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      • KCI등재

        Forty-five Years of HPM Activities: A Semi-personal Reflection on What I Saw, What I Heard and What I Learn

        Keung, Siu Man The Korean Society for History of Mathematics 2020 Journal for history of mathematics Vol.33 No.5

        HPM (History and Pedagogy of Mathematics) activities deal with integrating the history of mathematics with the teaching and learning of mathematics. As a teacher of mathematics the author will share his personal experience in the engagement of HPM activities during the past forty-five years with fellow teachers who are interested in such activities and who may wish to know how another teacher goes about doing it.

      • KCI등재

        Chinese Mathematics in Chosun

        이창구,홍성사,Lee, Chang Koo,Hong, Sung Sa The Korean Society for History of Mathematics 2013 Journal for history of mathematics Vol.26 No.1

        중국 수학을 토대로 조선 수학이 발전된 것은 잘 알려져 있다. 이 논문에서는 조선에 유입된 중국 산서의 역사를 조사하여 중국 수학이 조선 수학에 끼친 영향을 연구한다. 15세기 세종(世宗)대에 들어온 중국 수학, 17세기 서양 수학의 영향을 받은 중국 수학과 19세기 중국에서 재정리된 송, 원대의 수학으로 나누어 이들이 유입되는 과정도 함께 조사한다. It is well known that the development of mathematics in eastern Asia was based on Chinese mathematics. Investigating Chinese mathematics books that were brought into Chosun, we study how Chinese mathematics influenced Chosun mathematics. Chinese mathematics books were brought into Chosun in three stages, namely basic mathematics books in the era of King SeJong(1397-1450), Chinese mathematics books influenced by western mathematics in the 17th century and finally those with commentaries on mathematics of Song-Yuan era in the 19th century. We also study the process of their importations.

      • KCI등재

        Mathematical Structures of Joseon mathematician Hong JeongHa

        홍성사,홍영희,이승온,Hong, Sung Sa,Hong, Young Hee,Lee, Seung On The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.1

        From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.

      • KCI등재

        Mathematical Structures and SuanXue QiMeng

        홍성사,홍영희,이승온,Hong, Sung Sa,Hong, Young Hee,Lee, Seung On The Korean Society for History of Mathematics 2013 Journal for history of mathematics Vol.26 No.2

        주세걸(朱世傑) 산학계몽(算學啓蒙)은 조선 산학의 발전에 가장 중요한 역할을 한 산서이다. 천원술을 비롯한 산학계몽(算學啓蒙)의 내용은 조선 산학의 중요한 연구 대상이 되었다. 이 논문의 목적은 주세걸(朱世傑)이 수학적 구조를 강조하면서 산학계몽(算學啓蒙)을 저술한 것을 보여서 조선 산학자들에게 수학적 구조에 대한 이해를 크게 확장한 것을 드러내는 것이다. 이와 함께 주세걸(朱世傑) 이전의 산서에 나타나는 구조적 접근과 산학계몽(算學啓蒙)의 접근을 비교하여 주세걸(朱世傑)의 접근이 뛰어나고 또 현대에 사용되는 구조적 접근과 일치하는 것을 보인다. It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

      • KCI등재

        Siyuan Yujian in the Joseon Mathematics

        홍성사,홍영희,이승온,Hong, Sung Sa,Hong, Young Hee,Lee, Seung On The Korean Society for History of Mathematics 2017 Journal for history of mathematics Vol.30 No.4

        As is well known, the most important development in the history of Chinese mathematics is materialized in Song-Yuan era through tianyuanshu up to siyuanshu for constructing equations and zengcheng kaifangfa for solving them. There are only two authors in the period, Li Ye and Zhu Shijie who left works dealing with them. They were almost forgotten until the late 18th century in China but Zhu's Suanxue Qimeng(1299) had been a main reference for the Joseon mathematics. Commentary by Luo Shilin on Zhu's Siyuan Yujian(1303) was brought into Joseon in the mid-19th century which induced a great attention to Joseon mathematicians with a thorough understanding of Zhu's tianyuanshu. We discuss the history that Joseon mathematicians succeeded to obtain the mathematical structures of Siyuan Yujian based on the Zhu's tianyuanshu.

      • KCI등재

        和算家的累??

        Qu, Anjing The Korean Society for History of Mathematics 2013 Journal for history of mathematics Vol.26 No.5

        Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Takebe Katahiro (1664-1739) and Nakane Genkei (1662-1733), among a great number of mathematicians in Wasan, maybe the most famous ones. Taking Takebe and Nakane's indefinite problems as examples, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to these problems which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of Chinese tradition deeper.

      • KCI등재

        Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa

        홍성사,홍영희,김영욱,Hong, Sung Sa,Hong, Young Hee,Kim, Young Wook The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.3

        Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.

      • KCI등재

        Kaifangfa and Translation of Coordinate Axes

        홍성사,홍영희,장혜원,Hong, Sung Sa,Hong, Young Hee,Chang, Hyewon The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.6

        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.

      • KCI등재

        Division Algorithm in SuanXue QiMeng

        홍성사,홍영희,이승온,Hong, Sung Sa,Hong, Young Hee,Lee, Seung On The Korean Society for History of Mathematics 2013 Journal for history of mathematics Vol.26 No.5

        The Division Algorithm is known to be the fundamental foundation for Number Theory and it leads to the Euclidean Algorithm and hence the whole theory of divisibility properties. In JiuZhang SuanShu(九章算術), greatest common divisiors are obtained by the exactly same method as the Euclidean Algorithm in Elements but the other theory on divisibility was not pursued any more in Chinese mathematics. Unlike the other authors of the traditional Chinese mathematics, Zhu ShiJie(朱世傑) noticed in his SuanXue QiMeng(算學啓蒙, 1299) that the Division Algorithm is a really important concept. In [4], we claimed that Zhu wrote the book with a far more deeper insight on mathematical structures. Investigating the Division Algorithm in SuanXue QiMeng in more detail, we show that his theory of Division Algorithm substantiates his structural apporaches to mathematics.

      • KCI등재

        和算?中算的?承??新-以?孝和的內?法?例

        곡안경,Qu, Anjing The Korean Society for History of Mathematics 2013 Journal for history of mathematics Vol.26 No.4

        Japanese mathematics, namely Wasan, was well-developed before the Meiji period. Seki Takakazu (1642?-1708) is the most famous one. Taking Seki's interpolation as an example, the similarities and differences are made between Wasan and Chinese mathematics. According to investigating the sources and attitudes to this problem which both Japanese and Chinese mathematicians dealt with, the paper tries to show how and why Japanese mathematicians accepted Chinese tradition and beyond. Professor Wu Wentsun says that, in the whole history of mathematics, there exist two different major trends which occupy the main stream alternately. The axiomatic deductive system of logic is the one which we are familiar with. Another, he believes, goes to the mechanical algorithm system of program. The latter featured traditional Chinese mathematics, as well as Wasan. As a typical sample of the succession of Chinese tradition, Wasan will help people to understand the real meaning of the mechanical algorithm system of program deeper.

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