• Journal for History of Mathematics
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• v.18 no.4
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• pp.1-16
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• 2005

Chosun dynasty mathematician Park Yul (1621 - ?) wrote San Hak Won Bon(算學原本) which was posthumously published in 1700 by his son Park Du Se (朴斗世). It is the first mathematics book whose publishing date is known, although we have Muk Sa Jib San Bub (默思集算法) by Gyung Sun Jing (慶善徵, 1616-?). San Hak Won Bon is the first Chosun book which deals with tian yuan shu (天元術) and was quoted by many Chosun authors. We do find it in the library in Korea University. In this paper, we investigate its contents together with its historical significance and influences to the development of Chosun dynasty Mathematics and conclude that Park Yul is one of the most prominent Chosun dynasty mathematicians.

• Journal for History of Mathematics
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• v.21 no.1
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• pp.29-44
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• 2008

Fuzzy logic is introduced by Zadeh in 1965. It has been continuously developed by many mathematicians and knowledge engineers all over the world. A lot of papers concerning with the history of mathematics and the mathematical education related with fuzzy logic, but there is no paper concerning with Zadeh. In this article, we investigate his life and papers about fuzzy logic. We also compare two-valued logic, three-valued logic, fuzzy logic, intuisionistic logic and intuitionistic fuzzy sets. Finally we discuss about the expression of intuitionistic fuzzy sets.

• Journal for History of Mathematics
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• v.22 no.2
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• pp.53-68
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• 2009

From ancient Greek times, the infinite concepts had debated, and then they had been influenced by Hebrew's tradition Kabbalab. Next, those infinite thoughts had been developed by Roman Catholic theologists in the medieval ages. After Renaissance movement, the mathematical infinite thoughts had been described by the vanishing point in Renaissance paintings. In the end of 1800s, the infinite thoughts had been concreted by Cantor such as Set Theory. At that time, the set theoretical trend had been appeared by pointillism of Seurat and Signac. After 20 century, mathematician $M\ddot{o}bius$ invented <$M\ddot{o}bius$ band> which dimension was more 3-dimensional space. While mathematicians were pursuing about infinite dimensional space, artists invented new paradigm, surrealism. That was not real world's images. So, it is called by surrealism. In contemporary arts, a lot of artists has made their works by mathematical material such as Mo?bius band, non-Euclidean space, hypercube, and so on.

• Journal for History of Mathematics
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• v.33 no.6
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• pp.303-314
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• 2020

Extending the method of extractions of square and cube roots in Jiuzhang Suanshu, Jia Xian introduced zengcheng kaifangfa in the 11th century. The process of zengcheng kaifangfa is exactly the same with that in Ruffini-Horner method introduced in the 19th century. The latter is based on the synthetic divisions, but zengcheng kaifangfa uses the binomial expansions. Since zengcheng kaifangfa is based on binomial expansions, traditional mathematicians in East Asia could not relate the fact that solutions of polynomial equation p(x) = 0 are determined by the linear factorization of p(x). The purpose of this paper is to reveal the difference between the mathematical structures of zengcheng kaifangfa and Ruffini-Honer method. For this object, we first discuss the reasons for zengcheng kaifangfa having difficulties to connect solutions with linear factors. Furthermore, investigating multiple solutions of equations constructed by tianyuanshu, we show differences between two methods and the structure of word problems in the East Asian mathematics.

• Education of Primary School Mathematics
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• v.15 no.1
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• pp.41-52
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• 2012

The korean mathematics textbooks according to the 2007 revised mathematics curriculum and the MiC textbooks are similar in that they introduce mathematical materials in real life situations and are composed in such a way that require students to form their own mathematical concepts. However the MiC textbooks are focus more on situation-centered problems and context-centered problems where a set of procedures need to be followed in order to arrive at an answer. So, this paper is aim at comparing the units of statistics in the korean mathematics textbooks and the MiC textbooks in order to find the implications for writing textbook. By comparing the specific content and the used methods, I found Korean textbooks focused on understanding concepts and spending less time surveying and collecting data. On the other hand, MiC textbooks used activities that real mathematicians would be involved with, such as surveying and analyzing data to compose mathematical concepts.

• Journal of the Korean Mathematical Society
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• v.44 no.5
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• pp.1163-1184
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• 2007

In this presentation dedicated to the tricentennial birth anniversary of the great eighteenth-century Swiss mathematician, Leonhard Euler (1707-1783), we begin by remarking about the so-called Basler problem of evaluating the Zeta function ${\zeta}(s)$ [in the much later notation of Georg Friedrich Bernhard Riemann (1826-1866)] when s=2, which was then of vital importance to Euler and to many other contemporary mathematicians including especially the Bernoulli brothers [Jakob Bernoulli (1654-1705) and Johann Bernoulli (1667-1748)], and for which a fascinatingly large number of seemingly independent solutions have appeared in the mathematical literature ever since Euler first solved this problem in the year 1736. We then investigate various recent developments on the evaluations and representations of ${\zeta}(s)$ when $s{\in}{\mathbb{N}}{\backslash}\;[1],\;{\mathbb{N}}$ being the set of natural numbers. We emphasize upon several interesting classes of rapidly convergent series representations for ${\zeta}(2n+1)(n{\in}{\mathbb{N}})$ which have been developed in recent years. In two of many computationally useful special cases considered here, it is observed that ${\zeta}(3)$ can be represented by means of series which converge much more rapidly than that in Euler's celebrated formula as well as the series used recently by Roger $Ap\'{e}ry$ (1916-1994) in his proof of the irrationality of ${\zeta}(3)$. Symbolic and numerical computations using Mathematica (Version 4.0) for Linux show, among other things, that only 50 terms of one of these series are capable of producing an accuracy of seven decimal places.

• Journal for History of Mathematics
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• v.22 no.4
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• pp.1-14
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• 2009

Since western mathematics and astronomy had been introduced in Chosun dynasty in the 17th century, most of Chosun mathematicians studied Shu li jing yun(數理精蘊) for the western mathematics. In the last two decades of the 19th century, Chosun scholars have studied them which were introduced by Japanese text books and western missionaries. The former dealt mostly with elementary arithmetic and the latter established schools and taught mathematics. Lee Sang Seol(1870~1917) is well known in Korea as a Confucian scholar, government official, educator and foremost Korean independence movement activist in the 20th century. He was very eager to acquire western civilizations and studied them with the minister H. B. Hulbert(1863~1949). He wrote a mathematics book Su Ri(數理, 1898-1899) which has two parts. The first one deals with the linear part(線部) and geometry in Shu li jing yun and the second part with algebra. Using Su Ri, we investigate the process of transmission of western mathematics into Chosun in the century and show that Lee Sang Seol built a firm foundation for the study of algebra in Chosun.

• Journal of the Korean Geographical Society
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• v.49 no.4
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• pp.585-600
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• 2014

The purpose of this study is to consider the influence of the French Royal Academy of Science on the European mapping of China in the eighteenth century. For this, the historical background of French Jesuits mission of mathematicians sent to China by Louis XIV in 1685 was examined. It was found that making astronomical observations for the determination of Chinese geographic coordinates was one important reason of the French Jesuit mission. Secondly, Cassini instructed the longitude determination method to the missionaries and they reported their survey results to the Academy as correspondence member. Thirdly, the cartographic materials they accumulated in the first state were not sufficient to change the map of China. But after 1700, the map of China was broken with the Ptolemaic tradition and the longitude of Peking was moved westward about $20^{\circ}$. This reduced the width of China. Fourthly, the French Jesuit contributed to the making of Huangyu quanlan tu. The manuscipt was sent to France and it was published in d'Anvill's atlas. And his map was used as a standard map of China for more than 100 years.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.3
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• pp.212-217
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• 2007

The Alienor method is a powerful tool for solving global optimization problems. It allows the transformation of a multi-variable problem into a new one that depends on a single variable. Any one-dimensional global optimization method can then be used to solve the transformed problem. Several one-dimensional global optimization methods coupled with the Alienor method have been suggested by mathematicians and it is shown that the suggested methods are successful for test functions. However, there are problems with these methods in engineering practice. In this paper, Lipschitzian optimization without using the Lipschitz constant is coupled with the Alienor method and applied to the test functions. Using test functions, it is shown that the suggested method can be successfully applied to global optimization problems.

• Journal of the Korean School Mathematics Society
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• v.15 no.4
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• pp.627-641
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• 2012

We found a few students had an error in the function and equation units, because most of mathematicians omitted the multiplication signs. In the mathematical history, the multiplication and parentheses signs had various changes. Based on the Histogenetic Principle, high level students know that the letter in the functions and equations represents a number and the related principles, so they have no big problems. But since the low level students stay in the early days in the mathematical history, they have some problems in the modern function and equation. Therefore, while we study the function and equation units with the low level students, we present that we have to be cautious when we omit the multiplication and parentheses signs.