홍정하(洪正夏)의 수론(數論)

홍성사,홍영희,김창일,Hong, Sung-Sa,Hong, Young-Hee,Kim, Chang-Il 한국수학사학회 2011 Journal for history of mathematics Vol.24 No.4

조선의 가장 위대한 산학자 홍정하(洪正夏)의 저서 $\ll$구일집(九一集)$\gg$(1724)에 들어있는 최소공배수를 구하는 법을 조사하여 홍정하의 수론에 대한 업적을 밝혀낸다. 홍정하는 두 자연수 a, b의 최대공약수 d와 최소공배수 l 에 대하여 l = $a\frac{b}{d}$=$b\frac{a}{d}$, $\frac{a}{d}$, $\frac{b}{d}$는 서로 소인 것을 인지하여, 자연수 $a_1,\;a_2,{\ldots},a_n$의 최대공약수 D에 대하여, $\frac{a_i}{D}$($1{\leq}i{\leq}n$)도 서로 소이고, 이들의 최소공배수 L도 서로 소인 $c_i(1{\leq}i{\leq}n)$가 존재하여 L = $a_ic_i(1{\leq}i{\leq}n)$임을 보였다. 이 결과는 조선에서 얻어낸 수론에 관한 수학적 업적 중에 가장 뛰어난 것 중의 하나이다. 홍정하가 수학적 구조를 밝혀내는 과정을 드러내는 것이 이 논문의 목적이다. 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.

Mathematical Structures of Joseon mathematician Hong JeongHa

홍성사,홍영희,이승온,Hong, Sung Sa,Hong, Young Hee,Lee, Seung On The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.1

From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.

Hong JeongHa's Tianyuanshu and Zhengcheng Kaifangfa

홍성사,홍영희,김영욱,Hong, Sung Sa,Hong, Young Hee,Kim, Young Wook The Korean Society for History of Mathematics 2014 Journal for history of mathematics Vol.27 No.3

Tianyuanshu and Zengcheng Kaifangfa introduced in the Song-Yuan dynasties and their contribution to the theory of equations are one of the most important achievements in the history of Chinese mathematics. Furthermore, they became the most fundamental subject in the history of East Asian mathematics as well. The operations, or the mathematical structure of polynomials have been overlooked by traditional mathematics books. Investigation of GuIlJib (九一集) of Joseon mathematician Hong JeongHa reveals that Hong's approach to polynomials is highly structural. For the expansion of $\prod_{k=11}^{n}(x+a_k)$, Hong invented a new method which we name Hong JeongHa's synthetic expansion. Using this, he reveals that the processes in Zhengcheng Kaifangfa is not synthetic division but synthetic expansion.

女性의 財產權 行使의 限界와 그 性格

洪成杓(Hong Seong-pyo) 역사학회 1989 역사학보 Vol.122 No.-

콘크리트 내 수분분포에 따른 염분이동 예측

홍성인(Hong, Sung In),정민선(Jung, Min Sun),안기용(Ann, Ki Yong) 한국콘크리트학회 2017 한국콘크리트학회 학술대회 논문집 Vol.29 No.2

지하상가 임대료, 매출액, 고객수에 영향을 미치는 요인에 대한 실증분석

홍성효(Hong, Sung Hyo),임준홍(Im, Jun Hong) 한국지역개발학회 2017 韓國地域開發學會誌 Vol.29 No.4

This study empirically analyzes the determinants of rent, sales, and number of customers of underground shopping malls in Korea. According the results, the rent is not statistically significantly affected by infrastructure (e.g., hardware, customer’s service, or advertisement activities) or joint promotions (e.g., events, offerings event, regular sales, and so on) but by size of trade area, population in the neighborhood, existence of multi-use facilities, and number of stores in the underground shopping mall. However, joint promotions seem to increase sales of shops. As urbanization becomes accelerated, the importance of underground shopping malls with respect of both the effective use and commercial function of urban spaces increases. However, since the high rate of vacancy of underground shopping malls together with deterioration of the original downtown accompanies the negative effect of the inner city decline, it is required that the empirical analyses on the demand for renting stores in underground shopping malls or their rent be performed and policies based on the results be implemented. The empirical results of this paper imply that the efforts to revitalize underground shopping malls should be made along with regeneration of the original downtown and the effect of the efforts could be limited if they are focused on hardwares.

양수과다증의 원인, 진단 및 처치

홍성연 ( Seong Yeon Hong ) 대한주산의학회 2012 Perinatology Vol.23 No.2

Amniotic fluid plays an important role in fetal development and growth. Amniotic fluid volume should be maintained adequately throughout gestational periods. Polyhydramnios is a relatively common obstetrical problem, but is associated with poor perinatal outcome both in mother and fetus. For the proper management of polyhydramnios, it is important to find out accurate causes, but it is not easy even if obstetricians perform thorough prenatal assessments. It is also important to understand the regulation of amniotic fluid volume. Based on these backgrounds, this article will briefly review mechanisms of the regulation of amniotic fluid, and will also review diagnosis, etiologies, managements and prognosis of polyhydramnios.

집적의 경제와 충남 내 지역 간 양극화: 제조업 사례

홍성효 ( Sung Hyo Hong ) 충남연구원 2021 충남연구 Vol.5 No.2

본 논문은 집적의 경제와 충남 내 지역 간 양극화 사이의 관계를 제조업을 사례로 분석한다. 비유사성 지수에 의한 읍면동별 사업체수 분포의 지역 간 격차는 1995년 0.252에서 지속적으로 증가하여 2019년에는 0.440에 이른다. 이는 사업체수 기준 전산업 대비 제조업의 비중이 읍면동 간 균등하게 분포하기 위해 상대적으로 비중이 높은 읍면동에서 그렇지 않은 읍면동으로 이전해야 하는 제조업 사업체수 비중을 의미하기 때문에 동 기간 격차의 정도가 1.7배 증가하여, 제조업에 있어 충남 내 지역 간 양극화가 심화되었음을 의미한다. Tobit모형을 이용한 신생기업 입지결정에 대한 회귀분석결과는 충남 제조업에서 집적의 경제가 존재함을 나타낸다. 이는 지리적 군집을 통한 외부 편익이 혼잡으로 인한 외부비용을 능가함을 의미하여 적어도 단기적으로 충남 내 제조업 입지에서의 지역 간 양극화가 보다 심각해질 수 있음을 함축한다. 충남의 내륙권, 특히 청양군이나 예산군과 같이 인구감소가 지속되고 있는 지역에서의 제조업의 위축은 일자리 감소, 소득 하락, 정주 및 노동 공급 감소, 재화와 서비스에 대한 수요 감소, 재정건전성 악화, 공공재 공급 감축 등을 통한 악순환을 야기할 수 있기 때문에 북부권 중심의 제조업 집중에 따른 긍정적 외부효과를 지속시키되 이외 지역에서의 최저 산업규모를 유지하기 위한 정책적 노력이 필요하다. 고령-친화 산업의 육성이나 소비도시로서의 기능을 강화하는 것도 하나의 방편이 될 수 있을 것이다. This paper analyzes the relationship between agglomeration economies and the inter-regional polarization of the manufacturing industry in Chungnam in the form of a case study. According to the dissimilarity index, the regional disparity in the distribution of the number of businesses by administrative unit (Eup, Myeon or Dong) continued to increase from 0.252 in 1995 to 0.440 in 2019. This refers to the proportion of manufacturing establishments that would need to be relocated from regions with a relatively high ratio to regions with a relatively low ratio in order to evenly distribute the proportion of manufacturing compared to all industries, and it shows that the degree of disparity increased by a factor of 1.7 over the period mentioned. Thus, the inter-regional polarization in the manufacturing sector in Chungnam has deepened. The results of regression analyses of the location choices of new firms using the Tobit model indicate that there are agglomeration economies in the manufacturing industry in Chungnam. This implies that external benefits from geographic clustering outweigh external costs caused by congestion, which indicates that the inter-regional polarization in manufacturing locations in Chungnam may even become more serious, at least in the short term. Shrinking of the manufacturing sector in the inland area of Chungnam, especially in areas with continuing population decline such as Cheongyang-gun or Yesan-gun, would cause a vicious cycle through job loss, income decline, decrease in settlement and labor supply, decrease in demand for goods and services, deterioration of fiscal soundness, and supply of public goods. Therefore, it is not only necessary to maintain the positive externalities of the concentration of manufacturing in the northern region, but also to maintain some industries at or above a minimum margin in other regions. Fostering an aging-friendly industry or strengthening the consumption function of cities may be possible ways.

일본 신화에 나타난 고대 한일 교류의 편린 : 상어(와니)를 중심으로

홍성목(Hong Seong Mok) 일본어문학회 2017 일본어문학 Vol.77 No.-

海と共に暮してきた日本人には、サメは特別な存在であったと思われるが、こうしたサメに対する認識は、日本の神話と伝説を伝える『古事記』と『日本書紀』、そして『風土記』におけるサメのエピソードによく現れている。そして韓国の東海と面している日本の山陰地方には、サメに関わる様々な神話や伝説及びサメを使った多様な料理が今まで伝えられている。韓半島の場合、古代韓国の神話や伝説を伝える『三国史記』と『三国遺事』にサメは登場しないが、古代韓半島、特に新羅地方にはサメに関わる特別な呪術儀式や観念が存在した。これは慶尚道地方で海岸沿いだけでなく、大邱をはじめ内陸に位置する古代新羅の遺跡発掘調査で儀式や占いに使われたサメの骨が多く出土されたことからよくわかる。現在韓国の慶尚道地方では、祭祀の時必ずサメの肉であるド厶ベギを供え、おかずとして食べられる。ところが、新羅と地理的に近い日本の山陰地方でもサメを食べている。さらに記紀神話や風土記の伝承にはアメノヒボコをはじめ、新羅人の活躍が様々な形で伝えられ、そして山陰地方に残されている新羅神社の存在からも古代新羅と日本の文化的交流と新羅人の活躍が推測できよう。 For Japanese who have lived with the sea, it seems that the shark was a special existence, but the recognition of such sharks is well depicted in “Kojiki,” “Nihon Shoki,” and “Hudoky” that convey Japanese myths and legends, and it often appears in shark episodes. And in Japan’s San-in District, which is in contact with the Donhae of South Korea, various myths, legends, and diverse cuisines related to sharks have been reported so far.In the case of Korea, sharks do not appear in “Sankokusiki” and “Sankokuizi” that convey ancient Korean myths and legends, but in the ancient Korean peninsula, especially the Silla region, there were special magic rituals and ideas related to sharks. Anumber of shark bones used for rituals and fortune-telling were excavated not only along the coast in the Gyeongsang province but also in the excavation survey of the ancient Shilla located in the inland as well as Daegu. Currently in the Gyeongsang province of South Korea, they eat sharks as a side dish with donbe vegie which is the shark’s meat at the time of ritual. However, they also eat sharks in the San-in District of Japan which is geographically close to Shilla. In addition to the history of Kiki myths and “Hudoky”, Amenohiboko and other activities of the Shilla were conveyed in various forms, and from the existence of the Shilla Shrine left in the San-in District as well, we can estimate the cultural exchange between the ancient Shilla and Japan as well as the activity of the Shilla people.

18세기(世紀) 조선(朝鮮)의 구고술(句股術)

홍성사,홍영희,김창일,Hong, Sung-Sa,Hong, Young-Hee,Kim, Chang-Il 한국수학사학회 2007 Journal for history of mathematics Vol.20 No.4

18세기 초 중인(中人) 홍정하(洪正夏)($1684{\sim}?$)의 구일집(九一集)과 양반(兩班) 조태구(趙泰耉)($1660{\sim}1723$)의 주서관견(籌書管見)에 들어 있는 구고술(句股術)을 조사한다. 구조적 접근과 천원술(天元術)을 통하여 홍정하(洪正夏)는 동양(東洋)에서 가장 앞선 구고술(句股術)의 결과를 얻어내었다. 또 17세기 중엽에 서양(西洋) 수학(數學)이 조선(朝鮮)에 유입된 후 조선(朝鮮) 산학(算學)에 이론적 접근이 이루어지는 과정을 조태구(趙泰耉)의 구고술(句股術)을 통하여 연구한다. 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.