• Journal for History of Mathematics
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• v.23 no.1
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• pp.41-52
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• 2010

Ancient Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sturas in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. And rules or problems of the mathematics were transmitted both orally and in manuscript form.Indian mathematicians made early contributions to the study of the decimal number system, arithmetic, equations, algebra, geometry and trigonometry. And many Indian mathematicians were appearing one after another in Ancient. This paper is a comparative study of mathematics developments in ancient India and the other ancient civilizations. We have found that the Indian mathematics is quantitative, computational and algorithmic by the principles, but the ancient Greece is axiomatic and deductive mathematics in character. Ancient India and the other ancient civilizations mathematics should be unified to give impetus to further development of mathematics education in future times.

• Korean Journal of Child Studies
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• v.3
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• pp.35-48
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• 1982

The purpose of this study is to investigate the Piaget's theory of the child's conception of space, which explains the stage of child's congnitive development. This thesis consists of 4 Chapters, including introduction, which examines the concept of space perception, and the development of arithmetic conception, and suggests the outline of this study. In the Chapter II, the brief history of topological Psychology, and the current situation of this theory has been explained. According to Piaget's theory of the conception of space, the child's development of the conception of space develops orderly three stages, that is to say, the stage of conception of space by the topological relations, the stage of projective conception of space, and finally the stage of the Euclidian, conception of space. Children's development of the conception of space continuously, and orderly has been made by these stages. Also, in this Chapter, Piaget's experiment about the development of child's conception of space has been explained. In the Chapter III, the children's conception of geometry has been examined. Here explains the development of space representation, and of seriation or classification. In the Chapter IV, some theories of the conception of space has been examined, and some points of view has been made as a conclusion.

• Communications of Mathematical Education
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• v.23 no.2
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• pp.461-481
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• 2009

The semiotic approach to the mathematics education has been studied in last 20 years by PME, ICME conferences. New cultural developments in multi-media, digital documents and digital arts and cultures may influence mathematical education and teaching and learning activities. Hence semiotical interest in the mathematics education research and practice will be increasing. In this paper the basic ideas of semiotics, such as Peirce triad and Saussure's dyad, are introduced with some mathematical applications. There is some similarities between traditional research topics for concept, representation and social construction in mathematics education research and semiotic approach topics for the same subjects. some semiotic applications for an arithmetic problem for work, induction, deduction and abduction syllogisms with respect to Peirce's triad, its meaning in scientific discoveries and learning in geometry and symmetry.

• School Mathematics
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• v.4 no.4
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• pp.643-655
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• 2002

In this paper we emphasize the introduction of ‘incommensurability’ on the teaching and learning the irrational number because we think of the origin of number as ‘ratio’. According to Greek classification of continuity as a ‘never ending’ divisibility, discrete number and continuous magnitude belong to another classes. That is, those components were dealt with respectively in category of arithmetic and that of geometry. But the comparison between magnitudes in terms of their ratios took the opportunity to relate ratios of magnitudes with numerical ratios. And at last Stevin coped with discrete and continuous quantity at the same time, using his instrumental decimal notation. We pay attention to the fact that Stevin constructed his number conception in reflecting the practice of measurement : He substituted ‘subdivision of units’ for ‘divisibility of quantities’. Number was the result of such a reflective abstraction. In other words, number was invented by regulation of measurement. Therefore, we suggest decimal representation from the point of measurement, considering the foregoing historical development of number. From the perspective that the conception of real number originated from measurement of ‘continuum’ and infinite decimals played a significant role in the ‘representation’ of measurement, decimal expression of real number should be introduced through contexts of measurement instead of being introduced as a result of algorithm.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.18 no.12
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• pp.1970-1982
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• 1993

This paper describes an efficient array algorithm for parallel computation of vector-radix two-dimensional (2-D) fast discrete cosine transform (VR-FCT), and its VLSI implementation. By mapping the 2-D VR-FCT onto a 2-D array of processing elements (PEs), the butterfly structure of the VR-FCT can be efficiently importanted with high concurrency and local communication geometry. The proposed array algorithm features architectural modularity, regularity and locality, so that it is very suitable for VLSI realization. Also, no transposition memory is required, which is invitable in the conventional row-column decomposition approach. It has the time complexity of O(N+Nnzp-log2N) for (N*N) 2-D DCT, where Nnzd is the number of non-zero digits in canonic-signed digit(CSD) code, By adopting the CSD arithmetic in circuit desine, the number of addition is reduced by about 30%, as compared to the 2`s complement arithmetic. The computational accuracy analysis for finite wordlength processing is presented. From simulation result, it is estimated that (8*8) 2-D DCT (with Nnzp=4) can be computed in about 0.88 sec at 50 MHz clock frequency, resulting in the throughput rate of about 72 Mega pixels per second.

• Korean Journal of Childcare and Education
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• v.10 no.2
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• pp.175-192
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• 2014

The purpose of this study was to investigate the differences in perceived importance of mathematical education (perceived importance) and mathematical interaction of 5-year-olds' mothers according to contents of mathematical education. Second, we intended to examine whether mothers' understanding of purpose of mathematical education predicted on their perceived importance and mathematical interaction. Third, we analyzed relative influence between mothers' perceived effectiveness of concrete materials and worksheets on their perceived importance and mathematical interaction. The subjects consisted of 151 mothers of 5-year-olds lived in D city and K province in Korea. The results were as follows: First, mothers' perceived importance and mathematical interaction were higher in 'number and arithmetic'. Second, mothers' understanding of purpose of mathematical education predicted their perceived importance in all contents and mathematical interaction in 'number and arithmetic', 'geometry', and 'algebra'. Third, mothers' perceived effectiveness of concrete materials predicted better in most contents of mathematical education. Meanwhile, in 'number and operation', mothers' perceived effectiveness of worksheets did a predictive role in their importance awareness. These results were discussed in terms of necessity of a parent education program to provide practical information about contents and methods of mathematical education for their 5-year-old children.

• Journal of Educational Research in Mathematics
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• v.24 no.4
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• pp.607-622
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• 2014

The purpose of this paper is that it analyzes the historical development of the concept of trigonometric functions and discuss some didactical implications. The results of the study are as follows. First, the concept of trigonometric functions is developed from line segments measuring ratios to numbers representing the ratios. Geometry, arithmetic, algebra and analysis has been integrated in this process. Secondly, as a result of developing from practical calculation to theoretical function, periodicity is formalized, but 'trigonometry' is overlooked. Third, it must be taught trigonometry relationally and structurally by the principle of similarity. Fourth, the conceptual generalization of trigonometric functions must be recognized as epistemological obstacle, and it should be improved to emphasize the integration revealed in history. The results of these studies provide some useful suggestions to teaching and learning of trigonometry.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.1-14
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• 2009

Since western mathematics and astronomy had been introduced in Chosun dynasty in the 17th century, most of Chosun mathematicians studied Shu li jing yun(數理精蘊) for the western mathematics. In the last two decades of the 19th century, Chosun scholars have studied them which were introduced by Japanese text books and western missionaries. The former dealt mostly with elementary arithmetic and the latter established schools and taught mathematics. Lee Sang Seol(1870~1917) is well known in Korea as a Confucian scholar, government official, educator and foremost Korean independence movement activist in the 20th century. He was very eager to acquire western civilizations and studied them with the minister H. B. Hulbert(1863~1949). He wrote a mathematics book Su Ri(數理, 1898-1899) which has two parts. The first one deals with the linear part(線部) and geometry in Shu li jing yun and the second part with algebra. Using Su Ri, we investigate the process of transmission of western mathematics into Chosun in the century and show that Lee Sang Seol built a firm foundation for the study of algebra in Chosun.

• 한국전산유체공학회:학술대회논문집
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• 2010.05a
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• pp.551-555
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• 2010

Electrowetting is a versatile tool to handle tiny droplets and forms a backbone of digital microfluidics. Numerical analysis is necessary to fully understand the dynamics of electrowetting, especially in designing electrowetting-based devices, such as liquid lenses and reflective displays. We developed a numerical method to analyze the general contact-line problems, incorporating dynamic contact angle models. The method is based on the conservative level set method to capture the interface of two fluids without loss of mass. We applied the method to the analysis of spreading process of a sessile droplet for step input voltages and oscillation of the droplet for alternating input voltages in electrowetting. The result was compared with experimental data. It is shown that contact line friction significantly affects the contact line motion and the oscillation amplitude. The pinning process of contact line was well represented by including the hysteresis effect in the contact angle models. In level set method, in the mean time, material properties are made to change smoothly across an interface of two materials with different properties by introducing an interpolation or smoothing scheme. So far, the weighted arithmetic mean (WAM) method has been exclusively adopted in level set method, without complete assessment for its validity. We viscosity, thermal conductivity, electrical conductivity, and permittivity, can be an alternative. I.e., the WHM gives more accurate results than the WAM method in certain circumstances. The interpolation scheme should be selected considering various characteristics including type of property, ratio of property of two fluids, geometry of interface, and so on.

• The Journal of Engineering Geology
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• v.10 no.1
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• pp.13-25
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• 2000

A three-dimensional discrete fracture network model based on probabilistic characteristics of fracture geometry and transmissivity was designed to calculate the conductivity tensor and to estimate theanisotropy of conductivity. The conductivities, $K_p$, obtained from the numerical simulation of single-holepacker test corresponded well to those from the field tests. From this, it can be concluded that thefracture network model designed in this study can represent hydraulic characteristics of in-situ fractured rock mass. Block-scale conductivities, $K_b$, estimated from the modelling of steady-state flow through the REV-scale block were ranged between the arithmetic mean and harmonic mean of theconductivity estimates from packer tests. The conductivity along north-south direction was 1.4 timesgreater than that along the east-west direction. It was concluded that the anisotropy of conductivitywas insignificant. It was also found that there was a little correlation between $K_b$ and $K_p$. This would be to that the conductivities from the packer test simulation was strongly dependent on thetransmissivity and the number of fractures within the packer test intervals.