• Title, Summary, Keyword: Cho Tae Gu(趙泰耉, 1660-1723)

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Chosun Mathematics in the early 18th century (18세기(世紀) 초(初) 조선(朝鮮) 산학(算學))

  • Hong, Sung-Sa;Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.25 no.2
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    • pp.1-9
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    • 2012
  • After disastrous foreign invasions in 1592 and 1636, Chosun lost most of the traditional mathematical works and needed to revive its mathematics. The new calendar system, ShiXianLi(時憲曆, 1645), was brought into Chosun in the same year. In order to understand the system, Chosun imported books related to western mathematics. For the traditional mathematics, Kim Si Jin(金始振, 1618-1667) republished SuanXue QiMeng(算學啓蒙, 1299) in 1660. We discuss the works by two great mathematicians of early 18th century, Cho Tae Gu(趙泰耉, 1660-1723) and Hong Jung Ha(洪正夏, 1684-?) and then conclude that Cho's JuSeoGwanGyun(籌 書管見) and Hong's GuIlJib(九一集) became a real breakthrough for the second half of the history of Chosun mathematics.

Approximate Solutions of Equations in Chosun Mathematics (방정식(方程式)의 근사해(近似解))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • Journal for History of Mathematics
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    • v.25 no.3
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    • pp.1-14
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    • 2012
  • Since JiuZhang SuanShu(九章算術), the basic field of the traditional mathemtics in Eastern Asia is the field of rational numbers and hence irrational solutions of equations should be replaced by rational approximations. Thus approximate solutions of equations became a very important subject in theory of equations. We first investigate the history of approximate solutions in Chinese sources and then compare them with those in Chosun mathematics. The theory of approximate solutions in Chosun has been established in SanHakWonBon(算學原本) written by Park Yul(1621 - 1668) and JuSeoGwanGyun(籌書管見, 1718) by Cho Tae Gu(趙泰耉, 1660-1723). We show that unlike the Chinese counterpart, Park and Cho were concerned with errors of approximate solutions and tried to find better approximate solutions.

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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Finite Series in Chosun Dynasty Mathematics (조선(朝鮮) 산학(算學)의 퇴타술)

  • Hong Sung-Sa
    • Journal for History of Mathematics
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    • v.19 no.2
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    • pp.1-24
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    • 2006
  • We study the theory of finite series in Chosun Dynasty Mathematics. We divide it into two parts by the publication of Lee Sang Hyuk(李尙爀, 1810-?)'s Ik San(翼算, 1868) and then investigate their history. The first part is examined by Gyung Sun Jing(慶善徵, 1616-?)'s Muk Sa Jib San Bub(默思集算法), Choi Suk Jung(崔錫鼎)'s Gu Su Ryak(九數略), Hong Jung Ha(洪正夏)'s Gu Il Jib(九一集), Cho Tae Gu(趙泰耉)'s Ju Su Gwan Gyun(籌書管見), Hwang Yun Suk(黃胤錫)'s San Hak Ib Mun(算學入門), Bae Sang Sul(裵相設)'s Su Gye Soe Rok and Nam Byung Gil(南秉吉), 1820-1869)'s San Hak Jung Ei(算學正義, 1867), and then conclude that the theory of finite series in the period is rather stable. Lee Sang Hyuk obtained the most creative results on the theory in his Ik San if not in whole mathematics in Chosun Dynasty. He introduced a new problem of truncated series(截積). By a new method, called the partition method(分積法), he completely solved the problem and further obtained the complete structure of finite series.

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