• Title, Summary, Keyword: 구장산술

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A Study for the Values of the Nine Chapters on the Mathematical Art on Mathematics Educational Viewpoint (구장산술의 수학교육학적 가치에 대한 연구)

  • 한길준;서주연
    • Journal for History of Mathematics
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    • v.17 no.3
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    • pp.61-72
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    • 2004
  • In this paper, we investigate several values of the Nine Chapters on the Mathematical Art on mathematics educational viewpoint. We study them with four points of view: mathematical approach through problems of real life, algorithmization of concept and type, significance of affective domain and application of arithmetic. The result shows that the Nine Chapters on the Mathematical Art have great meaning of today's Korean mathematics education and possibility of application.

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한간 "산수서" 와 "구장산술" 의 비교

  • Cha, Jong-Cheon
    • Communications of Mathematical Education
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    • v.15
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    • pp.273-280
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    • 2003
  • 1983년 말 중국 형주시 소재 강릉장가산 247호 묘에서 죽간의 형태로 출토된 ${\ulcorner}$산수소${\lrcorner}$ 는 그것이 엮어진 시점이 유휘의 ${\ulcorner}$구장산술${\lrcorner}$ 보아 최소한 450년 가량이나 거슬러 올라간다는 점에서 동야수학사의 기원을 크게 앞당기게 하는 막중한 의의를 지니는 문서가 아닐 수 없다. 그러나 석문 자체가 최근 들어와서야 겨우 공개되었을 뿐, 현재로서는 자료에 대한 평가와 내용 분석은 물론, 변역마저도 제대로 이루어지지 못한 상태에 있다. 이 글은 ${\ulcorner}$산수서${\lrcorner}$${\ulcorner}$구장산술${\lrcorner}$ 의 내용을 배교하여 ${\ulcorner}$산수서${\lrcorner}$ 의 특징을 밝히는 동시에 동양수학의 초창기 발달의 궤적을 더듬어 보려는 시도이다. ${\ulcorner}$산수서${\lrcorner}$ 는 '상승(相乘)'에서 '이전(里田)'까지 이어지는 70개 제명(題名)하에 서술되어 있는데, 제명들은 주제를 나타내는 것과 산법을 나타내는 것을 혼재하는 것으로 나타난다. 내용 가운데에는 '여직(女織)', '우시(羽矢)', '소광(少廣)' 등이 문제처럼 ${\ulcorner}$구장산술${\lrcorner}$ 의 그것들과 기본적으로 같거나 유사한 것들이 다수 발견되어 고대수학 전통의 연속성을 엿볼 수 있게 하지만, 동시에 의료수가 문제인 '의(醫)'처럼 ${\ulcorner}$산수서${\lrcorner}$에서만 발견되는 것들도 더러 눈에 띈다. ${\ulcorner}$산수서${\lrcorner}$${\ulcorner}$구장산술${\lrcorner}$ 사이에 이루어진 수학 발달은, 이를테면, 제급근 사이에 있어서 전자의 경우에는 $\sqrt{240}$$15\frac{15}{31}$로 계산한 데서도 드러나듯이 보간법에 의존한 반면, 후자의 경우에는 온답을 제시하는 데 하등의 어려움을 겪지 않았다는 차에서도 확인된다.

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A Comparative Study of Contents between Ju-Seo-Gwan-Gyeon and Gu-Jang-San-Sul (「주서관견(籌書管見)」과 「구장산술(九章算術)」의 내용 비교)

  • Huh, Nan
    • Communications of Mathematical Education
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    • v.30 no.3
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    • pp.419-434
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    • 2016
  • Ju-Seo-Gwan-Gyeon is a mathematical book of Chosun dynasty in the early 18th century. This study is to analyze and compare the contents between Ju-Seo-Gwan-Gyeon and Gu-Jang-San-Sul. From this study, we are able to see the contents of Ju-Seo-Gwan-Gyeon that has been unknown in detail so far. In this comparative study, the following facts are found. First, many problems in Ju-Seo-Gwan-Gyeon are similar to the Gu-Jang-San-Sul on the contents and frame. Most of them are same type. But some of problems in Ju-Seo-Gwan-Gyeon have been developed. Second, there are distinct differences of description type. And Ju-Seo-Gwan-Gyeon was influenced by Gu-Jang-San-Sul but also other mathematical books. We expect that the results provide basic information for mathematics history in Korea.

Educational Meaning of the Nine Chapters (구장산술의 방정식론의 교육학적 의미)

  • Koh, Young-Mee;Ree, Sang-Wook
    • Journal for History of Mathematics
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    • v.23 no.1
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    • pp.25-40
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    • 2010
  • We first seek a principle of cognitive development processes by reviewing and summarizing Piaget's cognitive development theory, constructivism and Dubinsky's APOS theory, and also the epistemology on logics of 墨子 and 荀子. We investigate Chapter 8 方程 on the theory of systems of linear equations, of the Nine Chapters, one of the oldest ancient Asian mathematical books, from the viewpoint of our principle of cognitive development processes. We conclude the educational value of the chapter and the value of the research on Asian ancient mathematical works and heritages.

Historical and Social Environments and the Structure of The Nine Chapters on the Mathematical Art (역사(歷史) 사회(社會) 환경(環境)과 구장산술(九章算術의) 구조(構造))

  • Kang, Shin-Won
    • Journal for History of Mathematics
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    • v.19 no.4
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    • pp.1-12
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    • 2006
  • The Nine Chapters on the Mathematical Art has dominated the history of Chinese mathematics. It served as a textbook not only in China but also in the neighbouring countries and regions. The book is anonymous like many Chinese classics. The Nine Chapters contains 246 problems and their solutions, some of which date back to before the Qin Dynasty $(221\sim207\;B.C)$ and it seems to have been written by various writers over many generations. In this paper, we will investigate the structure of the Nine Chapters from the view points of ancient social environments which entail eventually mathematics in the Nine Chapters.

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Pedagogical Approach of the Nine Chapters on the Mathematical Art and Nam Byung Gil's GuJangSulHae (<구장산술九章算術>과 남병길의 <구장술해九章術解>의 교육적 활용 방안)

  • Jung, Hae-Nam
    • Education of Primary School Mathematics
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    • v.14 no.2
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    • pp.103-116
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    • 2011
  • 'The nine chapters on the mathematical art' has dominated the history of Chinese mathematics. It contains 246 problems and their solutions, which fall into nine categories that are firmly based on practical needs. But it has been greatly by improved by the commentary given Liu Hui and it was transformed from arithmetic text to mathematics. The improved book served as important textbook in China but also the East Asian countries for the past 2000 years. Also It is comparable in significance to Euclid's Elements in the West. In the middle of 19th century, Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) studied mathematical structures developed in Song(宋) and Yuan(元) eras on top of their early on 'The nine chapters' and 'ShuLiJingYun(數理精蘊)'. Their studies gave rise to a momentum for a prominent development of Choson mathematics in the century. Nam Byung Gil is also commentator on 'The Nine Chapters'. His commentary is 'GuJangSulHae(九章術解)'. This book provides figures and explanations of how the algorithms work. These are very helpful for prospective elementary teachers. We try to plan programs of elementary teacher education on the basis of 'The Nine Chapters' and 'GuJangSulHae'.

on perspective of Philosophy of Mathematics (수학철학적 관점에서 본 <구수략>)

  • Jung, Hae-Nam
    • Journal for History of Mathematics
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    • v.22 no.4
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    • pp.67-82
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    • 2009
  • We study Choi Suk Jung's on perspective of philosophy of mathematics. He explains Chosun mathematics as systems of Changes through and redefines on So Kang Gul's Sasang theory. This is the unique view on Chosun mathematics. we conjecture that Choi Suk Jung tries to establish the mathematical principle on So Kang Gul's Sasang theory.

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Understanding 《Jiuzhang suanshu 九章算術》 through 《Kujang sulhae 九章術解》 -Focusing on the Meaning of the Terms and Phrases in the First Half of Chapter One pangjeon 方田章, and Paying Attention to the Development of Concepts- (《구장술해》를 통한 《구장산술》의 이해 -방전장(方田章) 전반부의 용어와 어구의 의미를 중심으로 개념의 발달 과정에 주의하여-)

  • KANG, Min Jeong
    • Journal for History of Mathematics
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    • v.28 no.5
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    • pp.207-231
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    • 2015
  • We discuss several issues relating to the meaning of the terms and phrases in the first half of Chapter One fang tian 方田章 of ${\ll}$Jiuzhang suanshu九章算術${\gg}$. I understood those issues more clearly in the course of the translation of ${\ll}$Kujang sulhae 九章術解${\gg}$. Those are '今有' in the beginning of each problem, '積' and '冪' in the method of square field 方田術, '齊' in the method of reduction to a common denominator 齊同術, '經' and '有分者通之重有分者同而通之' in the method of dividing fraction 經分術, '實如法而一' in the calculation using the rods, '兩邪' in the method of trapezium field with a perpendicular side 邪田術. We may find out the value of ${\ll}$Kujang sulhae 九章術解${\gg}$ through our discussion.

구장산술에 포함된 증명의 유형과 역할

  • 이종희
    • Journal for History of Mathematics
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    • v.16 no.2
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    • pp.11-22
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    • 2003
  • In this paper, we investigate the types and roles of ancient mathematical proof by exploring Gu-Jang-Sal-Sul. Gu-Jang-Sal-Sul is a ancient Chinese mathematics book. Types of proof contained in Gu-Jang-Sal-Sul are enactive proof and intuitive proof and the role of proof is explanation. And we suggest social background of proof in Gu-Jang-Sal-Sul topographically, culturally, and logically.

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