Liu Hui

Date of birth and death unknown. A mathematician from the Wei to Jin dynasties of the Three Kingdoms period in China. In 263, he wrote an excellent commentary on the mathematical book "Nine Chapters on Mathematical Science." In the chapter on calculating the area of ​​rice fields, he pointed out the inaccuracy of the use of the number 3 for pi, and considered the area and circumference of a circle to be the limit of the area and circumference of a regular polygon inscribed in it when the number of sides is increased. He calculated up to a regular 192-sided polygon and obtained (314 + 64/625)/100, and gave an even more precise value of (314 + 4/25)/100 = 3.1416. In the chapter on calculating civil engineering works, he also wrote one volume of "Nine Chapters on Mathematical Science," adding a volume on "Weight Differences." However, the latter was later lost, and the former was handed down independently as one volume of "Haidao Suanjing." The content involves solving surveying problems using the properties of similar triangles.

[Kazuhiko Miyajima]

"Scientific Masterpieces 2: Chinese Astronomy and Mathematics" edited by Kiyoshi Yabuuchi, translated by Keizo Hashimoto and Hideki Kawahara (1980, Asahi Press) " "The History of Chinese Mathematics" edited by Qian Baocong, translated by Hideki Kawahara (1990, Misuzu Shobo) " "Chinese Mathematics" by Kiyoshi Yabuuchi (Iwanami Shinsho)

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

生没年不詳。中国、三国・魏(ぎ)から晋(しん)代の数学者。263年に数学書『九章算術』の優れた注釈書を著した。同書の方田（田の面積計算）の章で円周率に3が用いられていることの不正確さを指摘して、円の面積、円周は、それに内接する正多辺形の辺数を増していったときの面積と周の極限とみなし、正192辺形まで計算して（314＋64／625）／100を得、さらに精密な値として（314＋4／25）／100＝3.1416を示した。商功（土木工事関係の計算）の章でも体積の計算に極限の考えがみられる。同書の内容を補うため「重差」の巻を加え、『九章重差図』1巻を著したが、のちに後者は失われ、前者は独立して『海島算経』1巻として伝えられた。内容は、測量に関する問題を相似三角形の性質を用いて解くものである。

［宮島一彦］

『藪内清編、橋本敬造・川原秀城訳『科学の名著2　中国天文学・数学集』（1980・朝日出版社）』▽『銭宝琮編、川原秀城訳『中国数学史』（1990・みすず書房）』▽『藪内清著『中国の数学』（岩波新書）』

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