• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.17 no.3
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• pp.159-166
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• 2017

This paper proposes an algorithm for odd, doubly even, and singly even magic squares. In constructing an odd magic square, de la $Loub{\grave{e}}re^{\prime}s$ method is widely known and used, but it has an inherent defect of executing $O(n^2)$ steps. 2 types of cross algorithms have been proposed to the double even magic square, and more to the singly even magic square based on the odd magic square of ${\frac{n}{2}}{\times}{\frac{n}{2}}$, the most popular and simple of which is one proposed by Strachey. The algorithm proposed in this paper successfully constructs odd and doubly even magic squares by undergoing 3 steps and 4 steps respectively. It also directly constructs a singly even magic square without having its basis on the odd magic square.

• Communications of Mathematical Education
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• v.24 no.1
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• pp.195-220
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• 2010

The magic square is one of the number arrangements and the sums of each row, column, and diagonal are all equal. The meaning of "方" is "Square". If we don't consider the condition of 'square' then is it possible any number arrangement? There are many special number arrangements such as "magic five number circle(緊五圖)", "magic six number circle(聚六圖)", "magic eight number circle(聚八圖)", "magic nine number circle(攢九圖)", "magic eight camp circle(八陣圖)", "magic nine camp circle(連環圖)" in the ancient Chinese mathematics books such as "楊輝算法", "算法統宗". Also, there is a very special and beautiful number arrangement Jisuguimoondo(地數龜文圖) in the mathematics book "Goosuryak(九數略)" written by Choi suk jung(崔錫鼎) in the Joseon Dynasty. In this study, we introduce a various number arrangements and their properties.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.10 no.1
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• pp.11-19
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• 2006

In this paper, we propose an algorithm of generating magic squares of degree $3^k$(k = 2, 3, 4, $\cdots$) by using the magic square of degree 3.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.3
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• pp.109-113
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• 2016

In this paper, we propose efficient LED lighting control algorithm using a David star magic square. Such algorithms increases the power reduction, the heat efficiency and LED life cycle and the efficiency of the LED lighting control consumption. Lighting system using existing Magic square algorithm could be reduced to increase the heat efficiency of the LED because the LED lighting time of the reduced cross-lighting. but it has a limit to the lighting control. If should apply the this proposed algorithm, can reduces power consumption and increases LED life-cycle, heat efficiency of LED lighting module and efficiency of the lighting control of the LED. This paper proposed that algorithm is by using a David star magic square on the LED Matrix. Divided into twelve areas to move the pattern in constant time interval, to perform the cross rotation and inversion techniques to thereby light up. In this paper proposed algorithm of this paper was compared with existing Magic square approach. As a result, power consumption and heat-value and luminous flux was reduced as the conventional lighting system. And, the LED lighting control increase the efficiency.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.21-31
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• 2010

A latin square of order n is an $n{\times}n$ array with entries from a set of n numbers arrange in such a way that each number occurs exactly once in each row and exactly once in each column. Two latin squares of the same order are orthogonal latin square if the two latin squares are superimposed, then the $n^2$ cells contain each pair consisting of a number from the first square and a number from the second. In Europe, Orthogonal Latin squares are the mathematical concepts attributed to Euler. However, an Euler square of order nine was already in existence prior to Euler in Korea. It appeared in the monograph Koo-Soo-Ryak written by Choi Seok-Jeong(1646-1715). He construct a magic square by using two orthogonal latin squares for the first time in the world. In this paper, we explain Choi' s orthogonal latin squares and the history of the Orthogonal Latin squares.

• The Mathematical Education
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• v.32 no.3
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• pp.205-219
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• 1993

• Journal for History of Mathematics
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• v.27 no.2
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• pp.111-125
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• 2014

Jisuguimundo is an inimitable magic hexagon devised by Choi Seok-Jeong, who was the author of GuSuRyak as well as a prime minister in Joseon dynasty. Jisuguimundo, recorded in GuSuRyak, is also known as Hexagonal Tortoise Problem (HTP) because its nine hexagons resemble a tortoise shell. We call the sum of numbers in a hexagon in Jisuguimundo a magic sum, and show that the magic sum of hexagonal tortoise problem of order 2 varies 40 through 62 exactly and that of hexagonal tortoise problem of order 3 varies 77 through 109 exactly. We also find all of the possible solutions for hexagonal tortoise problem of oder 2.

• Journal of IKEEE
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• v.15 no.4
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• pp.261-266
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• 2011

In this paper, new efficient lighting control system for light devices is proposed to reduce power consumption and increases LED life-cycle and heat efficiency of LED lighting module. The new proposed lighting control system for light devices divides into 4 stages according to the illuminance surrounding by measuring illuminance and apply to automatic pattern lighting algorithm. And via level check will be light up for set time by applying intersection lighting algorithm of magic square pattern forming a fully symmetrical. Experimental analysis results, shows heating value and power consumption reduced to maximum 30 percent and lifetime of LED improved to maximum 60 percent in comparison with previous lighting system so applying system to LED streetlight, stable and high energy efficiency can be acquired.

• Journal of KIISE:Information Networking
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• v.32 no.1
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• pp.89-99
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• 2005

Advances of Internet and rC accelerate distribution and sharing of information, which make P2P(Peer-to-Peer) computing paradigm appear P2P computing Paradigm is the computing paradigm that shares computing resources and services between users directly. A fundamental problem that confronts Peer-to-Peer applications is the efficient location of the node that stoles a desired item. P2P systems treat the majority of their components as equivalent. This purist philosophy is useful from an academic standpoint, since it simplifies algorithmic analysis. In reality, however, some peers are more equal than others. We propose the P2P protocol considering differences of capabilities of computers, which is ignored in previous researches. And we examine the possibility and applications of the protocol. Simulating the Magic Square, we estimate the performances of the protocol with the number of hop and network round time. Finally, we analyze the performance of the protocol with the numerical formula. We call our p2p protocol the Magic Square. Although the numbers that magic square contains have no meaning, the sum of the numbers in magic square is same in each row, column, and main diagonal. The design goals of our p2p protocol are similar query response time and query path length between request peer and response peer, although the network information stored in each peer is not important.

• Education of Primary School Mathematics
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• v.21 no.2
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• pp.93-109
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• 2018

The purpose of this study is to develop the number puzzle program and the mathematical creativity test and to analyze the effects of the mathematical creativity and the creative attitude in mathematics. To accomplish this aim, the six-grade students elementary school of thirty-six participated and this students participated Magic square, Sudoku, KenKen Puzzle activities in to the morning activity time for 30 minutes every morning and the pre-test of before activity and the post-test of after activity were collected. The number puzzle activity helps improve the mathematical creativity and the creative attitude in mathematics of the elementary school students and improve the mathematical creativity of for female students rather than for male students.