• 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.

• 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'.

• 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.

• 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.

• 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.

• 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.

• Journal of the Korean Institute of Oriental Medical Informatics
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• v.17 no.2
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• pp.130-287
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• 2011

"zhenjiusunanyaozhi(鍼灸素難要旨)" is composed of three volumes and published in 1529 by Gao Wu(高武). Gao Wu(高武) is skillful in astronomy, the art of war and the law as well as a medical practitioner in Ming Dynasty. The books he wrote "zhenjiujuying(鍼灸聚英)", "zhizhi(直指)", "douzhenzhengzong(痘疹正宗)", "shexuezhinan(射學指南)", "zhenjiujieyao(鍼灸節要)". "zhenjiusunanyaozhi鍼灸素難要旨" is written by classifying the origin of acupuncture and moxibustion. In other words, it is edited by classifying the contents related to acupuncture and moxibustion out of the ancient Chinese medical book "yellow emperor's canon of medicine and yellow emperor eighty-one difficult" in which are composed of 3 volumes as follows, Volume 1 says the main diseases on "the nine acupuncture needles figure" (九針圖), "the reinforcing and reducing the meridian" (補瀉), "the needle depth" (針刺深淺), "the five shu points - metal, wood, water, fire, earth" (正,滎,輸,經,合) based on 18 chapters in terms of acupuncture in "yellow emperor eighty-one Difficult "難經"", in which it quotes the annotation of "the difficulty by the original meaning "難經本義"" written by Hua Shou(滑壽) in Yuan Dynasty. Volume 2 is composed of 2 parts. Part 1 says the method of treatment on 36 Chapters, the method of acupuncture use in the Linshu "靈樞" and the Suwen "素問" such as "the rule of acupuncture use" (用針方宜), "the nine-pin method" (九針式) and "the nine-pin to only use the time appropriate to consider nature of Heaven, Earth and person" (九針應天地人時以起用) etc., Part 2 says "the five difficult acupuncture(五亂刺)", "the rise and fall of energy and blood(氣血盛衰)". "the pain tolerance(耐痛)" and ect., in which are in terms of method of treatment collected the original texts of 59 chapters on acupuncture to each disease and of 8 chapters on moxibustion in the Linshu "靈樞" and the Suwen "素問". Volume 3 includes 10 chapters in which consist of "the stabbing to disease in 12 meridians (十二經病刺)", "the eight extra meridian disease (寄經八脈病)", "the twelve meridians(十二經脈)", "the fifteen collaterals (十五絡脈), the twelve meridian muscles (十二經筋)", "the acupoint (孔穴)" and etc. This is the book edited comprehensively by classifying the contents on the theory of acupuncture and moxibustion and the circulations of meridians in "yellow emperor's canon of medicine and yellow emperor eighty-one difficult" and there is no case story in particular except his comments in person. This study is for the purpose of helping researching and developing acupuncture and moxibustion and applying their clinical training.

• The Journal of the Society of Korean Medicine Diagnostics
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• v.17 no.2
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• pp.131-155
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• 2013

Objectives A study on the importance of observing face color in the Dongeuibogam and the other things to know when we observe face color. Methods We used Deyuk Dongeuibogam of Dongeuibogam publishing company from original photographic edition. Results (1) In all section(ex. Naekyungpyeon, Oehyeongpyeon and Japbyoungpyeon), the chapters related with observing face color were fifty-one. In Naekyungpyeon, the chapters related with observing face color were nineteen(37%). In Oehyeongpyeon, the chapters related with observing face color were ten(20%). In Japbyoungpyeon, the chapters related with observing face color were twenty-two(43%). In all section(ex. Naekyungpyeon, Oehyeongpyeon and Japbyoungpyeon), the statements related with observing face color were three-hundred and nine. In Naekyungpyeon, the statements related with observing face color were sixty-four(21%). In Oehyeongpyeon, the statements related with observing face color were fifty-two(17%). In Japbyoungpyeon, the statements related with observing face color were one hundred ninety-three(62%). (2) In each chapter, the number of statement related with observing face color was studied. Pediatric Chapter (75) were the most common, followed by The way of finding the cause of a disease (27) Face (26) Cold (24) Weak&Fatigue (12) Phlegm, Jaundice (8) Nose, Worm, Chronic indigestion (7) Mouth&Tongue, Woman, Stool (6) Bodyshape, Liver, Heart, Kidney, Cough (5) Eye, Carbunculosis (4) Blood, Voice, Spleen, Lung, Chest, Fire, Edema, Detoxification (3) in order. (3) In each section(ex. Naekyungpyeon, Oehyeongpyeon and Japbyoungpyeon), the rate of chapter related with observing face color was studied. Naekyungpyeon(73%) was the highest. Japbyoungpyeon(61%). Oehyeongpyeon(38%) was the lowest. Conclusions The importance of each chapter for observing face color in the Dongeuibogam was studied. In addition, the entire ocular inspection, the part ocular inspection, moisture and the difference of skin according to the personal constitution should be considered. There are not only the important parts of the past that does not mean but also the unimportant parts of the past that are meaningful now. Additional studies will be needed for the latter.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.1-26
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• 2003

Gougu Rule for the right triangles is the Chinese Pythagorean theorem. In the late age of the Chosun Dynasty, mathematicians of Chosun pioneered the study of the Chinese Nine Chapters and other advanced mathematical problems as well as the Easternism in spite of the various difficulties after the Imchinoeran(임진왜란), Chungyuchairan(정유재란) and Byungchahoran(병자호란) The technologies of the addition and addition twice are the methods of the solution of the problems in the right triangles. This paper is intended to introduce some problems using these methods of solution.

• 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.