• Journal for History of Mathematics
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• v.34 no.1
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• pp.1-20
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• 2021

Logic and intuition are considered as the opposite extremes of teaching geometry, and any teaching method of geometry is to be placed between these extremes. The purpose of this study is to identify the characteristics of logical and intuitive approaches for teaching geometry and to derive didactical implications by taking Euclid's Elements and Clairaut's Elements respectively representing the extremes. To this end, comparing the composition and contents of each book, we analyze which propositions Clairaut chose from Euclid's Elements, how their approaches differ in definitions, proofs, and geometrical constructions, and what unique approaches Clairaut took. The results reveal that Clairaut mainly chose propositions from Euclid's books 1, 3, 6, 11, and 12 to provide the contexts that show why such ideas were needed, rather than the sudden appearance of abstract and formal propositions, and omitted or modified the process of justification according to learners' levels. These propose a variety of intuitive strategies in line with trends of teaching geometry towards emphasis on conceptual understanding and different levels of justification. Specifically, such as the general principle of similarity and the infinite geometric approach shown in Clairaut's Elements, we could confirm that intuition-based geometry does not necessarily aim for tasks with low cognitive demand, but must be taught in a way that learners can understand.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.8 no.12
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• pp.4604-4623
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• 2014

Authentication mechanisms coupled with strong encryption techniques are used for network security purposes; however, given sufficient time, well-equipped intruders are successful for compromising system security. The authentication protocols often fail when they are analysed critically. Formal approaches have emerged to analyse protocol failures. In this study, Communicating Sequential Processes (CSP) which is an abstract language designed especially for the description of communication patterns is employed. Rank functions are also used for verification and analysis which are helpful to establish that some critical information is not available to the intruder. In order to establish this, by assigning a value or rank to each critical information, it is shown that all the critical information that can be generated within the network have a particular characterizing property. This paper presents an application of rank functions approach to an authentication protocol that combines delaying the decryption process with timed authentication while keys are dynamically renewed under pseudo-secure situations. The analysis and verification of authentication properties and results are presented and discussed.

• Journal of the Korean School Mathematics Society
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• v.11 no.1
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• pp.97-115
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• 2008

In high school mathematics class, to subtract a number b from a, we add the additive inverse of b to a and to divide a number a by a non-zero number b, we multiply a by the multiplicative inverse of b, which is the formal approach for operations of real numbers. This article aims to give a connection between the intuitive models in middle school mathematics class and the formal approach in high school for teaching operations of negative integers. First, we highlight the teaching methods(Hwang et al, 2008), by which subtraction of integers is denoted by addition of integers. From this methods and activities applying the counting model, we give new teaching methods for the rule that the product of negative integers is positive. The teaching methods with horizontal mathematization(Treffers, 1986; Freudenthal, 1991) of operations of integers, which is based on consistently applying the intuitive model(number line model, counting model), will remove the gap, which is exist in both teachers and students of middle and high school mathematics class. The above discussion is based on students' cognition that the number system in middle and high school and abstracted number system in abstract algebra course is formed by a conceptual structure.

• Journal of the Architectural Institute of Korea Planning & Design
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• v.34 no.11
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• pp.125-134
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• 2018

This study examines Dalibor Vesely's theoretical proposition of communicative space and tries to develop it through a review of the contemporary architectural case. Vesely poses a critical question about communication: how do the situational conditions of our everyday life and the spatial characteristics of the natural world in which we live communicate through representation. He emphasizes the spatial and situational conditions and the role of representation in communication, arguing that architecture should create the formation of communicative space to restore its primary role as the corporeal foundation of culture. This study thus focuses on one of the critical concepts of his theory: "the communicative movement," which is, according to him, ontological and situational because it animates and transforms human circumstances as a whole. Further, it pursues some practical knowledge of creating the communicative space, by examining the design theory and practice of Zaha Hadid, who thematizes communication and movement in her architectural approach. This study analyses the different levels of representation and modes of movement in her architectural space to reveal the possibilities and limits of its communicative roles. We will find that the representation of Hadid's architectural space is not the formal representation of reality, but a mathematical and projective representation of abstract concepts. Despite its apparent aesthetic consistency, the inward and self-referential relation between the individual elements of the architectural space reveals its limit for the communicative space.

• Journal of the Korean Operations Research and Management Science Society
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• v.20 no.2
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• pp.159-178
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• 1995

Supervisory control is an approach based on formal language. it is used to model and control discrete event systems in which each discrete event process is represented as an automation. A supervisor is a generator that switches control patterns in such a way that a given discrete evenet process behaves in obedience to various constraints. A flexible manufacturing cell (FMC) is one of discrete evenet systems. Functions necessary for the operation of an FMC are characterized by operational components and informational compoments. The operational components can be modeled using the finite state machines and the informational components can be modeled using the abstract formalism which describes supporting operations of the cell controller. In this paper, we addressed function required for FMC control specification, software engineering aspects on FMC control based on supervisory control, a concept of event queue for resolving synchronization problem, and complexity reduction. Based on the mathematical model of an FMC. we synthesized the controller by integrating a supervisor for FMC with control specification that specifies event-driven operation of the cell controller. The proposed control scheme is stable mathematically so that the system always behaves on a controlled way even under the existence of uncontrollable events. Furthermore, using an event queue concept, we can solve a synchronization problem caused by the violation of instantaneity assumption of supervisory control theory in real life situation. And also, we can propotype a control software rapidly due to the modularity of the proposed control scheme.

• Journal of the Korean Society of Costume
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• v.6
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• pp.65-87
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• 1982

1. Purpose: The purpose is to apply and adapt ancient textile pattern to practical life, and to contribute to the promotion of the creative development of modernization and Koreanization of textile pattern by the survey of the extent of taste for the textile pattern existent in Korean costume among costumes. 2. Hypothesis: Textile pattern is in most classical one expressed in fact, but nowadays abstract or geometric one is more exist. Consumers are in most part in forties, and so the taste cannot be ignored. Therefore aesthetic consciousness found Korean costume is more important rather than excessively bold or mordern one. 3. Method and Process: (1) This research is analysed 386 one through college student and parents of a primary or high school. (2) Taste of the pattern is comparisoned and analyzed as age. education, pocket money of the student or an income of a month in home through computer. And the analysis of the statistics research is operation through the Chi-Square Goodness of-Fit-Test. 4. Conclusion: (1) The Korean costume put on mostly party or formal dress, therefore it should be researched as an outdoor dress with traditional costume. (2) The most one is concerned in textile pattern, it's taste is different from color, constitution. Textile industry is developed not only weave pattern, gold-coverning pattern but embroidry pattern, dye pattern, therefore the various side of pattern design should be researched. (3) In Side of form, plant pattern is not only most various but highest in popularity. According to approach nowadays, all of the pattern becomes composition or geometric one with abstract tendency and so from these day pattern is necessary combinationed, researched with our people emotion. (4) The color of textile pattern is choiced individual taste. Through investige, research in various side of the modern taste and our costume, we take growing interest in the color, composition of textile, and should dressed with beauty and grace. (5) In side of size, textile pattern is choiced to individual face and body shape through research on form, color, size of these pattern, we should endeavor to dress well. (6) In side of application, most people is concerned in not only interior ornament but the costume is high. Costume research by some people of the outside and symbol with interior through the pattern analysis is not only very important but also is due to people culture.

• Journal of The Korean Association For Science Education
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• v.5 no.1
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• pp.49-61
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• 1985

In this study, I compared and analyzed the new and old secondary school science textbooks to find the charateristics of them and the differences between them. The results of the study are the following. Major concepts in the new textbook are almost similar to those in the old one. The-new textbook reinforces the functions of the introudction and checking the result of learning, and presents more and diverse learning materials and reduces the degree of learning difficulty by omitting the several abstract knowledges and mathematical formulas which can be understood through formal operational thinking. The results show that the new textbook is more effective in arousing student's interest and curiosity there fore it increases the efficiency of learning. But the new textbook is less suitable for inquiry because it is mainly composed of explanation and fact rather than experiment and observation. I think that this is the result from the actual approach to the real conditions of school when the curriculum was reformed and the new textbook was written.