• Title/Summary/Keyword: 구장산술

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Study on the Volume of a Sphere in the Historical Perspective and its Didactical Implications (구의 부피에 대한 수학사적 고찰 및 교수학적 함의)

  • Chang, Hye-Won
    • Journal for History of Mathematics
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    • v.21 no.2
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    • pp.19-38
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    • 2008
  • This study aims to investigate the evolution of calculating the volume of a sphere in eastern and western mathematical history. In western case, Archimedes', Cavalieri's and Kepler's approaches, and in eastern case, Nine Chapters';, Liu Hui's and Zus' approaches are worthy of noting. The common idea of most of these approaches is the infinitesimal concept corresponding to Cavalieri's or Liu-Zu's principle which would developed to the basic idea of Calculus. So this study proposes an alternative to organization of math-textbooks or instructional procedures for teaching the volume of a sphere based on the principle.

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History of Indeterminate Equations (불정방정식의 역사)

  • Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.18 no.3
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    • pp.1-24
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    • 2005
  • Although indeterminate equations were dealt in Jiu zhang suan shu and then in Sun zi suan fing and Zhang Giu Jian suan Jing in China, they did not get any substantial development until Qin Jiu Shao introduced da yan shu in his great book Shu shu jiu zhang which solves goneral systems of linear congruences. We first investigate his da yan shu and then study the history of indeterminate equations in Chosun Dynasty. Further, we compare Qin's da yan shu with that in San Hak Jung Eui written by Chosun mathematician Nam Byung Gil.

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On the pronunciation of Hanja based on Gujang Sansul Eumeui (구장산술음의에 비추어본 한자의 독음에 관한 논의)

  • Koh, Youngmee;Ree, Sangwook
    • Journal for History of Mathematics
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    • v.29 no.3
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    • pp.147-155
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    • 2016
  • Ancient books from East Asia, especially, Korea, China and Japan, are all written in Chinese. Ancient mathematical books like 九章算術(Gujang Sansul in Korean sound, Jiuzhang Suanshu in Chinese) is not exceptional and also was written in Chinese. The book 九章算術音義(Gujang Sansul Eumeui in Korean, Jiuzhang Suanshu Yinyi in Chinese), a dictionary-like book on 九章算術was published by official 李籍(Lǐ Jí) of 唐(Tang) dynasty (AD 618-907). We discuss how to pronounce Chinese characters based on 九章算術音義. To do so, we compare the pronunciation of the characters used in the words which are explained in 九章算術音義, to those of the current Korean and Chinese. Surprisingly, the pronunciations of the Chinese characters are almost all accordant with those of both Korean and Chinese.

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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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.

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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Logic of Ancient Mathematics of East Asia : Epistemology by Xun zi, Logic by Mozi (동양 산학의 논리학 : 순자의 인식론과 묵자의 논리학)

  • Koh, Young-Mee;Ree, Sang-Wook
    • Journal for History of Mathematics
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    • v.23 no.3
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    • pp.33-44
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    • 2010
  • We investigate what kind of logic is used in the ancient East Asian mathematics from their philosophical viewpoints. Such viewpoints are the logic by Mozi and the epistemology by Xun zi. We conclude that the logic residng in the ancient East Asian mathematics is surely existent and that the logic is the mathematics itself.

Solutions of Equations in Chosun Mathematics (조선산학(朝鮮算學)의 방정식 해법(解法))

  • Kim, Chang-Il;Yun, Hye-Soon
    • Journal for History of Mathematics
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    • v.22 no.4
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    • pp.29-40
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    • 2009
  • we know that Zeng Cheng Kai Fang Fa is the generalization of the method of square roots and cube roots of ancient through the investigation of China mathematics. In this paper, we have research on traditional solutions equations of China mathematics and the development solutions of equations used by Chosun mathematicians.

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Philosophical Background of East Asian Mathematics and Its Educational Implication with a Focus on GyeSaJeon (동아시아 수학의 철학적 배경과 교육적 함의: 계사전을 중심으로)

  • Jung, Hae-Nam
    • Journal for History of Mathematics
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    • v.32 no.6
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    • pp.301-313
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    • 2019
  • This paper briefly examines the Book of Changes that is the philosophical background of East Asian ancient mathematics and its collection of complementary(ShíYì), and then examines the structure and contents of GyeSaJeon, which explains the basic principles of Book of Changes as one of ShíYì. GyesaJeon reveals the unique East Asian thought of dealing with numbers in the process of explaining the formation of Eight-Gwae(Bagua) and Sixty-four-Gwae based on Yin-Yang theory. It understands numbers in terms of symbols, not quantitative, and use them to represent characteristics or hierarchy of certain classes, and to explain certain principles. Based on this, the implications of using East Asian mathematics history in the mathematics classroom are discussed.

Right Triangles in Traditional Mathematics of China and Korea (산학서의 직각 삼각형)

  • Her Min
    • Journal for History of Mathematics
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    • v.18 no.3
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    • pp.25-38
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    • 2005
  • We briefly survey the history of Chinese mathematics which concerns the resolution of right triangles. And we analyse the problems Yucigugosulyodohae(劉氏勾股述要圖解) which is the mathematical book of Chosun Dynasty and contains the 224 problems about right triangles only. Among them, 210 problems are for resolution of right triangles. We also present the methods for generating the Pythagorean triples and constructing polynomial equations in Yucigugosulyodohae which are needed for resolving right triangles.

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