• Journal for History of Mathematics
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• v.24 no.3
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• pp.59-76
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• 2011

Starting from a collection V as a model which satisfies the axioms of NBG, we call the elements of V as sets and the subcollections of V as classes. We reconstruct the G$\ddot{o}$del's proof of the consistency of GCH and AC with the axioms of Zermelo-Fraenkel set theory by using Mostowski-Shepherdson mapping theorem, reflection principles in Tarski-Vaught theorem and Montague-Levy theorem and the fact that NBG is a conservative extension of ZF.

• Journal for History of Mathematics
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• v.30 no.2
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• pp.71-86
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• 2017

When looking for solutions of Jisuguimundo with magic number 88~92 and 94~98, alternating method is applied to each possible partitions of each magic number. But this method does not apply in case of finding solutions of Jisuguimundo with magic number 87, 93, and 99. In this study, it is shown that solutions of Jisuguimundo with magic number 87, 93, and 99 can be found by applying alternating method to two partitions. These two partitions are derived partitions obtained by each partitions of magic number 87, 93, and 99. If every number from 1 to 30 which satisfy every unit path of Jisuguimundo can be found in all components of these two derived partitions, that arrangement is just a solution of Jisuguimundo. The method suggested in this study is more developed one than the method which is applied to just one partition.

• Journal for History of Mathematics
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• v.16 no.2
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• pp.55-70
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• 2003

This study investigated tile intuitive level of justification in geometry, as the former step to the aximatization, with concrete examples. First, we analyze limitations that the axiomatic method has in tile context of discovery and the educational situation. This limitations can be supplemented by the proper use of the intuitive method. Then, using the histo-genetic analysis, this study shows the process of the development of geometrical thought consists of experimental, intuitive, and axiomatic steps. The intuitive method of proof which is free from the rigorous axiom has an advantage that can include the context of discovery. Finally, this paper presents the issue of intuitive proving that the three angles of an arbitrary triangle amount to 180$^{\circ}$, as an example of the local systematization.

• 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 for History of Mathematics
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• v.27 no.1
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• pp.81-93
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• 2014

The $L^1$-convergence of Fourier series problems through additional assumptions for Fourier coefficients were presented by W. H. Young in 1913. We say that they are the classical results. Using modified trigonometric series is the convenience method to study the $L^1$-convergence of Fourier series problems. they are called the neoclassical results. This study concerns with the $L^1$-convergence of Fourier series. We introduce the classical and neoclassical results of $L^1$-convergence sequentially. In particular, we investigate $L^1$-convergence results focused on the results of Bhatia's studies. In conclusion, we present the research minor lineage of Bhatia's studies and compare the classes of $L^1$-convergence mutually.

• Journal for History of Mathematics
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• v.27 no.6
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• pp.395-402
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• 2014

When the circle inscribed in a square is projected to a picture plane, one sees, in general, an ellipse in a convex quadrilateral. This ellipse is poorly described in the works of Alberti and Durer. There are one parameter family of ellipses inscribed in a convex quadrilateral. Among them only one ellipse is the perspective image of the circle inscribed in the square. We call this ellipse "the projected ellipse." One can easily find the four tangential points of the projected ellipse and the quadrilateral. Then we show how to find the center of the projected ellipse. Finally, we describe a pair of conjugate vectors for the projected ellipse, which finishes the construction of the desired ellipse. Using this algorithm, one can draw the perspective image of the squared-circle tiling.

• Journal for History of Mathematics
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• v.31 no.3
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• pp.151-166
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• 2018

The rule of the game of Chomp is simple and the existence of a winning strategy can easily be proved. However, the existence tells us nothing about what strategies are winning in reality. Like in Chess or Baduk, many researchers studied the winning moves using computer programs, but no general patterns for the winning actions have not been found. In the paper, we aim to construct practical winning strategies based on backward induction. To do this we develop how to analyze Chomp and prove and find the winning strategies of the simple games of Chomp.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.139-156
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• 2008

We investigate the inducing method of irrational numbers in junior high school, under algebraic as well as geometric point of view. Also we study the treatment of irrational numbers in the 7th national curriculum. In fact, we discover that i) incommensurability as essential factor of concept of irrational numbers is not treated, and ii) the concept of irrational numbers is not smoothly interconnected to that of rational numbers. In order to understand relationally the incommensurability, we suggest the method for inducing irrational numbers using construction in junior high school.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.99-116
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• 2009

In this paper we study errors related with constructing regular polygons in the book 'Method of Ruler and Compass' written three hundreds years ago. It is well known that regular heptagon and regular nonagon are not constructible using compass and ruler. But in this book construction methods of these regular polygons is suggested. We show that the construction methods are incorrect, it include some errors.

• The Pure and Applied Mathematics
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• v.4 no.1
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• pp.71-76
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• 1997

A new proof of the well-known identity involved in the Beta function B(p, q) is given by using the theory of hypergeometric series and a brief history of Gamma function is also provided. The method here is shown to be able to apply to evaluate some definite integrals.