• Title/Summary/Keyword: Hong Jung Ha(洪正夏, 1684~?)

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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.

Chosun Mathematician Hong Jung Ha's Genealogy (조선(朝鮮) 산학자(算學者) 홍정하(洪正夏)의 계보(系譜))

  • Kim, Chang-Il;Hong, Sung-Sa;Hong, Young-Hee
    • Journal for History of Mathematics
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    • v.23 no.3
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    • pp.1-20
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    • 2010
  • Hong Jung Ha(洪正夏, 1684~?) is the greatest mathematician in Chosun dynasty and wrote a mathematics book Gu Il Jib(九一集) which excels in the area of theory of equations including Gou Gu Shu. The purpose of this paper is to find his influence on the history of Chosun mathematics. He belongs to ChungIn(中人) class and works only in HoJo(戶曹) and hence his contact to other mathematicians is limited. Investigating his colleagues and kinship relations including the affinity and consanguinity, we conclude that he gave a great influence to those people and find that three great ChungIn mathematicans Gyung Sun Jing(慶善徵, 1684~?), Hong Jung Ha and Lee Sang Hyuk(李尙爀, 1810~?) are all related through marriage.

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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Hong Jung Ha's Number Theory (홍정하(洪正夏)의 수론(數論))

  • Hong, Sung-Sa;Hong, Young-Hee;Kim, Chang-Il
    • Journal for History of Mathematics
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    • v.24 no.4
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    • pp.1-6
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    • 2011
  • We investigate a method to find the least common multiples of numbers in the mathematics book GuIlJib(구일집(九一集), 1724) written by the greatest mathematician Hong Jung Ha(홍정하(洪正夏), 1684~?) in Chosun dynasty and then show his achievement on Number Theory. He first noticed that for the greatest common divisor d and the least common multiple l of two natural numbers a, b, l = $a\frac{b}{d}$ = $b\frac{a}{d}$ and $\frac{a}{d}$, $\frac{b}{d}$ are relatively prime and then obtained that for natural numbers $a_1,\;a_2,{\ldots},a_n$, their greatest common divisor D and least common multiple L, $\frac{ai}{D}$($1{\leq}i{\leq}n$) are relatively prime and there are relatively prime numbers $c_i(1{\leq}i{\leq}n)$ with L = $a_ic_i(1{\leq}i{\leq}n)$. The result is one of the most prominent mathematical results Number Theory in Chosun dynasty. The purpose of this paper is to show a process for Hong Jung Ha to capture and reveal a mathematical structure in the theory.