• Title/Summary/Keyword: 동양수학

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Ancient Greece Mathematics and Oriental Mathematics (고대 그리스 수학과 동양 수학)

  • Kim, Jong-Myung
    • Journal for History of Mathematics
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    • v.20 no.2
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    • pp.47-58
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    • 2007
  • In this paper, we shall try to give a comparative study of mathematics developments in ancient Greece and ancient Oriental mathematics. We have found that the Oriental Mathematics. is quantitative, computational and algorithmetic, but the ancient Greece is axiomatic and deductive mathematics in character. The two region mathematics should be unified to give impetus to further development of mathematics in future times.

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Mathematical Rhymes in Oriental Mathematics and Their Didactical Implications (동양 수학에서의 구결 및 그 교수학적 함의)

  • Chang, Hye-Won
    • Journal for History of Mathematics
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    • v.19 no.4
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    • pp.13-30
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    • 2006
  • The purpose of this study is to investigate the meaning and roles of rhymes in oriental mathematics. To do this, we consider the rhymes in traditional chinese, korean, indian, arabian mathematical books and the mathematical knowledge which they implicate. And we discuss the reasons for which they were often used and the roles which they played. In addition, we suggest how to use them in teaching mathematics.

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A Study on The Application of Oriental History of Mathematics in School mathematics (수학 교수-학습에서의 동양 수학사 활용에 관한 연구)

  • Yang, Sung-Ho;Lee, Kyung-Eon
    • The Mathematical Education
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    • v.49 no.1
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    • pp.15-37
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    • 2010
  • In this study, we investigated the application of oriental history of mathematics in school mathematics teaching. We set up three study problems to achieve this purpose. First, we analyze the middle and high school mathematics textbooks and auxiliary books. Second, we survey the mathematics teacher's knowledge and degree of application on history of mathematics. Third, we develop the teaching and learning materials on oriental history of mathematics. We performed three study-methods to settle above study problem. First, we analyzed 24 textbooks and auxiliary books for study problem 1. There were 6 middle school mathematics textbooks and 6 auxiliary books and also 6 high school mathematics textbooks and 6 auxiliary books. We categorized the contents into "anecdote", "systematization", "application of problem", "expansibility of thought", and "comparative of the contents". Second, we surveyed the 78 mathematics teachers's knowledge and degree of application using questionnaire about knowledge and application on history of mathematics. The questionnaire was made up of four types of question; the effect of material about history of mathematics, the understanding of western history of mathematics, the understanding of oriental history of mathematics; the direction of development of teaching material. Third, we exemplified the teaching and learning materials about three categories: "anecdote", "comparative of the contents".

The Role and Meaning of Joseon Mathematics in the History of Asian Mathematics (동양수학사에서의 조선수학의 역할과 의미)

  • Ree, Sangwook
    • Journal for History of Mathematics
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    • v.31 no.4
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    • pp.169-181
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    • 2018
  • We here discuss about the roles and meaning of Joseon mathematics in the history of Asian mathematics from cultural perspective. To do so, we focus on culture. We first look at the meanings and the definitions of the terms, civilization and culture, and their differences. We next discuss on the cultural perspective to look at the mathematical history of Korea, which is considered as a part of the history of Asian mathematics. It is notable that Joseon mathematics of Korea made Asian mathematics develop further, and played the roles of academic bridges among China, Korea and Japan. It also kept and prolonged the life of the Asian mathematics up to the beginning of the 20th century.

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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The geometry of Sulbasu${\={u}}$tras in Ancient India (고대 인도와 술바수트라스 기하학)

  • Kim, Jong-Myung;Heo, Hae-Ja
    • Journal for History of Mathematics
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    • v.24 no.1
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    • pp.15-29
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    • 2011
  • This study was carrying out research on the geometry of Sulbas${\={u}}$tras as parts of looking for historical roots of oriental mathematics, The Sulbas${\={u}}$tras(rope's rules), a collection of Hindu religious documents, was written between Vedic period(BC 1500~600). The geometry of Sulbas${\={u}}$tras in ancient India was studied to construct or design for sacrificial rite and fire altars. The Sulbas${\={u}}$tras contains not only geometrical contents such as simple statement of plane figures, geometrical constructions for combination and transformation of areas, but also algebraic contents such as Pythagoras theorem and Pythagorean triples, irrational number, simultaneous indeterminate equation and so on. This paper examined the key features of the geometry of Sulbas${\={u}}$tras and the geometry of Sulbas${\={u}}$tras for the construction of the sacrificial rite and the fire altars. Also, in this study we compared geometry developments in ancient India with one of the other ancient civilizations.

Reasoning through scheme (도형에 의한 추론 (Schematic Reasoning) : 통시적 사례 연구)

  • Cheong, Kye-Seop
    • Journal for History of Mathematics
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    • v.19 no.4
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    • pp.63-80
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    • 2006
  • Along with natural and algebraic languages, schema is a fundamental component of mathematical language. The principal purpose of this present study is to focus on this point in detail. Schema was already in use during Pythagoras' lifetime for making geometrical inferences. It was no different in the case of Oriental mathematics, where traces have been found from time to time in ancient Chinese documents. In schma an idea is transformed into something conceptual through the use of perceptive images. It's heuristic value lies in that it facilitates problem solution by appealing directly to intuition. Furthermore, introducing schema is very effective from an educational point of view. However we should keep in mind that proof is not replaceable by it. In this study, various schemata will be presented from a diachronic point of view, We will show with emaples from the theory of categories, Feynman's diagram, and argand's plane, that schema is an indispensable tool for constructing new knowledge.

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