割圓術??english??

圓周率是圓周長和直徑的比值，<<周髀算經>>約成於西元前100年，是目前仍被保留下來的最早中國古算書。書中記載「徑一周三」，顯示春秋戰國至秦朝之間，人們以3表示圓周率。
後漢(約西元78~139年)天文學家張衡認為圓周率是3.1622。
三國魏末晉初(約西元263年)，劉徽利用「割圓術」(如右)計算圓周率至3.141024，他的方法是先作一圓，再做圓內接正6邊形，依序再做正12邊形、正24邊形、正48邊形、正96邊形，這些正多邊形的周長逐漸逼近圓周長，因此逼近圓周率。
南北朝時代的南朝的祖沖之(西元429~500年)承接劉徽的方法，求得圓周率介於3.1415926和3.1415927之間。

Yahoo!翻訳:
I calculate that I pass through what pi promises 髀 of a week before Nishimoto at the ratio of circumference Nagawa diameter for 100 years and gives and earliest China which I still reserve it for the present, and is lowered is old and is to calculate a book. A mention writes a thing equal to "one Wednesday of a diameter" and expresses that Lu and the Warring States Ages reaches it between the Qin dynasty, and people show pi by being 3.
It is 3.1622 that Zhang Heng of back Han (I promise 78 of Nishimoto for 139 years) astronomer thinks with pi.
Youngest Susumu first (I promise Nishimoto for 263 years) 劉徽 of 魏 of three countries uses what (it seems to be the right) to "cut 圓術" measures so that pi reaches 3.141024, and his method makes equilateral form of the side of 6 of 圓内接 with 1 yuan ahead product again and makes again equilateral form of the side of 12 by the opening, and circumference gradually approaches the head, and that is why equilateral form of the side of 24, equilateral form of the side of 48, equilateral form of the side of 96, the lap head of these regular polygons approach pi.
(429 500 years of Nishimoto) that charged through a father of south morning of the north and south morning service age catches a method of 劉徽 and asks so that pi exists among 3.1415926 and 3.1415927 ken.