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홍성사,Hong Sung-Sa 한국수학사학회 2006 Journal for history of mathematics Vol.19 No.2
조선 산학의 퇴타술의 역사를 연구한다. 이상혁(李尙爀)$(1810\sim?)$의 익산(翼算)(1868)이 출판되기 전의 역사와 익산(翼算)의 결과로 나누어 연구한다. 경선징(慶善徵)$(1616\sim?)$의 묵사집산법(默思集算法)부터 남병길(南秉吉)$(1820\sim1869)$의 산학정의(算學正義)(1867)까지의 산서를 통하여 익산(翼算) 이전의 퇴타술은 큰 발전을 이루지 못한 것을 조사한다. 이상혁(李尙爀)은 조선(朝鮮) 산학(算學)에서 가장 독창적인 방법을 써서 새로운 결과를 얻어낸다. 그는 퇴타술을 구조적으로 해결하고, 또 새로운 문제인 절적(截積)과 이를 위한 분적법(分積法)을 도입하여 이의 구조도 완전히 밝혀내었다.
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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.
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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.
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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.
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Volumes of Solids in Joseon Mathematics
홍성사,홍영희,김창일,Hong, Sung Sa,Hong, Young Hee,Kim, Chang Il The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.2
Joseon is mainly an agricultural country and its main source of national revenue is the farmland tax. Since the beginning of the Joseon dynasty, the assessment and taxation of agricultural land became one of the most important subjects in the national administration. Consequently, the measurement of fields, or the area of various plane figures and curved surfaces is a very much important topic for mathematical officials. Consequently Joseon mathematicians were concerned about the volumes of solids more for those of granaries than those of earthworks. The area and volume together with surveying have been main geometrical subjects in Joseon mathematics as well. In this paper we discuss the history of volumes of solids in Joseon mathematics and the influences of Chinese mathematics on the subject.
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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.
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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.
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Approximate Solutions of Equations in Chosun Mathematics
홍성사,홍영희,김창일,Hong, Sung-Sa,Hong, Young-Hee,Kim, Chang-Il The Korean Society for History of Mathematics 2012 Journal for history of mathematics Vol.25 No.3
구장산술이래 동양의 전통 수학은 유리수체를 기본으로 이루어져 있다. 따라서 방정식의 무리수해는 허용되지 않으므로 근사해를 구하는 방법은 방정식론에서 매우 중요한 과제가 되었다. 중국의 사료에 나타나는 근사해에 관한 역사를 먼저 기술하고, 이를 조선산학에 나타나는 근사해에 관한 사료와 비교한다. 조선의 근사해에 대한 이론은 박율(1621 - 1668) 의 산학원본 (算學原本) 과 조태구 (趙泰耉, 1660-1723) 의 주서관견(籌書管見)에 이미 정립되었다. 중국의 이론과 달리 두 산학자 모두 근사해의 오차에 관심을 가지고 더 좋은 근사해를 구하는 방법을 얻어내었음을 밝힌다.
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홍성사,홍영희,Hong, Sung-Sa,Hong, Young-Hee 한국수학사학회 2009 Journal for history of mathematics Vol.22 No.2
Zhu Shi Jie's Suan Xue Qi Meng is one of the most important books which gave a great influence to the development of Chosun Mathematics. Investigating San Hak Gye Mong Ju Hae(算學啓蒙註解) published in the middle of the 19th century, we study the development of Chosun Mathematics in the century. The author studied western mathematics together with theory of equations in Gu Il Jib (九一集) written by Hong Jung Ha(洪正夏) and then wrote the commentary, which built up a foundation on the development of Algebra of Chosun in the century.
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홍성사,홍영희,김창일,Hong, Sung-Sa,Hong, Young-Hee,Kim, Chang-Il 한국수학사학회 2008 Journal for history of mathematics Vol.21 No.2
As a sequel to the previous paper Gou Gu Shu in the 18th century Chosun, we study the development of Chosun mathematics by investigating that of Gou Gu Shu in the 19th century. We investigate Gou Gu Shu obtained by Hong Gil Ju, Nam Byung Gil, Lee Sang Hyuk and Cho Hee Soon among others and find some characters of the 19th century Gou Gu Shu in Chosun.
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