• Communications of Mathematical Education
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• v.17
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• pp.115-126
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• 2003

수학사는 수학적 사실이나 수학자에 대한 연대기적 나열만을 의미하는 것은 아니다. 수학사에서는 수학적 개념들, 정리들, 연구 방법의 발생, 축적, 그리고 발전에 대한 폭넓은 견해를 접할 수 있다. 특히, 수학사에서 접할 수 있는 수학 문제해결의 다양한 방법은 수학 교수-학습 과정에서 교사의 올바른 교수학적 선택을 위한 중요한 기초 자료가 될 수 있다. 본 연구에서는 그리스의 수학자 아르키메데스가 구의 부피를 구하기 위해 사용했던 공학적 문제해결 방법을 살펴보고, 공학적 방법의 활용에 관련된 수학적 기초를 살펴보고, 공학적 문제해결 방법을 중등학교 수학 영재교육에 활용할 수 있는 가능성을 모색할 것이다.

• 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.

• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.221-221
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• 2010

고대의 인도수학은 산스크리트어로 쓰여 있고, 최초의 기하학은 베다문헌으로 경전 속에 포함되어 있으며, 성스런 제단이나 사원을 설계하기위해서 발전하였다. 고대 인도의 많은 수학자들은 힌두교의 성직자들로 일찍이 십진법, 계산법, 방정식, 대수학, 기하학, 삼각법 등의 연구에 공헌하였다. 인도 기하학은 양적이며 계산적이지만 원리를 가지고 문제를 해결하는 특성이 있다. 그러나 고대 그리스 기하학은 공리적이고 연역적으로 전개되는 완전한 학문으로 발전하였다. 고대 인도와 타 문명권의 기하학을 비교하는 것은 오늘날 문제해결을 중시하는 현대과학의 시대에 가치와 의미가 있는 것으로 사료된다.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.57-73
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• 2010

Transcendental numbers are important in the history of mathematics because their study provided that circle squaring, one of the geometric problems of antiquity that had baffled mathematicians for more than 2000 years was insoluble. Liouville established in 1844 that transcendental numbers exist. In 1874, Cantor published his first proof of the existence of transcendentals in article [10]. Louville's theorem basically can be used to prove the existence of Transcendental number as well as produce a class of transcendental numbers. The number e was proved to be transcendental by Hermite in 1873, and $\pi$ by Lindemann in 1882. In 1934, Gelfond published a complete solution to the entire seventh problem of Hilbert. Within six weeks, Schneider found another independent solution. In 1966, A. Baker established the generalization of the Gelfond-Schneider theorem. He proved that any non-vanishing linear combination of logarithms of algebraic numbers with algebraic coefficients is transcendental. This study aims to examine the concept and development of transcendental numbers and to present students with its open problems promoting a research on it any further.

• 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.

• Journal for History of Mathematics
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• v.23 no.1
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• pp.41-52
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• 2010

Ancient Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sturas in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. And rules or problems of the mathematics were transmitted both orally and in manuscript form.Indian mathematicians made early contributions to the study of the decimal number system, arithmetic, equations, algebra, geometry and trigonometry. And many Indian mathematicians were appearing one after another in Ancient. This paper is a comparative study of mathematics developments in ancient India and the other ancient civilizations. We have found that the Indian mathematics is quantitative, computational and algorithmic by the principles, but the ancient Greece is axiomatic and deductive mathematics in character. Ancient India and the other ancient civilizations mathematics should be unified to give impetus to further development of mathematics education in future times.

• Journal of Educational Research in Mathematics
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• v.25 no.4
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• pp.473-498
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• 2015

The purpose of this study is to examine thinking process of the mathematically gifted students and how invariants affect the construction and discovery of curve when carry out activities that produce and reproduce the algebraic curves, mathematician explored from the ancient Greek era enduring the trouble of making handcrafted complex apparatus, not using apparatus but dynamic geometry software. Specially by trying research that collect empirical data on the role and meaning of invariants in a dynamic geometry environment and research that subdivide the process of utilizing invariants that appears during the mathematically gifted students creating a new curve, this study presents the educational application method of invariants and check the possibility of enlarging the scope of its appliance.

• Journal for History of Mathematics
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• v.20 no.3
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• pp.167-180
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• 2007

In this study, we explored the role of analysis in the algebra development. For this, we classified ancient geometric analysis into an analysis by reduction and a Pappusian problematic analysis. this shows that both analyses have the function of reduction. Pappus' analysis consists of four steps; transformation, resolution, construction, demonstration. The transformation, by which conditions of given problem is transformed into other conditions which suggest a problem-solving, seems to be a kind of reduction. Mathematicians created new problems as a result of the reductional function of analysis, and became to see mathematics in the different view. An analytical thinking was a background at the birth of symbolic algebra, the reductional function of analysis played an important role in the development of symbolic algebra.

• Journal of Ginseng Culture
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• v.1
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• pp.28-42
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• 2019

What is unknown about Leibniz (Gottfried Wilhelm Leibniz, 1646~1716), a great philosopher and mathematician, is that he inquired about ginseng. Why Leibniz, one of the leading figures of the Enlightenment, became interested in ginseng? This paper excavates Leibniz's references on ginseng in his vast amount of correspondences and traces the path of his personal life and cultural context where the question about ginseng arose. From the sixteenth century, Europe saw a notable growth of medical botany, due to the rediscovery of such Greek-texts as Materia Medica and the introduction of a variety of new plants from the New World. In the same context, ginseng, the renowned panacea of the Old World began to appear in a number of European travelogues. As an important part of mercantilistic projects, major scientific academies in Europe embarked on the researches of valuable foreign plants including ginseng. Leibniz visited such scientific academies as the Royal Society in London and $Acad{\acute{e}}mie$ royale des sciences in Paris, and envisioned to establish such scientific society in Germany. When Leibniz visited Rome, he began to form a close relationship with Jesuit missionaries. That opportunity amplified his intellectual curiosity about China and China's famous medicine, ginseng. He inquired about the properties of ginseng to Grimaldi and Bouvet who were the main figures in Jesuit China mission. This article demonstrates ginseng, the unnoticed subject in the Enlightenment, could be an important clue that interweaves the academic landscape, the interactions among the intellectuals, and the mercantilistic expansion of Europe in the late 17th century.