• 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.

• Journal for History of Mathematics
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• v.25 no.4
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• pp.1-10
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• 2012

In Chinese mathematics, there have been two numeral systems, namely one in spoken language for recording and the other by counting rods for computations. They concerned with problems dealing with practical applications, numbers in them are concrete numbers except in the process of basic operations. Thus they could hardly develop a pure theory of numbers. In Song dynasty, 0 and TianYuanShu were introduced, where the coefficients were denoted by counting rods. We show that in this process, counting rods took over the role of the numeral system in spoken language and hence counting rod numeral system plays the role of that for abstract numbers together with the tool for calculations. Decimal fractions were also understood as denominate numbers but using the notions by counting rods, decimals were also admitted as abstract numbers. Noting that abacus replaced counting rods and TianYuanShu were lost in Ming dynasty, abstract numbers disappeared in Chinese mathematics. Investigating JianJie YiMing SuanFa(簡捷易明算法) written by Shen ShiGui(沈士桂) around 1704, we conclude that Shen noticed repeating decimals and their operations, and also used various rounding methods.

• Communications of Mathematical Education
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• v.28 no.3
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• pp.375-394
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• 2014

The purpose of this study is to examine the transition of mathematical representation in Joseon mathematics, which is focused on numbers and operations, letters and expressions. In Joseon mathematics, there had been two numeral systems, one by chinese character and the other by counting rods. These systems were changed into the decimal notation which used Indian-Arabic numerals in the late 19th century passing the stage of positional notation by Chinese character. The transition of the representation of operation and expressions was analogous to that of representation of numbers. In particular, Joseon mathematics represented the polynomials and equations by denoting the coefficients with counting rods. But the representation of European algebra was introduced in late Joseon Dynasty passing the transitional representation which used Chinese character. In conclusion, Joseon mathematics had the indigenous representation of numbers and mathematical symbols on our own. The transitional representation was found before the acceptance of European mathematical representations.

• Journal of Educational Research in Mathematics
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• v.13 no.4
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• pp.429-446
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• 2003

Gu-il-jip is a mathematical book of Chosun dynasty in the 18c. It consists of nine chapters including more than 473 problems and their solutions. Analyzing the problems and their solutions, we can appreciate the mathematical researches by the professional mathematicians of Chosun. Especially, it is worth noting the followings: - units for measuring and decimal notations - $\pi$, area of circle, volume of sphere - naming the powers - counting rods - excess and deficit: calculation technique for excess-deficit relations among quantities - rectangular arrays: calculation technique for simultaneous linear equations - 'Thien Yuan' notation: method for representing equations - 'Khai Fang': algorithm for numerical solution of quadratic, cubic and higher equations Based on these analyses, some pedagogical applications are proposed.

• Journal of the Optical Society of Korea
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• v.18 no.5
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• pp.598-604
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• 2014

A polarization fluorescence correlation spectroscopy system based on a confocal microscope was built to study the rotational and translational diffusion of CdSe/CdS quantum rods (Q-rods), with the same and different polarization states between the polarizer and the analyzer (i.e. the XXX and XYY states). The rotational diffusion amplitude showed the dependences on polarization of $0.75{\pm}0.05$ in the XXX state and $0.26{\pm}0.03$ in the XYY state, when the translational diffusion amplitude was 1. The diffusion coefficients of the Q-rods were found based on their translational and rotational diffusion times in the two polarization states, in solutions with viscosity ranging from 0.9 to 6.9 cP. The translational and rotational diffusion coefficients ranged from $1.5{\times}10^{-11}$ to $2.6{\times}10^{-12}m^2s^{-1}$ and from $2.9{\times}10^5$ to $5.6{\times}10^4s^{-1}$, respectively.

• Journal for History of Mathematics
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• v.19 no.4
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• pp.13-30
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• 2006

The purpose of this study is to investigate the meaning and roles of rhymes in oriental mathematics. To do this, we consider the rhymes in traditional chinese, korean, indian, arabian mathematical books and the mathematical knowledge which they implicate. And we discuss the reasons for which they were often used and the roles which they played. In addition, we suggest how to use them in teaching mathematics.

• The Journal of the Korea Contents Association
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• v.9 no.11
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• pp.247-253
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• 2009

We investigated the cell growth rate according to the change of temperature of the Thermo-rod used for the local hyperthermia therapy. For this study, we fabricated the Thermo-rods (TR) using Duplex Stainless Steels having magnetic properties as well as non magnetic properties. To evaluate cell growth rates up to 15 days, we conducted cell proliferation test using cell counting methods. For the tests, the CAPEs and Osteoblats were seeded on the 6-we11 plates with the induction heated thermo-rods 30 mins a day for 15 days with 2 days interval and without induction heated thermo-rods as control group respectively. We calculated cell growth rates, 6 hours after heating. From the results, in case of CAPEs and Osteobalsts seeded groups, the cell growth rates in all groups increased drastically for 6 days after seeding, but decreased irregularly after 6 days. In conclusion, the cell growth rates showed no significant difference among all groups and it indicated that there were no effects of temperate ($41^{\circ}C$) on cell growth rates.