泛的兴趣，特别是对天文、数学和机械制造，更有强烈的爱好和深入的钻研。

在中国古代，人们从实践中认识到，圆的周长是“圆径一而周三有余”，也就是圆的周长是圆直径的三倍多，但是多多少，意见不一。在祖冲之之前，中国数学家刘徽提出了计算圆周率的科学方法－－“割圆术”，用圆内接正多边形的周长来逼近圆周长，用这种方法，刘徽计算圆周率到小数点后4位数。 祖冲之在前人的基础上，经过刻苦钻研，反复演算，将圆周率推算至小数点后7位数（即3.1415926与3.1415927之间），并得出了圆周率分数形式的近似值。

      祖冲之计算得出的圆周率，外国数学家获得同样结果，已是一千多年以后的事了。为了纪念祖冲之的杰出贡献，有些外国数学史家建议把圆周率π叫做“祖率”。 除了在计算圆周率方面的成就，祖冲之还与他的儿子一起，用巧妙的方法解决了球体体积的计算。他们当时采用的原理，在西方被称为“卡瓦列利”（Cavalieri）原理，但这是在祖冲之以后一千多年才由意大利数学家卡瓦列利发现的。为了纪念祖氏父子发现这一原理的重大贡献，数学上也称这一原理为“祖原理”。

      他将自己的数学研究成果汇集成一部著作，名为《缀术》 ，唐朝国学曾经将此书定为数学课本。他编制的《大明历》，第一次将“岁差”引进历法。提出在391年中设置144个闫月。推算出一回归年的长度为365.24281481日，误差只有50秒左右。他不仅是一位杰出的数学家和天文学家，而且还是一位杰出的机械专家。他重新造出早已失传的指南车、千里船等巧妙机械多种。此外，他对音乐也有研究。著作有《释论语》、《释孝经》、《易义》、《老子义》、《庄子义》及小说《述异记》等，均早已遗失。