• Journal for History of Mathematics
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• v.26 no.1
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• pp.1-9
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• 2013

It is well known that the development of mathematics in eastern Asia was based on Chinese mathematics. Investigating Chinese mathematics books that were brought into Chosun, we study how Chinese mathematics influenced Chosun mathematics. Chinese mathematics books were brought into Chosun in three stages, namely basic mathematics books in the era of King SeJong(1397-1450), Chinese mathematics books influenced by western mathematics in the 17th century and finally those with commentaries on mathematics of Song-Yuan era in the 19th century. We also study the process of their importations.

• 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.

• Communications of Mathematical Education
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• v.25 no.1
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• pp.1-19
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• 2011

HPM(History and Pedagogy of Mathematics) become an important issue to us now. Study on old Korean mathematics books were made recently. We study mathematics books in Kyujanggak in this article. Horng Wann-Sheng 洪萬生, an math. historian and a member of editorial board of Historia Mathematica, visited Kyujanggak, the royal library of Joseon Dynasty. After his visit, he published a paper, "The first visit to mathematics books in Kyujanggak 奎章閣收藏算書初訪"(2008 Kyujanggak 32, p. 283-293). In his paper, he also raised several research problems on the history of Korean mathematics. In this paper, we analyze his paper "The first visit to mathematics books in Kyujanggak" and give some answers to those raised problems on Korean mathematics. Also we correct some misunderstanding of Horng on some facts. Especially, we make it clear that the author of SinJungSanSul(New Arithmetics 新訂算術) was not Lee Sang-Seol(李相卨), whom Horng considered as the author, but Lee Gyo-Seung(李敎承) through the correct translation of its preface and an article about its copyright lawsuit. And we added some pathways how Chinese mathematics books were imported by Joseon. We introduce the case of Hong Dae-Yong(洪大容) in detail.

• Journal for History of Mathematics
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• v.29 no.3
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• pp.147-155
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• 2016

Ancient books from East Asia, especially, Korea, China and Japan, are all written in Chinese. Ancient mathematical books like 九章算術(Gujang Sansul in Korean sound, Jiuzhang Suanshu in Chinese) is not exceptional and also was written in Chinese. The book 九章算術音義(Gujang Sansul Eumeui in Korean, Jiuzhang Suanshu Yinyi in Chinese), a dictionary-like book on 九章算術was published by official 李籍(Lǐ Jí) of 唐(Tang) dynasty (AD 618-907). We discuss how to pronounce Chinese characters based on 九章算術音義. To do so, we compare the pronunciation of the characters used in the words which are explained in 九章算術音義, to those of the current Korean and Chinese. Surprisingly, the pronunciations of the Chinese characters are almost all accordant with those of both Korean and Chinese.

• Journal for History of Mathematics
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• v.28 no.1
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• pp.15-29
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• 2015

This study aims to analyze how the history of mathematics is used in Chinese mathematics textbooks. As a framework for analysis, we categorized nine types of using the history of mathematics in textbooks. We analyzed 18 mathematics textbooks for Chinese elementary and middle schools. As a result, we found that various types of using the history of mathematics were adopted in Chinese textbooks except for explorations of mathematical errors in history. We also noticed three characteristics: preference to using for motivation and reading matters in elementary school levels, high frequencies of using problems from traditional mathematical books and origins of mathematical concepts or symbols, and emphasis on ethnic superiority through the Chinese traditional mathematics. Based on the results of analysis, we discussed and induced some implications for using the history in our mathematics textbooks.

• Journal for History of Mathematics
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• v.33 no.2
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• pp.75-101
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• 2020

We considered the context of the publications and transmissions of mathematics books using the Korean traditional book lists and the catalogues of woodblocks in the Joseon Dynasty and DaeHan大韓 Empire period. Among the results, this paper first describes the context of the publication and transmission of mathematics textbooks of national math exams算學取才 in the first half of Joseon, adding a step more specific to the facts known so far. In 1430, 『YangHui SanFa楊輝算法』, 『XiangMing SuanFa詳明算法』, 『SuanXue QiMeng算學啓蒙』, 『DiSuan地算』, 『WuCao SuanJing五曹算經』 were selected as the textbooks of national math exams算學取才. 『YangHui SanFa』, 『XiangMing SuanFa』, 『DiSuan』 were included in the catalogues of woodblocks in the Joseon Dynasty before the Japanese invasion in 1592, and we could see that Gyeongju慶州, Chuncheon春川, and Wonju原州 were the printing centers of these books. Through other lists, literature records and real text books, it came out into the open that 『XiangMing SuanFa』 was published as movable print books three times at least, 『SuanXue QiMeng』 four times at least in the first half of Joseon Dynasty. And 『XiangMing SuanFa』 was published at about 100 years later than 『YangHui SanFa楊輝算法』 as xylographic books, 『SuanXue QiMeng』 was published twice as xylographic books in the second half of Joseon Dynasty. Whether or not the list of royal books included the Korean or Chinese versions of these books, and additional notation in that shows how the royal estimation of these books changed.

• Journal of Educational Research in Mathematics
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• v.27 no.3
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• pp.451-467
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• 2017

This study examined how the distributive principles(DP) works in our elementary school textbooks and work books to figure out the implications for developing the elementary mathematics curriculum and textbooks. For this purpose, Chinese and Japanese elementary textbooks were reviewed and five criteria for the analysis of Korean textbooks and workbooks were prepared by the review. The analysis showed that Korean textbooks and work books are inefficient to handle DP in many ways. Based on these findings, this study suggested that the DP should be codified into the curriculum and explicitly dealt with in elementary math textbooks.

• 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.

• 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.24 no.2
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• pp.1-15
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• 2011

Approximation is a very useful approach in mathematics research. It was the same in traditional Chinese and Chosun mathematics. This study derived five characteristics from approximation approaches which were found in Chinese and Chosun mathematical books: improvement of approximate values, common and inevitable use of approximate values, recognition of approximate values and their reasons, comparison of their exactness, application of approximate principles. Through these characteristics, we can infer what Chinese and Chosun mathematicians recognized approximate values and how they manipulated them. They took approximate approaches by necessity or for the sake of convenience in mathematical study and its applications. Also, they tried to improve the degree of exactness of approximate values and use the inverse calculations to check them.