• Journal for History of Mathematics
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• v.18 no.1
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• pp.49-66
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• 2005

We briefly survey the history of abacus and counting rods which had been most widespread devices for arithmetical calculations. And we explain and compare the methods and principles of calculation on the abacus and counting rods. Only multiplication and division are presented here with examples. In these course we can see that the principles of calculation on the abacus are inherited from that of calculation on the counting rods. We also discuss the educational value of the abacus.

• Proceedings of the Korean Society for History of Mathematics Conference
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• 2004.10a
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• pp.4.2-4.2
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• 2004

• 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.