• Journal for History of Mathematics
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• v.19 no.3
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• pp.21-42
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• 2006

We investigate chinese mathematicians and their works including their books. We also compare the present transcription of chinese mathematicians and their mathematics books with that in published books on history of chinese mathematics.

• Journal for History of Mathematics
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• v.33 no.1
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• pp.1-19
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• 2020

Under 2009 Revised Mathematics Curriculum and 2015 Revised Mathematics Curriculum, mathematics teachers can help students inductively express real life problems related to sequences but have difficulties in dealing with problems asking the general terms of the sequences defined inductively due to 'Guidelines for Teaching and Learning'. Because most of textbooks mainly deal with the simple calculation for the sums of sequences, students tend to follow them rather than developing their inductive and deductive reasoning through finding patterns in the sequences. In this study, we reconstruct 8 problems to find the sums of sequences in MukSaJipSanBup which is known as one of the oldest mathematics book of Chosun Dynasty, using the terminology and symbols of the current curriculum. Such kind of problems can be given in textbooks and used for teaching and learning. Using problems in mathematical books of Chosun Dynasty with suitable modifications for teaching and learning is a good method which not only help students feel the usefulness of mathematics but also learn the cultural value of our traditional mathematics and have the pride for it.

• 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.17 no.1
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• pp.1-14
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• 2004

Iksan(翼算) written by Lee Sang Hyuk(李相赫, 1810∼\ulcorner) is unique among mathematical books published in Chosun Dynasty since it is the only book which accomplishes the conceptualization of theory of equations if not that of mathematics itself. We investigate its process by his other publications and mathematical interaction with Nam Byung Gil(南秉吉, 1820∼1869).

• Journal for History of Mathematics
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• v.16 no.1
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• pp.9-16
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• 2003

This paper aims to investigate how Chinese and Korean evaluate $\pi$ and measure tile area of circle by reviewing the problems in the old mathematical books. The books are Gu-Jang-San-Sul(The nine chapters on tile mathematical art) for China and Gu-Il-Jib for Chosun Dynasty. The result shows that our ancestors used the different values of ${\pi}$ in relation to the accuracy and the various methods for measuring the area of circle.

• Journal for History of Mathematics
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• v.20 no.1
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• pp.1-16
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• 2007

In the 19th century, Chosun mathematicians studied the most distinguished mathematicians Qin Jiu Shao(泰九韶), Li Ye(李治) Zhu Shi Jie(朱世傑) in Song(宋), Yuan(元) Dynasty and they established a solid theoretical development on the theory of equations. These studies began with their study on Si yuan yu jian xi cao(四元玉鑑細艸) compiled by Luo Shi Lin(羅士琳). Among those Chosun mathematicians, Lee Sang Hyuk(李尙爀, $1810{\sim}?$) and Nam Byung Gil(南秉吉 $1820{\sim}1869$) contributed prominently to the research. Relating to Si yuan yu jian xi cao, Nam Byung Gil and Lee Sang Hyuk compiled OgGamSeChoSangHae(玉監細艸詳解) and SaWonOgGam(四元玉鑑), respectively and then later they wrote SanHakJeongEi(算學正義) and IkSan(翼算), respectively. The latter in particular contains most creative results in Chosun Dynasty mathematics. Using these books, we study the relation between the development of Chosun mathematics and Si yuan yu jian.

• Journal for History of Mathematics
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• v.11 no.1
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• pp.1-9
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• 1998

This article explores what is the genuine Koreanness in Korean arithmetic by examining what kind of influence the Chinese arithmetic had on the Korean arithmetic and how the Korean arithmetic scholars had accepted and utilized it. Because the main stream of Korean culture before the end of Chosun dynasty was located under the umbrella of the Chinese philosophy, technique, and culture, it is necessary to make researches on the historical documents and materials in order to establish the milestone in the Korean arithmetic history for the Korean arithmetic scholars. For this research, the arithmetic books published in between the sixteenth century and the end of Chosun dynasty are mainly consulted and discussed, dealing with the bibliographical introduction in the arithmetic Part in Re Outline History of the Korean Science & Technology written by Prof. Yong-Woon Kim.

• 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.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 for History of Mathematics
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• v.18 no.1
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• pp.33-48
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• 2005

The Rule of False Position is known as an arithmetical solution of algebraical equations. On the other hand, the Excess-Deficit Rule is an algorithm for calculating about excessive or deficient quantitative relations, which is found in the ancient eastern mathematical books, including the nine chapters on the mathematical arts. It is usually said that the origin of the Rule of False Position is the Excess-Deficit Rule in ancient Chinese mathematics. In relation to these facts, we pose two questions: - As many authors explain, the excess-deficit rule is a solution of simultaneous linear equations？ - Which relation is there between the two rules explicitly？ To answer these Questions, we consider the Rule of Single/Double False Position and research the Excess-Deficit Rule in some ancient mathematical books of Chosun Dynasty that was heavily affected by Chinese mathematics. And we pursue their historical traces in Egypt, Arab and Europe. As a result, we can make sure of the status of the Excess-Deficit Rule differing from the Rectangular Arrays(the solution of simultaneous linear equations) and identify the relation of the two rules: the application of the Excess-Deficit Rule including supposition in ancient Chinese mathematics corresponds to the Rule of Double False Position in western mathematics. In addition, we try to appreciate didactical value of the Rule of False Position which is apt to be considered as a historical by-product.