我想問一些關於祖沖之的背景和他的發現?

Zu Chongzhi (祖冲之, pinyin Zǔ Chōngzhī, Wade-Giles Tsu Ch'ung-chih) (429-500) was a Chinese mathematician and astronomer during the Liu Song and Southern Qi Dynasties (of the Southern Dynasties).

His ancestors hailed from Qiu district, Fanyang Commandery (part of modern Beijing). To flee from the ravages of war, Zu Chongzhi's grandfather Zu Chang moved from Hebei, in north China, to south of the Yangtze River, as part of the massive population movement during the Eastern Jin Dynasty. Zu Chang at one point held the position of "Minister of Great Works" (Dàjiàngqīn) within the Song Dynasty (420-479) and was in charge of government construction projects. Zu Chongzhi's father also served the court and was greatly respected for his erudition.

Zu Chongzhi was born in 429 in Jiankang (today Nanjing). His family had historically been involved in astronomy research, and from childhood Zu Chongzhi was exposed to both astronomy and mathematics. When he was only a youth his talent earned him much repute. When Emperor Xiaowu heard of him, he was sent to an Academy, the "Huálín Xuéshěng", and later at the Imperial Nanking University(Zongmingguan) to perform research. In 461 in Nanxu (today Zhenjiang in Jiangsu) he was engaged in work at the office of the local governor.

His achievements included:

the Daming calendar (大明曆) introduced in 465.
deriving two approximations of pi, which held as the most accurate approximation for π for over nine hundred years. His best approximation was between 3.1415926 and 3.1415927, with 355⁄113 (密率, Milü, detailed approximation) and 22⁄7 (约率, Yuelü, rough approximation) being the other notable approximations.
finding the volume of a sphere as being 4πr³/3, where r is radius.

沖之生於南北朝（西元409-502）范陽薊縣人。

他利用割圓術求得圓內接二四五七六邊形的周長，從而推算出圓周率的值是在3.1415926和3.1415927之間。而且他采用22/7作為約率，355/113作為密率。這些結果都比西方早超過數個世紀。要知道當時只有算籌這種計算工具，計算工作是很繁重的。由於他不畏艱苦，有堅強的毅力才能獲得這光輝的成果。

祖沖之為了求圓周率小數後的第七位準確值，把正六邊形的邊長計算到小數後二萬八千六百七十二位，是很了不起的成就。這當中有三點值得我們注意的，

他是自己做的，因為開平方不能你求小數後第一位到第八位，同時間，有另外一人求第九位到第十六位，.......
目前使用的算盤到了十二世紀才出現，祖沖之那個時代還沒有算盤，可見其開平方的艱辛。
祖沖之不可能使用阿拉伯數字，阿拉伯數字在十二、十三世紀才傳入中國，可以想像其計數之麻煩。
祖沖之不單是個數學家，還是天文學家、文學家、機械發明家。在天文方面，他提出了當時最好的歷法「大明曆」，而且還算出地球繞太陽一周所需的時間是365.24281481日，和現在由製儀器得到的數據365.2422日，他的數字準確到小數後三個。他也曾算出月球繞地球一周為27.21223日，和現在公認的27.21222日，在小數第五位才有1的誤差，一千多年前他這個成果是值得我們驕傲的。他還發明了指南車、水碓磨與千里船等，還成功製造了類似諸葛孔明的「木牛流馬」的運輸工具，從中見到祖沖之是如何的聰明。

祖沖之在世時並不得意，不但沒有大官做，而且在生前還見不到「大明曆」的採用。最令人惋惜的是記載他和兒子數學成果的書《綴術》在宋朝失傳了。今日在月球上很多座以偉大科學家命名的山，祖沖之是其中一個，亦是中國的唯一一個，由此可見到他是如何的偉大呢！