• Journal for History of Mathematics
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• v.22 no.4
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• pp.41-52
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• 2009

This study investigates a mathematical subject, 'triangles' in mathematics books of Chosun Dynasty, in special Muk Sa Jib San Bub(默思集算法), Gu Il Jib(九一集), San Hak Ib Mun(算學入門), Ju Hae Su Yong(籌解需用), and San Sul Gwan Gyun(算術管見). It is likely that they apt to avoid manipulating general triangles except the right triangles and the isosceles triangles etc. Our investigation says that the progress of triangle-related contents in Chosun mathematics can fall into three stages: measurement of the triangle-shaped fields, transition from the object of measurement to the object of geometrical study, and examination of definition, properties and validation influenced by western mathematics.

• Journal for History of Mathematics
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• v.19 no.3
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• pp.1-20
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• 2006

The administrative service in Chosun Dynasty relating to mathematics was carried out by the middle class(中人) mathematicians selected by the official selection examination(取才). They belong to HoJo(戶曹) department and their ranks are GyeSa(計士), ByulJe(別提), HunDo(訓導 = mathematics teacher), and GyoSu(敎授 = mathematics professor). We call them SanWon(算員). HunDo and GyoSu played very important role although their ranks are low, for they educate SanWon and manage the official selection examination. Using JuHakSeonSaengAn(籌學先生案, List of mathematics teachers) and JuHakIpGyukAn(籌學入格案, List of successful candidates in the official selection examination for mathematics), we investigate HunDo and GyoSu in Chosun Dynasty.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.61-78
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• 2009

We first of all emphasize the importance of the research on the history of Korean mathematics. We next make a survey of the brief history of Chosun mathematics as a seed knowledge for further research on Korean mathematics. We hope that our survey will serve researchers as a seed knowledge of their research.

• Journal for History of Mathematics
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• v.17 no.4
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• pp.1-16
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• 2004

Investigating theory of equations in Chosun Dynasty mathematics books Mooksa-jipsanbub, Guiljib(九一集), Chageunbangmonggu(借根方夢求), Sanhakjungeui (算學正義), and Iksan(翼算), we study the history of equation theory in Chosun Dynasty. We first deal with development of representation of polynomials and equations and then method how to solve them.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.1-14
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• 2009

Since western mathematics and astronomy had been introduced in Chosun dynasty in the 17th century, most of Chosun mathematicians studied Shu li jing yun(數理精蘊) for the western mathematics. In the last two decades of the 19th century, Chosun scholars have studied them which were introduced by Japanese text books and western missionaries. The former dealt mostly with elementary arithmetic and the latter established schools and taught mathematics. Lee Sang Seol(1870~1917) is well known in Korea as a Confucian scholar, government official, educator and foremost Korean independence movement activist in the 20th century. He was very eager to acquire western civilizations and studied them with the minister H. B. Hulbert(1863~1949). He wrote a mathematics book Su Ri(數理, 1898-1899) which has two parts. The first one deals with the linear part(線部) and geometry in Shu li jing yun and the second part with algebra. Using Su Ri, we investigate the process of transmission of western mathematics into Chosun in the century and show that Lee Sang Seol built a firm foundation for the study of algebra in Chosun.

• Journal of the Korean School Mathematics Society
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• v.23 no.1
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• pp.25-44
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• 2020

This study investigated the representation and algorithms of western mathematics reflected on the algebra domains of Chosun-Sanhak in the 18th century. I also analyzed the co-occurrences and replacement phenomenon between western algorithms and traditional algorithms. For this purpose, I analyzed nine Chosun mathematics books in the 18th century, including Gusuryak and Gosasibijip. The results of this study are as follows. First, I identified the process of changing to a calculation by writing of western mathematics, from traditional four arithmetical operations using Sandae and the formalized explanation for the proportional concept and proportional expression. Second, I observed the gradual formalization of mathematical representation of the solution for a simultaneous linear equation. Lastly, I identified the change of the solution for square root from traditional Gaebangsul and Jeungseunggaebangbeop to a calculation by the writing of western mathematics.

• 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.

• Journal of Educational Research in Mathematics
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• v.27 no.4
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• pp.811-831
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• 2017

The purpose of this study is to analyze the contents of pi of Chosun-sanhak and organize the teaching and learning activities to help to understand the concept of pi deeply using the analysis results. The results of this study are as follows. First, Chosun-sanhak used various approximate values of pi and those were represented as the form to reveal the meaning of the ratio of radius and circumference. Second, There were the freedom of selection of the approximate values of pi suitably. Lastly, the enriched leaning about pi need to draw a distinction pi from approximate values of pi, choose the suitable approximate values of pi and compare the method of calculation of circumference and the area of circle of Chosun-sanhak and today's mathematics. In conclusion, I proposed several issues which is worth exploring further in relation to pi and Chosun-Sanhak.

• Journal for History of Mathematics
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• v.26 no.2_3
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• pp.123-130
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• 2013

It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.39-54
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• 2005

In Chinese Mathematics, Jia Xian(要憲) introduced Zeng cheng kai fang fa(增乘開方法) to get approximations of solutions of Polynomial equations which is a generalization of square roots and cube roots in Jiu zhang suan shu. The synthetic divisions in Zeng cheng kai fang fa give ise to two concepts of Fan il(飜積) and Yi il(益積) which were extensively used in Chosun Dynasty Mathematics. We first study their history in China and Chosun Dynasty and then investigate the historical fact that Chosun mathematicians Nam Byung Gil(南秉吉) and Lee Sang Hyuk(李尙爀) obtained the sufficient conditions for Fan il and Yi il for quadratic equations and proved them in the middle of 19th century.