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Kaifangfa and Translation of Coordinate Axes

개방법(開方法)과 좌표축(座標軸)의 평행이동(平行移動)

  • Received : 2014.11.07
  • Accepted : 2014.12.14
  • Published : 2014.12.31

Abstract

Since ancient civilization, solving equations has become one of the most important subjects in mathematics and mathematics education. The extractions of square roots and cube roots were first dealt in Jiuzhang Suanshu in the setting of subdivisions. Extending these, Shisuo Kaifangfa and Zengcheng Kaifangfa were introduced in the 11th century and the subsequent development became one of the most important contributions to mathematics in the East Asian mathematics. The translation of coordinate axes plays an important role in school mathematics. Connecting the translation and Kaifangfa, we find strong didactical implications for improving students' understanding the history of Kaifangfa together with the translation itself although the latter is irrelevant to the former's historical development.

Keywords

Shisuo Kaifangfa;Zengcheng Kaifangfa;Translation of coordinate axes;Fanji;Yiji

References

  1. Hong Sung Sa, Hong Young Hee, Kim Young Wook, Hong JeongHa's Tianyuanshu and Zengcheng Kaifangfa, Journal for History of Mathematics, 27(3) (2014), 155-164. https://doi.org/10.14477/jhm.2014.27.3.155
  2. Guo ShuChun ed. ZhongGuo Kexue Jishu Dianji Tonghui Shuxuejuan, Henan Jiaoyu Pub. Co., 1993. 郭書春主編, "中國科學技術典籍通彙" 數學卷全五卷, 河南敎育出版社, 1993.
  3. Hong JeongHa, GuIlJib (1724), Seoul National University Library. 洪正夏, "九一集" (1724), 서울大學校圖書館.
  4. Hong Sung Sa, Theory of Equations in the history of Chosun Mathematics, Proceeding Book 2, The HPM Satellite Meeting of ICME-12, 719-731, 2012.
  5. Hong Sung Sa, Hong Young Hee, Chang Hyewon, History of Fan Ji and Yi Ji, The Korean Journal for History of Mathematics, 18(3) (2005), 39-54. 홍성사, 홍영희, 장혜원, 飜積과 益積의 歷史, 한국수학사학회지 18(3) (2005), 39-54.
  6. Hong Sung Sa, Hong Young Hee, Kim Young Wook, Liu Yi and Hong JungHa's KaiFangShu, The Korean Journal for History of Mathematics, 24(1) (2011), 1-13. 홍성사, 홍영희, 김영욱, 劉益과 洪正夏의 開方術, 한국수학사학회지 24(1) (2011), 1-13.
  7. Hong Sung Sa, Hong Young Hee, Kim Young Wook, Kim Chang Il, KaifangShu in San-Hak JeongEui, Journal for History of Mathematics, 26(4) (2013), 213-218. https://doi.org/10.14477/jhm.2013.26.4.213
  8. Luo Shilin, Siyuan Yujian Xichao (1835), Shangwu Pub. Co., 1967. 羅士琳, "四元玉鑑細艸" (1835), 臺灣商務印書館, 1967.
  9. Ogawa Tsugane, Sato Kenichi, Takenouchi Osamu, Morimoto Mitsuo, Takebe no Sugaku, Kyoritsu Pub. Co., 2008. 小川束, 佐藤健一, 竹之內脩, 森本光生, "建部賢弘の數學", 共立出版, 2008.
  10. Seki Takakazu, Takebe Kataakira, Takebe Katahiro, Taisei Sankei, 1711, Tohoku University Library. 關孝和, 建部賢明, 建部賢弘, "大成算經" (1711), 東北大學圖書館