• Journal for History of Mathematics
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• v.24 no.3
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• pp.1-12
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• 2011

It is well known that the sexagesimal cycle(干支) has been playing very important role in ordinary human affairs including astrology and almanacs and the arts of divination(術數). Yin-Yang school related the cycle with the sixty four hexagrams and the system of five notes(五音) and twelve pitch-pipes(十二律), and the processes to relate them are called respectively NaJia(納甲) and NaYin(納音) and quoted in Shen Kuo's Meng qi bi tan(夢溪筆談, 1095). Yang Hui obtained the process NaYin in the context of mathematics. In this paper we show that Yang Hui introduced the concept and notion of functions and then using congruences and the composite of functions, he could succeed to describe perfectly the process in his Xu gu zhai qi suan fa(續古摘奇算法, 1275). We also note that his concept and notion of functions are the earliest ones in the history of mathematics.

• Korean Journal of Heritage :History & Science
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• v.47 no.1
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• pp.116-133
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• 2014

The memorial stones of Sumanotap were known to have been sequentially produced in 1719, 1773, 1874, 1653, 1874. However, after examining the chronological era (年號) and sexagesimal cycle (干支), it was found that the second and fourth memorial stones were both recorded in 1713. The reason why the records of the same period were divided into two is assumed that since the subject to repair was divided into main structure and flagpole of the temple, and it was recorded per each monk in charge and donator. On the fifth tablet of the memorial stone of Sumanotap contains all the names of monks who were in charge of repairing Sumanotap as well as the names of common donators. These people are not verified in detail though, through comparing the Buddhist names on the third memorial stone with Buddhist paintings and painting records, 12 monks were identified to be in the same names. Generally, they were active in Gangwon province, Gyeongsang province, Seoul and Gyeonggi province in the late 19th century and even after the Sumanotap repair, they took up other duties of various temples. The most notable name among the donators recorded in the memorial stones of Sumanotap was Kim Jwageun. He was the donator for the chest of gold and silver that was enshrined in the pagoda in 1874. His name was recorded with Mrs. Yang from Cheongsin and, at that time, was known just as a donator. However, actually, the donator was not Kim Jwageun but his mistress Mrs. Yang who used to be a gisaeng, called Na-hap and was from Naju. Kim Jwageun deceased in 1869 already. It is exceptional that Mrs. Yang who were the mistress of the prime minister Kim Jwageun personally participated in the Buddhist event in which king, queen, mothers of king and queen, noblewoman participated. Besides, the event of Sumanotap repair was carried out by royal family in order to celebrate the hundredth day of the prince, Sunjong and his grandfather, Heungseon Daewongun did not participate for political reason. In this situation, the domination of Mrs. Yang is considered remarkable. Meanwhile, the temples that frequently appeared among the 10 temples recorded in the memorial stone of Sumanotap are Gakhwa-sa temple in Bonghwa-gun, Gyeongsangbuk-do and Bodeok-sa temple in Yeongwolgun, Gangwon-do. Gakhwa-sa temple was a temple where the historical achievements were kept so was under the government's control. Bodeok-sa temple was the buddhist temple praying for the soul of the Danjong buried in the tomb and was managed by the government. Therefore, the face these two temples participated in the Sumanotap repair proves that Sumanotap was repaired by the supports form these two temples and the stature of Sumanotap at that time was as high as the temples where the historical achievements are store or the royal buddhist temples for praying for ancestors' souls.