What Chengtian - Kashoten

An astronomer, mathematician, and thinker during the Northern and Southern Dynasties period in China. Born in Donghai Tan (present-day Tancheng County, Shandong Province), he served under the Liu Song Dynasty. Based on his father-in-law's observation records and his own observations, he pointed out the discrepancies in the previous Jingchu calendar (established by Emperor Ming of Wei and used for about 200 years), and submitted a new Yuanjia calendar in 443. The Yuanjia calendar was used from 445 to 509. Initially, he proposed a fixed lunar calendar that incorporated inequalities in the movement of the moon to correct the discrepancies between solar and lunar eclipses and the lunar eclipses, but this was not adopted. The greatest improvement of the Yuanjia calendar was the day-adjusting method, which is a method of approximating real numbers with rational numbers. When calculating the length of a month and expressing the fractional part of a day as a fraction, he devised a method to approximate the observed value by sandwiching the observed value between two fractions, the strong fraction (the larger one) and the weak fraction (the smaller one), and calculated one month as 29 + (399/752) days. He also participated in the compilation of the National Book of Song (later known as the "Song Shu"), but was unable to complete it during his lifetime, and his disciples took over the work.

[Editorial Department, January 19, 2016]

Source: Shogakukan Encyclopedia Nipponica About Encyclopedia Nipponica Information | Legend

中国の南北朝時代の天文学者、数学者、思想家。東海郯(とうかいたん)（現在の山東省郯城県）に生まれる。劉宋朝(りゅうそうちょう)に仕えた。義父の観測記録と彼自身の観測に基づき、それまでの景初暦（魏(ぎ)の明帝が制定し約200年使われた）のずれを指摘して、新たに元嘉暦(げんかれき)を443年に上奏した。元嘉暦は445年から509年まで用いられた。当初、日月食と朔望(さくぼう)のずれを修正するために月の運行の不等を取り入れる定朔を提案したが採用されなかった。元嘉暦の一番の改良点は調日法である。調日法とは実数を有理数で近似する方法である。1か月の長さを計算して日の端数を分数で表すときに、観測値を二つの分数、強率（大きいほう）と弱率（小さいほう）で挟んで観測値に近づける方法を考案し、1か月を29+(399/752)日と計算した。また宋の国書（のちの『宋書』）の編纂(へんさん)にも携わったが、生前には完成できず、弟子たちが作業を引き継いだ。

［編集部　2016年1月19日］

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