• Journal for History of Mathematics
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• v.31 no.4
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• pp.169-181
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• 2018

We here discuss about the roles and meaning of Joseon mathematics in the history of Asian mathematics from cultural perspective. To do so, we focus on culture. We first look at the meanings and the definitions of the terms, civilization and culture, and their differences. We next discuss on the cultural perspective to look at the mathematical history of Korea, which is considered as a part of the history of Asian mathematics. It is notable that Joseon mathematics of Korea made Asian mathematics develop further, and played the roles of academic bridges among China, Korea and Japan. It also kept and prolonged the life of the Asian mathematics up to the beginning of the 20th century.

• Journal for History of Mathematics
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• v.35 no.5
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• pp.131-146
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• 2022

This study is to find out how to use the materials of East Asian history in mathematics classroom. Although the use of the history of mathematics in classroom is gradually considered advantageous, the usage is mainly limited to Western mathematics history. As a result, students tend to misunderstand mathematics as a preexisting thing in Western Europe. To fix this trend, it is necessary to deal with more East Asian history of mathematics in mathematics classrooms. These activities will be more effective if they are organized in the context of students' real life or include experiential activities and discussions. Here, the study suggests a way to utilize the mathematical ideas of Bāguà and Liùshísìguà, which are easily encountered in everyday life, and some concepts presented in 『Nine Chapter』 of China and 『GuSuRyak』 of Joseon. Through this activity, it is also important for students to understand mathematics in a more everyday context, and to recognize that the modern mathematics culture has been formed by interacting and influencing each other, not by the east and the west.

• Journal for History of Mathematics
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• v.32 no.6
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• pp.301-313
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• 2019

This paper briefly examines the Book of Changes that is the philosophical background of East Asian ancient mathematics and its collection of complementary(ShíYì), and then examines the structure and contents of GyeSaJeon, which explains the basic principles of Book of Changes as one of ShíYì. GyesaJeon reveals the unique East Asian thought of dealing with numbers in the process of explaining the formation of Eight-Gwae(Bagua) and Sixty-four-Gwae based on Yin-Yang theory. It understands numbers in terms of symbols, not quantitative, and use them to represent characteristics or hierarchy of certain classes, and to explain certain principles. Based on this, the implications of using East Asian mathematics history in the mathematics classroom are discussed.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.53-66
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• 2009

The east-asian mathematics is highly evaluated in mathematics education. In this paper, we search the geometric problems of east-asian mathematics in high school textbooks and various examinations and investigate how to use such problems. We also confirm that the geometric problems of east-asian mathematics can be widely used as real life materials for introducing new mathematical topics, real life applications for mathematical topics, and valuable source for mathematical discourse.

• Journal for History of Mathematics
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• v.29 no.6
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• pp.317-324
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• 2016

Since Jiuzhang Suanshu, mathematical structures in the traditional East Asian mathematics have been revealed by practical problems. Since then, polynomial equations are mostly the type of $p(x)=a_0$ where p(x) has no constant term and $a_0$ is a positive number. This restriction for the polynomial equations hinders the systematic development of theory of equations. Since tianyuanshu (天元術) was introduced in the 11th century, the polynomial equations took the form of p(x) = 0, but it was not universally adopted. In the mean time, East Asian mathematicians were occupied by kaifangfa so that the concept of zeros of polynomials was not materialized. We also show that Suanxue Qimeng inflicted distinct developments of the theory of equations in three countries of East Asia.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.33-44
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• 2010

We investigate what kind of logic is used in the ancient East Asian mathematics from their philosophical viewpoints. Such viewpoints are the logic by Mozi and the epistemology by Xun zi. We conclude that the logic residng in the ancient East Asian mathematics is surely existent and that the logic is the mathematics itself.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.387-394
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• 2014

Since ancient civilization, solving equations has become one of the most important subjects in mathematics and mathematics education. The extractions of square roots and cube roots were first dealt in Jiuzhang Suanshu in the setting of subdivisions. Extending these, Shisuo Kaifangfa and Zengcheng Kaifangfa were introduced in the 11th century and the subsequent development became one of the most important contributions to mathematics in the East Asian mathematics. The translation of coordinate axes plays an important role in school mathematics. Connecting the translation and Kaifangfa, we find strong didactical implications for improving students' understanding the history of Kaifangfa together with the translation itself although the latter is irrelevant to the former's historical development.

• East Asian mathematical journal
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• v.28 no.4
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• pp.383-401
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• 2012

The purpose of mathematics education includes two important areas; cognitive area that emphasizes mathematical knowledge and understanding and affective area that stresses mathematical interest and attitude. The purpose of mathematics education is not only in acquiring the contents and knowledge but also rousing up interest and attention toward mathematics. Therefore, effort to accomplish this affective purpose has to be made. Introducing history of mathematics to teaching can be a important method for the students to arouse interest and attention toward mathematics. History of mathematics can help the students who are familiar to only manipulation of the symbols to develop a new way of thinking and mathematical thoughts arousing reflective thinking. According to the survey, although the effect of using mathematics history has been recognized, the mathematics history has neither been developed as teaching materials nor reflected in the courses of study. The purpose of this research is to develop the reading materials into suit for the mathematics curriculum to extract contents of the mathematics valuable in using in elementary mathematics teaching, and to investigate the effect of reading materials using the history of mathematics on learning attitude in elementary school. The way of developing materials in this study is as follows. First, to select the interesting and instructive subject for the elementary students such as the story and life of a mathematician, developmental stages of mathematical theory and calculation currently used and finding the patterns of the rules that requires mathematical thoughts. Second, to classify the selected items according to mathematics curriculum. Third, to reorganize the classified items of the appropriate grade with the reading materials of dialogue pattern in order to draw attention and interest from the students I developed 18 kinds materials in accordance with the above procedure and applied 5 materials among them to one class in 4th grade. Analysing the student's responses, First, using history of mathematics helps the students to arouse interest and confidence on mathematical learning attitude. And the students became better attitude of studying by oneself and attention on class. Second, as know by opinions after lesson, most students have a chance refresh one's thinking of mathematics, want to know the other content of history of mathematics and responded to study hard in mathematics. As a result, the reading materials on the basis of the history of mathematics motivates students for mathematics and helps them become confident in mathematics. If the materials are complemented properly, they will be useful and effective for students and teachers.

• Journal for History of Mathematics
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• v.27 no.3
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• pp.155-164
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• 2014

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.

• East Asian mathematical journal
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• v.14 no.2
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• pp.321-327
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• 1998

There have been various proofs of the Legendre duplication formula for the Gamma function. Another proof of the formula is given here and a brief history of the Gamma function is also provided.