• 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.

• Communications of the Korean Mathematical Society
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• v.30 no.3
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• pp.313-325
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• 2015

An H-magic labeling in a H-decomposable graph G is a bijection $f:V(G){\cup}E(G){\rightarrow}\{1,2,{\cdots},p+q\}$ such that for every copy H in the decomposition, $\sum{_{{\upsilon}{\in}V(H)}}\;f(v)+\sum{_{e{\in}E(H)}}\;f(e)$ is constant. f is said to be H-V -super magic if f(V(G))={1,2,...,p}. In this paper, we prove that complete bipartite graphs $K_{n,n}$ are H-V -super magic decomposable where $$H{\sim_=}K_{1,n}$$ with $n{\geq}1$.

• Journal for History of Mathematics
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• v.31 no.4
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• pp.183-196
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• 2018

In this study, we propose an approximate method to make Jisuguimundo with magic number 93 to 109. In this method, for two numbers p, q with a relationship of M = 2p+q, we use eight pairs of two numbers with sum p and five pairs of two numbers with sum q. Such numbers must be between 1 and 30. Instead of determining all positions of thirty numbers, this method shows that Jisuguimundo with magic number 93 to 109 can be made by determining positions of thirteen numbers $a_i$(i = 1, 2, ${\cdots}$, 8), $b_5$, $c_i$(i = 1, 2, 3, 4). Method 1 is used to make Jisuguimundo with magic number 93 to 108, and method 2 is used to make Jisuguimundo with magic number 109.

• Journal for History of Mathematics
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• v.33 no.6
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• pp.315-325
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• 2020

In this study, how Choi Seok-Jeong made Hadoguodo is presumed. Choi SeokJeong's Hadoguodo does not actually reflect the Hado. But it is verified that Hadoguodo reflecting Hado can be made. In addition, it is verified that Hadoguodo can be made so that not only the sum of the nine numbers of each square are all 207 but also the sum of the nine numbers in the horizontal and vertical directions are all 207.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.435-445
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• 2017

Let D be a directed graph with p vertices and q arcs. A vertex out-magic total labeling is a bijection f from $V(D){\cup}A(D){\rightarrow}\{1,2,{\ldots},p+q\}$ with the property that for every $v{\in}V(D)$, $f(v)+\sum_{u{\in}O(v)}f((v,u))=k$, for some constant k. Such a labeling is called a V-super vertex out-magic total labeling (V-SVOMT labeling) if $f(V(D))=\{1,2,3,{\ldots},p\}$. A digraph D is called a V-super vertex out-magic total digraph (V-SVOMT digraph) if D admits a V-SVOMT labeling. In this paper, we provide a method to find the most vital nodes in a network by introducing the above labeling and we study the basic properties of such labelings for digraphs. In particular, we completely solve the problem of finding V-SVOMT labeling of generalized de Bruijn digraphs which are used in the interconnection network topologies.

• Journal of Elementary Mathematics Education in Korea
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• v.15 no.1
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• pp.77-93
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• 2011

Jisuguimundo(地數龜文圖) is a magic hexagon created by Suk-Jung Choi in his book about three hundreds years ago in Korea. Recently attention is focused on jisuguimundo, and it is known that jisuguimundos exist when magic number is from 77 to 108, however a general method making jisuguimundos is not known so far. Up to now, methods of making jisuguimundos using computers are known. In this study, a method making jisuguimundos is suggested using pairs of two numbers with sum p and q ($p{\neq}q$) alternately when magic number is from 88 to 92, and from 94 to 98, without using computer in elementary math class as a task for problem solving. Mathematical theory is introduced for this method, and jisuguimundos are presented which are found out through this method. Elementary students are expected to make their own jisuguimundo using this method.

• 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.