• Title/Summary/Keyword: The Nine Chapters

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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'.

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.

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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중국 및 조선시대 산학서에 나타난 원주율과 원의 넓이에 대한 고찰

  • 장혜원
    • Journal for History of Mathematics
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    • v.16 no.1
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    • pp.9-16
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    • 2003
  • This paper aims to investigate how Chinese and Korean evaluate $\pi$ and measure tile area of circle by reviewing the problems in the old mathematical books. The books are Gu-Jang-San-Sul(The nine chapters on tile mathematical art) for China and Gu-Il-Jib for Chosun Dynasty. The result shows that our ancestors used the different values of ${\pi}$ in relation to the accuracy and the various methods for measuring the area of circle.

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유휘와 구장산술

  • 홍성사;홍영희
    • Journal for History of Mathematics
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    • v.11 no.1
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    • pp.27-35
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    • 1998
  • As Chinese philosophy has developed by commentary for the original texts, the Nine Chapters has been greatly improved by the commentary given by Liu Hui and it was transformed from an arithmetic text to Mathematics. Comparing his commentary and Chinese philosophical development up to his date, we conclude that Liu Hui was able to make such a great leap by his thorough understanding of philosophical development.

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AN ANALYSIS OF RECENT RESEARCH ON THE METHOD OF EXCESS AND DEFICIT (Ying NÜ and Ying Buzu Shu) (영뉵(盈朒)과 영부족술(盈不足術)에 관한 최근 동서양의 연구 분석)

  • Lee, Sang-Gu;Lee, Jae Hwa
    • Korean Journal of Mathematics
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    • v.20 no.1
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    • pp.137-159
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    • 2012
  • In this paper, we deal with recent researches on Ying N$\ddot{u}$ and Ying Buzu(盈不足) which were addressed in the book Jiu Zhang Suan Shu(九章算術, The Nine Chapters on the Mathematical Art). Ying N$\ddot{u}$(Ying Buzu) is a concept on profit and loss problems. Ying Buzu Shu(盈不足術, the method of excess and deficit) represents an algorithm which has been used for solving many mathematical problems. It is known as a rule of double false position in the West. We show the importance of Ying Buzu Shu via an analysis of some problems in 'Ying Buzu' chapter. In 1202, Fibonacci(c.1170-c.1250) used Ying Buzu Shu in his book. This shows some of Asian mathematics were introduced to the West even before the year 1200. We present the origin of Ying Buzu Shu, and its relationship with Cramer's Rule. We have discovered how Asia's Ying Buzu Shu spread to Europe via Arab countries. In addition, we analyze some characters of Ying N$\ddot{u}$(Ying Buzu) in the book Suan Xue Bao Jian(算學寶鑑).

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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구장산술의 원판과 영문번역판의 간격

  • 유인영
    • Journal for History of Mathematics
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    • v.16 no.4
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    • pp.1-14
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    • 2003
  • The Nine Chapters by Liu Hui(劉徽) in the three kingdoms(220∼265 AD) is the fundamental source of the traditional Chinese Mathematics and has not only remained the lighthouse of the traditional Chinese Mathematics over the last 2000 years, but also has exerted a profound influence on the development of mathematics in the neigh-bouring countries and regions. At last it also translated into English. In this paper, some differences between the Orignal and the New Translated Nine Chapters will be introduced and a problem of Mathematical Treatise in Nine Sections (Shushu Jiuzhang, 수서구장, 1247) of Qin Jiushao(진구소, 1202∼1261 AD) in the Song (송, 960∼1261 AD) Dynasty It looks like an insect in the amber but not error.

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Early History of Linear Algebra (초기 선형대수학의 역사)

  • Lee, Sang-Gu;Lee, Jae Hwa;Ham, Yoon Mee
    • Communications of Mathematical Education
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    • v.26 no.4
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    • pp.351-362
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    • 2012
  • Until the 1950s, linear algebra was considered only as one of abstract and advanced mathematics subject among in graduate mathematics courses, mainly dealing with module in algebra. Since the 1960s, it has been a main subject in undergraduate mathematics education because matrices has been used all over. In Korea, it was considered as a course only for mathematics major students until 1980s. However, now it is a subject for all undergraduate students including natural science, engineering, social science since 1990s. In this paper, we investigate the early history of linear algebra and its development from a historical perspective and mathematicians who made contributions. Secondly, we explain why linear algebra became so popular in college mathematics education in the late 20th century. Contributions of Chinese and H. Grassmann will be extensively examined with many newly discovered facts.