【漢英對照】祖沖之圓周率 Zu Chongzhi's Value of π
【原文】
《隋書·律曆志》
古之九數(shù)，圓周率三，圓徑率一，其術疏舛[1]。自劉歆[2]、張衡[3]、劉徽[4]、王蕃[5]、皮延宗[6] 之徒，各設新率，未臻折衷。
宋末[7]，南徐州從事史[8] 祖沖之，更開密法，以圓徑一億為一丈， 圓周盈數(shù)[9] 三丈一尺四寸一分五厘九毫二秒七忽，朒數(shù)[10] 三丈一尺四寸一分五厘九毫二秒六忽，正數(shù)在盈、朒二限之間。密率，圓徑一百一十三，圓周三百五十五。約率，圓徑七，周二十二。
【English Translation】
"Book of Sui'' (Treatise on the Calendar)
According to the nine? computational methods of antiquity, the ratio of the circumference to the? diameter is 3 to 1. This method is inaccurate. Liu Xin, Zhang Heng, Liu Hui,? Wang Fan, Pi Yanzong each found a new ratio, yet could not reach a consensus.
Towards the end of Song,? the assistant prefectural governor of southern Xu Zhou, Zu Chongzhi, further? devised a precise method. Taking a circle of diameter 10000000 to be 1 zhang,? the excess value of the circumference is 3 zhang 1 chi 4 cun 1 fen 5 li 9 hao 2 miao 7 hu, and the deficit value is 3 zhang 1 chi 4 cun 1 fen 5 li 9 hao 2 miao 6 hu. The actual number lies between the excess and deficit values. The precise ratio is a diameter of 113 to a circumference of 355. The approximate ratio is a diameter of 7 to a circumference of 22.
【注釋】
[1] 疏舛shū chuǎn：粗疏，因為太小而不準確。
Crude, inaccurate for being too small.
[2] 劉歆（公元前50年 – 公元23年）漢代經學家、天文學家。
Liu Xin (50 BC – 23 AD) scholar of classics and astronomy of the Han dynasty.
[3] 張衡（公元78年 – 139年）漢代文學家、天文學家、發(fā)明家。
Zhang Heng (79 – 139 AD) literary scholar, astronomer, and inventor of the Han dynasty.
[4] 劉徽（約公元225年 – 295年）魏晉時期數(shù)學家。
Liu Hui (c. 225 – 295 AD) mathematician of the Three Kingdoms and Jin dynasty.
[5] 王蕃（公元228 – 266年）三國時代吳國天文學家、數(shù)學家。
Wang Fan (228 – 266 AD) astronomer and mathematicians of the Three Kingdoms period.
[6] 皮延宗（公元5世紀）南北朝數(shù)學家。
Pi Yanzong (fl. 5th century AD) mathematician of the Northern and Southern dynasties period.
[7] 宋sòng：南朝宋（公元420年 – 479 年）。
The Liu-Song dynasty (420 – 479 AD).
[8] 從事史cóng shì shǐ：負責主眾曹文書的官員。
An official in charge of compiling and managing archives.
[9] 盈數(shù)yíng shù：過大數(shù)值。
Excess number or excess value.
[10] 朒數(shù)nǜ shù：不足數(shù)值。
Deficit number or deficit value.
【今譯】
據(jù)古代的九數(shù)，圓周與直徑的比率是3:1。此算法粗疏。自劉歆、張衡、劉徽、王蕃、皮延宗，各設新圓周率，但未達到折衷。
宋末，南徐州的從事史祖沖之，重新發(fā)現(xiàn)精密的圓周算法，以圓10000000的直徑為1丈，圓周盈數(shù)是3丈1尺4寸1分5厘9毫2秒7忽，朒數(shù)是3丈1尺4寸1分5厘9毫2秒6忽。正數(shù)落在盈數(shù)和朒數(shù)二限之間。密率的直徑113比圓周355。約率的直徑7比圓周22。
