• Proceedings of the Korean Society for History of Mathematics Conference
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• 2005.11a
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• pp.10-10
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• 2005

• Journal for History of Mathematics
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• v.24 no.1
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• pp.1-13
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• 2011

In Tian mu bi lei cheng chu jie fa(田畝比類乘除捷法) of Yang Hui suan fa(楊輝算法)), Yang Hui annotated detailed comments on the method to find roots of quadratic equations given by Liu Yi in his Yi gu gen yuan(議古根源) which gave a great influence on Chosun Mathematics. In this paper, we show that 'Zeng cheng kai fang fa'(增乘開方法) evolved from a process of binomial expansions of $(y+{\alpha})^n$ which is independent from the synthetic divisions. We also show that extending the results given by Liu Yi-Yang Hui and those in Suan xue qi meng(算學啓蒙), Chosun mathematican Hong Jung Ha(洪正夏) elucidated perfectly the 'Zeng cheng kai fang fa' as the present synthetic divisions in his Gu il jib(九一集).

• Journal for History of Mathematics
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• v.29 no.4
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• pp.219-232
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• 2016

In this paper, the problem posed in Yeonhwando is presumed like the following: "Make the sum of eight numbers in each 13 octagons to be 292, and the sum of four numbers in each 12 squares to be 146 using every numbers once from 1 to 72." Regarding this problem, in this paper, firstly, it is commented that there can be a lot of derived solutions from the Yang Hui's solution. Secondly, the Yang Hui's solution is generalized by using sequence 1 in which the sum of neighbouring two numbers are 73, 73-x by turns, and sequence 2 in which the sum of neighbouring two numbers are 73, 73+x by turns. Thirdly, the Yang Hui's solution is generalized by using the alternating method.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2004.10a
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• pp.10.1-10.1
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• 2004

• East Asian mathematical journal
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• v.27 no.2
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• pp.243-259
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• 2011

The Yang-Hui arithmetic(楊輝算法) is a crucial textbook on mathematics for make out the Orient mathematics. In this thesis, compare the Yang-Hui arithmetic and the part of the equation and the function both in the middle school mathematics of the 7th Educational Curriculum Revision. As well, drawing a parallel between two things is the solution that had given in the Yang-Hui arithmetic and have given in the middle school textbook of the 7th Educational Curriculum Revision.

• Communications of Mathematical Education
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• v.26 no.1
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• pp.1-13
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• 2012

Ki-Won Chang(1903-1966) is considered as the first mathematician who made a contribution to the study of the history of Korean mathematics. In this paper, we introduce contributions of Ki-Won Chang, his discovery of old Korean literatures on mathematics, and his academic contribution on the history of Korean mathematics. Then we analyze and compare his conclusions on old Korean mathematics with recent works of others. This work shows some interesting discovery.

• Journal for History of Mathematics
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• v.31 no.6
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• pp.273-289
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• 2018

The KaiFangFa開方法 of traditional mathematics was completed in ${\ll}$JiuZhang SuanShu九章算術${\gg}$ originally, and further organized in Song宋 $Yu{\acute{a}}n$元 dinasities. The former is the ShiSuoKaiFangFa釋鎖開方法 using the coefficients of the polynomial expansion, and the latter is the ZengChengKaiFangFa增乘開方法 obtaining the solution only by some mechanical numerical manipulations. ${\ll}$SanHak JeongEui算學正義${\gg}$ basically used the latter and improved the estimate-value array by referring to the written-calculation in ${\ll}$ShuLi JingYun數理精蘊${\gg}$. As a result, ZengChengKaiFangFa was more refined so that the KaiFangFa algorithm is more consistent.

• Journal for History of Mathematics
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• v.31 no.5
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• pp.223-234
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• 2018

Ancient Chinese mathematics education has a long history of more than 3,000 years, and many excellent mathematicians have been fostered. However, the systematic framework for teaching mathematics should be considered to be started from the Zhou Dynasty. In this paper, we examined the educational goals, trainees(learners), providers(educators), and contents in mathematics education in the ancient Chinese Zhou Han Dynasty, Tang Dynasty and Song Dynasty.

• 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.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.195-220
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• 2010

The magic square is one of the number arrangements and the sums of each row, column, and diagonal are all equal. The meaning of "方" is "Square". If we don't consider the condition of 'square' then is it possible any number arrangement? There are many special number arrangements such as "magic five number circle(緊五圖)", "magic six number circle(聚六圖)", "magic eight number circle(聚八圖)", "magic nine number circle(攢九圖)", "magic eight camp circle(八陣圖)", "magic nine camp circle(連環圖)" in the ancient Chinese mathematics books such as "楊輝算法", "算法統宗". Also, there is a very special and beautiful number arrangement Jisuguimoondo(地數龜文圖) in the mathematics book "Goosuryak(九數略)" written by Choi suk jung(崔錫鼎) in the Joseon Dynasty. In this study, we introduce a various number arrangements and their properties.