• School Mathematics
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• v.18 no.3
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• pp.647-666
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• 2016

This study investigates pre-service teacher's understanding of the concept and representations of irrational numbers. We classified the representations of irrational numbers into six categories; non-fraction, decimal, symbolic, geometric, point on a number line, approximation representation. The results of this study are as follows. First, pre-service teachers couldn't relate non-fractional definition and incommensurability of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations. Thirdly, pre-service teachers had more difficulty moving between symbolic representation and point on a number line representation of ${\pi}$ than that of $\sqrt{5}$ We suggested the concept of irrational numbers should be learned in relation to various representations of irrational numbers.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.33B no.3
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• pp.109-119
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• 1996

We propsoed a multiplexed optical correlation filter method for an optical parallel addition based on symbolic substitution. In the proposed mthod, we used redundant binary number which was easy to minimize the number of the symbolic substitution rules. We chose MACE filter which had very low sidelobes and good correlation peak compared with SDF filter as the optical correlation recognition filter and encoded input numbers properly to increase the discrimination capability. In order to minimize the number of symbolic substitution rules, sixteen input patterns were divided into six groups of the same addition results and six filters for recognizing the input patterns were used. these filters were multiplexed in two MMACE filter planes and the corresponding substitution method was proposed. Through the computer simulation, we confirmed the proposed method was suitable to implement the optical parallel adder.

• Journal of architectural history
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• v.24 no.2
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• pp.7-16
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• 2015

This article deals with a proportional analysis of Cologne Cathedral with regard to the medieval tradition of geometry and figurate numbers that were commonly used in the medieval period. It first outlines symbolic and geometric notions of the geometry and numbers during the medieval period, and then, interprets the proportional design of the plan and section of the cathedral in analogy with the notion. It concludes that the proportional design of the cathedral was not quite arbitrary but carefully designed for the systematic and symbolic quality of the medieval aesthetic tradition.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.1
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• pp.269-280
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• 1996

We proposed a symbolic substitution method based on an optical correlator for an optical parallel addition. In the proposed symbolic substitution method, we used redundant binary number of the symbolic substitution rules as a number system and chose MAC3E filter which had very low sidelobes and good correlation peak compared with SDF filter as the optical correlation filter. We encoeded input numbers property to increase the discrimination capability and divided inpt patterns into 5 groups of the same addition results to minimize the number of symbolic substitution rules. Through the computer simulation, we confirmed the proposed method was suitable to implement the optical parallel adder.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• The Journal of Korean Medicine
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• v.41 no.2
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• pp.9-22
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• 2020

Objectives: The purpose of this study is to consider the concept of Meridian Points(經穴) and to establish the directions in further research. Methods: First, based on the latest results from the researches of Meridian and Collateral(經絡), it was to infer the original concept of Meridian Points(經穴). Second, the meaning of Meridian Points(經穴) has been investigated and its directions in further research was studied founded upon Symbolic Mathematical Study(象數學). Results ＆ Conclusions : Firstly, Meridian Points(經穴) are considered to be the source of information that contains 365 numbers of human physiological information which includes physiological information of Viscera and Bowels(藏府) and Meridian and Collateral(經絡). Secondly, advanced researches are required further to clarify the meaning of Meridian Points(經穴) as Symbolic Mathematical Study(象數學) has established the systems of Meridian Points(經穴). In addition, the efficacy of each Meridian Points(經穴) needs to be revised through literature studies. Clinical studies are essential to practically verify the results from the former theoretical research. Thirdly, the contention to oppose the presence of Meridian and Collateral(經絡) and Meridian Points(經穴) was acknowledged to be incorrect. Lastly, for broadening the theoretical systems of Korean Medicine(韓醫學) with integration of Western scientific knowledge, a paradigm shift is necessary to revise the concepts of Viscera and Bowls(藏府), Meridian and Collateral (經絡) and Meridian Points(經穴) in Korean Medicine(韓醫學). In order to accomplish the shift, the ambiguity in theories of Korean Medicine(韓醫學) should be clarified through the study of Symbolic Mathematical Study(象數學).

• Proceedings of the Korea Society for Simulation Conference
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• 1992.10a
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• pp.7-7
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• 1992

Extending discrete event modelling formalisms to facilitate greater symbol manipulation capabilities is important to further their use in intelligent control and design of high autonomy systems. This paper defines an extension to the DEVS formalism that facilitates symbolic expression of discrete event times by extending the time base from the real numbers to the field of linear polynomials over the reals. A simulation algorithm is developed to generate the branching trajectories resulting from the underlying non-determinism. To efficiently manage linear polynomial constraints based on feasibility checking algorithm borrowed from linear programming. The extended formalism offers a convenient means to conduct multiple, simultaneous explorations of model behaviors. Examples of application are given with consideration on fault model analysis.

• School Mathematics
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• v.19 no.2
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• pp.319-343
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• 2017

In this study, we hope to reveal specialized content knowledge(SCK) and its features necessary to analyze student's errors and difficulties about the concept of irrational numbers. The instruments and interview were administered to 3 in-service mathematics teachers with various education background and teaching experiments. The results of this study are as follows. First, specialized content knowledge(SCK) were characterized by the fixation to symbolic representation like roots when they analyzed the concentration and overlooking of the representations of irrational numbers. Secondly, we observed the centralization tendency on symbolic representation and the little attention to other representations as the standard of judgment about irrational numbers. Thirdly, In-service teachers were influenced by content of students' error when they analyzed the error and difficulties of students. Lately, we confirmed that the content knowledge about the viewpoint of procept and actual infinity of irrational numbers are most important during the analyzing process.

• Proceedings of the IEEK Conference
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• 1998.10a
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• pp.987-990
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• 1998

An optical adder for a modified signed-digit(MSD) number system using joint spatial encoding method is proposed. In order to minimize the numbers of symbolic substitution rules, nine input patterns were divided into five groups of the same addition results. For recognizing the input reference patterns, masks and reference patterns without any other spatial operations are used. This adder is implemented by smaller system in size than a conventional adder.

• East Asian mathematical journal
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• v.34 no.2
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• pp.203-217
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• 2018

This study examined preservice elementary teachers' patterns and tendencies in thinking of drawn models of multiplication with fractions. In particular, it investigated preservice elementary teachers' work in a context where they were asked to select among drawn models for symbolic expressions illustrating multiplication with non-whole number fractions including a mixed number. Preservice teachers' interpretations of fraction multiplication used in interpreting different types of drawn models were analysed-both quantitatively and qualitatively. Findings and implications are discussed and further research is suggested.