• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.18 no.2
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• pp.89-103
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• 2018

A genius "Prince of Mathematician" Gaussian and "Father of Communication" Shannon comes up with the creative idea of motivation to meet each other? The answer is a coin leaf. Gaussian found some creative ideas in the matter of obtaining a sum of 1 to 100. This is the same as the probability distribution curve when a coin leaf is thrown. Shannon extended the Gaussian probability distribution to define the entropy, taking the source symbol and the reciprocal logarithm to obtain the weighted average. These where the genius Gaussian and Shannon meet in the same coin leaf. This paper focuses on this point, and easily proves Gaussian distribution and Shannon entropy. As an application example, we have obtained the capacity and transition probability of Jeongju seminal vesicle, and the Shannon channel capacity is 1 when the equivalent transition probability is 1/2.

• Journal for History of Mathematics
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• v.22 no.3
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• pp.171-186
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• 2009

$Poincar\acute{e}$ is mathematician and the episodes in his mathematical invention process give suggestions to scholars who have interest in how mathematical invention happens. He emphasizes the value of unconscious activity. Furthermore, $Poincar\acute{e}$ points the complementary relation between unconscious activity and conscious activity. Also, $Poincar\acute{e}$ emphasizes the value of intuition and logic. In general, intuition is tool of invention and gives the clue of mathematical problem solving. But logic gives the certainty. $Poincar\acute{e}$ points the complementary relation between intuition and logic at the same reasons. In spite of the importance of relation between intuition and logic, school mathematics emphasized the logic. So students don't reveal and use the intuitive thinking in mathematical problem solving. So, we have to search the methods to use the complementary relation between intuition and logic in mathematics education.

• Journal of Educational Research in Mathematics
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• v.24 no.2
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• pp.103-124
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• 2014

The process of analogical reasoning can be conventionally summarized in five steps : Representation, Access, Mapping, Adaptation, Learning. The purpose of this study is to develop more detailed model for reason of analogies considering the distinct characteristics of the mathematical education based on the process of analogical reasoning which is already established. Ultimately, This model is designed to facilitate students to use analogical reasoning more productively. The process of developing model is divided into three steps. The frist step is to draft a hypothetical model by looking into historical example of Leonhard Euler(1707-1783), who was the great mathematician of any age and discovered mathematical knowledge through analogical reasoning. The second step is to modify and complement the model to reflect the characteristics of students' thinking response that proves and links analogically between the law of cosines and the Pythagorean theorem. The third and final step is to draw pedagogical implications from the analysis of the result of an experiment.

• Journal for History of Mathematics
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• v.18 no.3
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• pp.91-106
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• 2005

History of mathematics must be analysed to discuss mathematical reality and thinking. Analysis of history of mathematics is the method of understanding mathematical activity, by these analysis can we know how historically mathematician' activity progress and mathematical concepts develop. In this respects, we investigate teaching algebra through historico-genetic analysis and propose historico-genetic analysis as alternative method to improve of teaching school algebra. First the necessity of historico-genetic analysis is discussed, and we think of epistemological obstacles through these analysis. Next we focus two concepts i.e. letters(unknowns) and negative numbers which is dealt with school algebra. To apply historico-genetic analysis to school algebra, some historical texts relating to letters and negative numbers is analysed, and mathematics educational discussions is followed with experimental researches.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.26 no.6
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• pp.1413-1419
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• 2016

In these days, there are a lot of research results on the Post-Quantum Cryptography according to developing of quantum computing technologies and the announcement of the NIST's Post-Quantum Cryptography standard project. The key size of the existing symmetric key block ciphers are needed to increase and the security of discrete logarithm based public key cryptography can be broken by Grover's algorithm and Shor's algorithm. By this reason, a lot of cryptologist and mathematician research on safe cryptography against the quantum computer which is called as the Post-Quantum Cryptography. In this paper, we survey on recent technical trend on the Hash-Based Signature Scheme which is one of the Post-Quantum Cryptography and suggest the prospect of the Hash-Based Signature Scheme.

• Communications of Mathematical Education
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• v.24 no.3
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• pp.659-689
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• 2010

Taxicab distance function is a practical distance notion which gives us information of real world pathway distance that really taxi can go through. As one of the non-Euclidean geometry, this study of an ideal city with all roads running horizontal or vertical, was introduced by the Russian Mathematician H. Minkowski and synthetically reported by the E. F. Kraus in 1986. After that, there were many reports and papers on this topic and still being researched. At this point of view, our research about taxicab geometry provides its differences from Euclidean plane geometry, and considers about several theorems on plane geometry using the taxicab distance function.

• Communications of Mathematical Education
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• v.24 no.4
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• pp.939-947
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• 2010

The Golden ratio which was started to be use by Eudoxos, Greek mathematician, is being used as a tool to explain beauty in various fields like architecture, art, society, nature and so on. In addition, people not only use the golden ratio, also use obesity to consider a standard of beauty. This study's subjects are students of H university. We researched their Golden ratios of their whole body, upper body and lower body. Also, to research their obesity levels, we used Obesity degree, Waist-hip ratio and Percent body fat. According to different features of the subjects, we study differences between the golden ratio and obesity and how the golden ratio of body affects obesity.

• The Bulletin of The Korean Astronomical Society
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• v.43 no.2
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• pp.48.4-49
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• 2018

We studyed an Korean astrolabe made by Ryu Geum (1741~1788), the late Joseon Confucian scholar. It has a diameter of 17 cm and a thickness of 6 mm and is now owned by Museum of Silhak. In the 1267 of the reign of Kublai Khan of Mogol Empire, Jamal al Din, an Ilkhanate astronomer, present an astrolabe to his emperor together with 6 astronomical instruments. In 1525, an astrolabe was first made in Korea by Lee, Sun (李純, ?~?), a Korean astronomer and royal official of Joseon Dynasty. He was referred to Gexiang xinshu, a Mongloian-Chinese book by Zhao, Youqin (1280-1345), an astronomer of Mongolian Empire. This astrolabe has not been left. In the mid-17th century, an astrolabe was introduced to Joseon again through Hungai tongxian tushuo (渾蓋 通憲圖設) edited by Chinese Mathematician Li Zhi-zao (李之藻, 1565~1630), that originated from Astrolabium (1593) of Christoph Clavius (1538-1612). It seems that Ryu refered to Hungai tongxian tushuo which affect to Hongae-tongheon-ui (渾蓋通憲儀) edited by Nam, Byeong-Cheol (南秉哲, 1817~1863). We analysis lots of circles on the mother and a set of index from the rete of of Ryu's astrolabe. We find that the accuracy of circles has about 0.2~0.4 mm in average if the latitude of this astrolabe is 38 degrees. 11 indices of the rete point bright stars of the northern and southern celestial hemisphere. Their tip's accuracies are about $2^{\circ}.9{\pm}3^{\circ}.2$ and $2^{\circ}.3{\pm}2^{\circ}.8$ on right ascension and declination of stars respectively.

• The Journal of the Convergence on Culture Technology
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• v.5 no.2
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• pp.111-116
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• 2019

This paper considers the historical background of the emergence of 'thinking-machine,' that has changed the ontological statue of human and machine. In particular, British mathematician Charles Babbage's Calculating Engines is examined as a material iteration of thinking-machine, focusing on the discursive process by which thought is not the faculty of human, but the function of machine. In Chapter II, I review the dualism of René Descartes who denied the possibility of machine intelligence by separating the substance of body and mind. In Chapter III, Babbage's philosophical assertions which emphasized the function of human associated with thought by rejecting the fundamental opposition between human and machine. Therefore, this paper verifies that the conception of 'thinking-machine' essentially causes the reorganization and reformulation of concepts involved with human identity, and provides the sophisticated sources to prepare new perspective on the artificial technology nowadays.

• The Journal of the Korea Contents Association
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• v.13 no.10
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• pp.113-122
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• 2013

The movie "Beautiful Mind" directed by Ron Howard is about a genius global mathematician, John Nash's life. In the movie, the main actor, John Nash is a schizophrenic patient who suffers from hallucination and delusion, and his illusion appears as three distinct characters. Each researcher has had a different opinion on the interpretation of these three characters, but many parts of their opinions are losing consistency. Especially the girl is assumed to be a character from the main actor's hallucination because she is ageless or there is no interpretation of the girl. Although the director Ron Howard did not adopt Aldous Huxley's theory "the more you know the more you see" for the movie, he analyzed the characters in the way of his own with thinking that he can analyze them in accordance with the knowledge level of audience. The imaginary characters come out from John Nash's head and who he wants to be. They are the basic human needs, earthly desire, sexual desire and the desire for honor. John Nash minutely reflects these three kinds of desires in an imaginary world through the three characters. This thesis is to newly suggest the symbolic meaning of the imaginary characters in the movie by clearly analyzing the meaning of the controversial three characters.