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              Zu Chongzhi and Pi
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                         Zu Chongzhi

              Zu Chongzhi (zǔ chōng zhī 祖沖之) 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 圓周率) has been internationally acknowledged. Liu Hui (liú huī 劉徽), a mathematic in Three Kingdoms period (sān guó shí qī 三國時期), proposed a way to calculate the value of pi—Cutting Circle Method (gē yuán shù 割圓術). 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 綴術) 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.

              祖沖之與圓周率
              Zu Chongzhi      祖沖之(公元429年─公元500年),字文遠,南北朝時期人,漢族人,是中國杰出的數學家,科學家。生于未文帝元嘉六年,卒于齊昏侯永元二年,祖籍范陽郡遒縣(今河北淶水縣)。祖沖之對于自然科學和文學、哲學都有廣泛的興趣,特別是對天文、數學和機械制造,更有強烈的愛好和深入的鉆研。

                在中國古代,人們從實踐中認識到,圓的周長是“圓徑一而周三有余”,也就是圓的周長是圓直徑的三倍多,但是多多少,意見不一。在祖沖之之前,中國數學家劉徽提出了計算圓周率的科學方法--“割圓術”,用圓內接正多邊形的周長來逼近圓周長,用這種方法,劉徽計算圓周率到小數點后4位數。 祖沖之在前人的基礎上,經過刻苦鉆研,反復演算,將圓周率推算至小數點后7位數(即3.1415926與3.1415927之間),并得出了圓周率分數形式的近似值。

                    祖沖之計算得出的圓周率,外國數學家獲得同樣結果,已是一千多年以后的事了。為了紀念祖沖之的杰出貢獻,有些外國數學史家建議把圓周率π叫做“祖率”。 除了在計算圓周率方面的成就,祖沖之還與他的兒子一起,用巧妙的方法解決了球體體積的計算。他們當時采用的原理,在西方被稱為“卡瓦列利”(Cavalieri)原理,但這是在祖沖之以后一千多年才由意大利數學家卡瓦列利發現的。為了紀念祖氏父子發現這一原理的重大貢獻,數學上也稱這一原理為“祖原理”。

                    他將自己的數學研究成果匯集成一部著作,名為《綴術》 ,唐朝國學曾經將此書定為數學課本。他編制的《大明歷》,第一次將“歲差”引進歷法。提出在391年中設置144個閆月。推算出一回歸年的長度為365.24281481日,誤差只有50秒左右。他不僅是一位杰出的數學家和天文學家,而且還是一位杰出的機械專家。他重新造出早已失傳的指南車、千里船等巧妙機械多種。此外,他對音樂也有研究。著作有《釋論語》、《釋孝經》、《易義》、《老子義》、《莊子義》及小說《述異記》等,均早已遺失。
               

               

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