• Title, Summary, Keyword: 구고술

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Gou Gu Shu in the 19th century Chosun (19세기(世紀) 조선(朝鮮)의 구고술(句股術))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • Journal for History of Mathematics
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    • v.21 no.2
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    • pp.1-18
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    • 2008
  • As a sequel to the previous paper Gou Gu Shu in the 18th century Chosun, we study the development of Chosun mathematics by investigating that of Gou Gu Shu in the 19th century. We investigate Gou Gu Shu obtained by Hong Gil Ju, Nam Byung Gil, Lee Sang Hyuk and Cho Hee Soon among others and find some characters of the 19th century Gou Gu Shu in Chosun.

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Gou Gu Shu in the 18th century Chosun (18세기(世紀) 조선(朝鮮)의 구고술(句股術))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • Journal for History of Mathematics
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    • v.20 no.4
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    • pp.1-21
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    • 2007
  • We investigate the Gou Gu Shu(句股術) in Hong Jung Ha's Gu Il Jib(九一集) and Cho Tae Gu's Ju Su Gwan Gyun(籌書管見) published in the early 18th century. Using a structural approach and Tien Yuan Shu(天元術), Hong has obtained the most advanced results on the subject in Asia. Using Cho's result influenced by the western mathematics introduced in the middle of the 17th century, we study a process of a theoretical approach in Chosun mathematics in the period.

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Gou Gu Shu and Theory of equations in Chosun (조선(朝鮮)의 구고술(勾股術)과 방정식론)

  • Yun, Hye-Soon
    • Journal for History of Mathematics
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    • v.24 no.4
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    • pp.7-20
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    • 2011
  • Investigating constructions of equations by Gou gu shu(勾股術) in Hong Jung Ha(洪正夏)'s GuIlJib(九一集), Nam Byung Gil(南秉吉)'s YuSiGuGoSulYoDoHae(劉氏勾股術要圖解) and Lee Sang Hyuk(李尙爀)'s ChaGeunBangMongGu(借根方蒙求), we study the history of development of Chosun mathematics. We conclude that Hong's greatest results have not been properly transmitted and that they have not contributed to the development of Chosun mathematics.

An Analysis of the Contents and Expression Methods of Jeong Yag-yong's 『Gugo Wonlyu』 (정약용의 『구고원류』의 내용과 표현방법 분석)

  • Lee, Kyung Eon
    • Journal for History of Mathematics
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    • v.29 no.1
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    • pp.1-16
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    • 2016
  • This study analyzes the contents and expression methods of Jeong Yag-yong's "Gugo Wonlyu". The 530-page long "Gugo Wonlyu" discusses 1541 formulas about Gu, Go, Hyun, Hwa, Gyo; however, it has only the results of formulas and no explanations about their inducement method. Therefore we do not know how he derives and verifies the formulas. In addition, it did not follow the basic form of oriental mathematics textbooks: problem-answer-solution, and presented all the formulas only with characters without using numbers. This is a very distinctive aspect compared to other mathematical textbooks. In addition, the formulas about 5-Hwa and 5-Gyo are addressed exactly in fixed order and covers a formula in various directions. This is a clear evidence that Jeong Yag-yong analyzed and studied the Gugosul thoroughly.

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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조선조대 구고의 양화술

  • 유인영
    • 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.

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Chosun mathematics in the 17th Century and Muk Sa Jib San Beob (17세기 조선 산학(朝鮮 算學)과 ${\ll}$묵사집산법(默思集筭法)${\gg}$)

  • Jin, Yuzi;Kim, Young-Wook
    • Journal for History of Mathematics
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    • v.22 no.4
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    • pp.15-28
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    • 2009
  • In this paper, we study the 17th Century Chosun's mathematics book ${\ll}$Muk Sa Jib San Beob${\gg}$ written by Chosun's mathematician Kyeong Seon Jing. Our study of thebook shows the ${\ll}$Muk Sa Jip San Beop${\gg}$ as an important 17th Century mathematics book and also as a historical data showing the mathematical environment of 17th Century Chosun.

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Jin-Yuan Mathematics and Quanzhen Taoism (금원수학여전진도(金元数学与全真道))

  • Guo, Shuchun
    • Journal for History of Mathematics
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    • v.29 no.6
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    • pp.325-333
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    • 2016
  • Chinese Mathematics during the period of Jin (1115-1234) and Yuan (1271-1368) is an integral part of the high achievements of traditional mathematics during the Song (962-1279) and Yuan dynasties, which is another peak in the history of Chinese mathematics, following the footsteps of the high accomplishments during the Warring States period (475-221 BCE), the Western Han (206 BCE-24 ADE), Three Kingdoms (220-280 AD), Jin dynasty (265-420 AD), and Southern and Northern Dynasties (420-589 AD). During the Jin-Yuan period, Quanzhen Taoism was a dominating branch in Taoism. It offered certain political protection and religious comforts to many during troubled times; it also provided a relatively stable environment for intellectual development. Li Ye (1192-1279), Zhu Shijie (fl. late 13th C to early 14th C) and Zhao Youqin (fl. late 13th C to early 14th C), the major actors and contributors to the Jin-Yuan Mathematics achievements, were either heavily influenced by the philosophy of Quanzhen Taoism, or being its followers. In certain Taoist Classics, Li Ye read the records of the relations of a circle and nine right triangles which has been known as Dongyuan jiurong 洞渊九容 of Quanzhen Taoism. These relations made significant contributions in the study of the circles inscribed in a right triangle, the reasoning of which directly led to the birth of the Method of Celestial Elements (Tianyuan shu 天元术), which further developed into the Method of Two Elements (Eryuan shu ⼆元术), the Method of Three Elements (Sanyuan shu 三元术) and the Method of Four Elements (Siyuan shu 四元术).