• Title, Summary, Keyword: 오일러

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A Study on Learning Environments for Euler's formula with activities ('오일러 공식과 오일러 표수' 탐구 활동을 위한 학습 환경 연구)

  • Song, Min Ho
    • Journal for History of Mathematics
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    • v.26 no.2_3
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    • pp.131-148
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    • 2013
  • Euler's formula provides the topological characteristics of geometrical objects including polyhedra, and so an important mathematical concept. Descriptions on Euler's formula had been in the textbooks according to the 3rd through 7th National Mathematics Curriculum. However, they are gone after that. In this study, we focus on Euler characteristic and Euler's formula as an educational material for educations for the gifted or after-school educations. We first look at the mathematical history and the applications of Euler's formula and national curriculums to search for its mathematical and educational meaning. We further make a suggestion for a learning environment which provides a better education relying on search activities, not just depending on memorization, illuminated from the education of Euler's formula.

Euler's Mathematical Theology (오일러의 수학신학)

  • Hyun, Woo-Sik
    • Journal for History of Mathematics
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    • v.25 no.2
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    • pp.11-21
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    • 2012
  • The interdisciplinary study explores the Euler's theology through his mathematical landmarks. From the mathematico-theological perspective, we first address Euler's theological backgrounds, and then show the implications of Euler's identity as his mathematical Christology.

A Framework in Developing CAD System Kernel for Non-manifold Models (비다양체 모델을 지원하는 CAD 시스템 커널 개발을 위한 기반 구축)

  • Han, Young-Hyun;Lee, Kun-Woo;Lee, Sang-Hun;Kim, Sung-Hwan;Kim, Young-Jin;Bae, Seock-Hoon;Ahn, Jae-Hong;Lee, Kyoung-Jin
    • IE interfaces
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    • v.8 no.3
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    • pp.141-153
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    • 1995
  • 기존의 솔리드 모델링 시스템은 형상 표현에 있어서의 제약성과 통합 시스템으로서의 폐쇄성으로 인하여 응용 범위에 제약이 따른다. 이러한 약점을 극복하고자 하는 노력의 일환으로서, 최근에 등장한 것이 비다양체 모델을 지원하는 CAD 시스템 커널이다. 본 논문에서는 이러한 비다양체 모델을 지원할 수 있는 모델링 커널 시스템 개발의 기초가 되는 비다양체 자료구조와 이것을 바탕으로 한 오일러 공식 및 오일러 작업에 대해 소개한다. 그리고 이러한 오일러 작업을 실제로 구현하여 모델링 작업을 수행해 봄으로써, 본 논문에서는 제안된 비다양체 자료구조와 오일러 작업의 유용성을 보인다.

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다면체에 대하여 오일러 수만 중요한가\ulcorner

  • 박종률;김선부;김동수;조규인
    • Communications of the Korean Mathematical Society
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    • v.15 no.4
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    • pp.669-674
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    • 2000
  • 다면체에 대한 오일러 수의 개념은 잘 알려져 있다. 이 수는 위상 불변량이기 때문에 중요하다. 본 논문에서는 다면체의 꼭지점, 모서리, 면의 개수로 정의된 함수 중에서 본질적으로 올리러 수만이 위상 불변량임을 증명한다.

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Euler: Reflections on his Life, Works, and Thoughts (오일러의 삶, 업적, 그리고 사상)

  • Park, Chang-Kyun
    • Journal for History of Mathematics
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    • v.20 no.2
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    • pp.19-32
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    • 2007
  • This Paper aims to introduce Euler's life, works and thoughts, to show that it is his Christian worldview that enables his achievements. His life teaches us the lesson that examining philosophical base and historical background is crucial to understand mathematics or mathematicians, and that it is necessary to overcome given conditions and environments rather than expect better environments to reach meaningful achievements.

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On Euler : His Life and Mathematics, and Euler Archive (오일러가 수학사에 미친 영향에 대한 소고 오일러의 탄생 300주년을 기념하며)

  • Koh, Young-Mee;Ree, Sang-Wook
    • Journal for History of Mathematics
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    • v.20 no.3
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    • pp.27-42
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    • 2007
  • Many countries in the world are celebrating the tercentenary of the birth of L. Euler. One of them to notice is the construction of the Euler Archive, which is an online archive, made by two Ph.D. graduates from Dartmouth College. On the appearance of the archive, the authors remind of the life and works of mathematician L. Euler, who is considered as the most prolific, prominent, and versatile mathematician with the huge volume of his works as well as their importances, in the history of mathematics. Celebrating the 300th birthyear of L. Euler and the appearance of Euler Archive, authors suggest The Korean Society for History of Mathematics of investigating on Euler by ourselves as Koreans, and furthermore translating some works of his. Such works may stimulate interests in mathematics and its history to students as well as scholars.

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오일러를 앞선 최석정의 오일러방진

  • Song, Hong-Yeop
    • Information and Communications Magazine
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    • v.30 no.10
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    • pp.101-108
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    • 2013
  • 본고에서는 2013년 대한민국 과학기술 명예의 전당에 조선시대 수학자 최석정(崔錫鼎 1646~1715) 선현이 헌정된 것을 기념하여 그의 저서 구수략(九數略)에 기록된 '직교라틴방진'이 조합수학(Combinatorial Mathematics)의 효시로 일컫는 오일러(Leonhard Euler, 1707~1783)의 '직교라틴방진' 보다 최소 61년 앞섰다는 사실이 국제적으로 인정받게 된 경위를 소개하고 최석정의 9차 직교라틴방진의 특성을 살펴본다.

On the historical investigation of Bernoulli and Euler numbers associated with Riemann zeta functions (수학사적 관점에서 오일러 및 베르누이 수와 리만 제타함수에 관한 탐구)

  • Kim, Tae-Kyun;Jang, Lee-Chae
    • Journal for History of Mathematics
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    • v.20 no.4
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    • pp.71-84
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    • 2007
  • J. Bernoulli first discovered the method which one can produce those formulae for the sum $S_n(k)=\sum_{{\iota}=1}^n\;{\iota}^k$ for any natural numbers k. After then, there has been increasing interest in Bernoulli and Euler numbers associated with Riemann zeta functions. Recently, Kim have been studied extended q-Bernoulli numbers and q-Euler numbers associated with p-adic q-integral on $\mathbb{Z}_p$, and sums of powers of consecutive q-integers, etc. In this paper, we investigate for the historical background and evolution process of the sums of powers of consecutive q-integers and discuss for Euler zeta functions subjects which are studying related to these areas in the recent.

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3D gravity inversion with Euler deconvolution as a priori information (오일러 디컨벌루션을 사전정보로 이용한 3 차원 중력 역산)

  • Rim, Hyoung-Rae;Park, Yeong-Sue;Lim, Mu-Taek;Koo, Sung-Bon;Kwon, Byung-Doo
    • Geophysics and Geophysical Exploration
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    • v.10 no.1
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    • pp.44-49
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    • 2007
  • It is difficult to obtain high-resolution images by 3D gravity inversion, because the problem is extremely underdetermined - there are too many model parameters. In order to reduce the number of model parameters we propose a 3D gravity inversion scheme utilising Euler deconvolution as a priori information. The essential point of this scheme is the reduction of the nonuniqueness of solutions by restricting the inversion space with the help of Euler deconvolution. We carry out a systematic exploration of the growing body process, but only in the restricted space within a certain radius of the Euler solutions. We have tested our method with synthetic gravity data, and also applied it to a real dataset, to delineate underground cavities in a limestone area. We found that we obtained a more reasonable subsurface density image by means of this combination between the Euler solution and the inversion process.

Dynamics Formulations of the Universal-joint System Under Effect on Precession (세차운동을 고려한 유니버설 조인트 시스템의 동역학적 정식화)

  • Yun, Seong-Ho
    • Proceedings of the Computational Structural Engineering Institute Conference
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    • pp.23-26
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    • 2010
  • 본 논문에서는 유니버설 조인트의 동역학적인 해석을 위하여 오일러 각 순서에 의한 방법과 4원수에 의한 방법으로 운동방정식을 유도하였다. 원동축과 종동축의 회전은 물론 세차운동을 하는 회전축을 포함할 때 각 방법의 상이점을 발견하였다. 이러한 시스템의 동역학적 정식화를 바탕으로 한 수치 예제를 통하여 기존의 오일러 각 방법과 제시한 4원수 방법의 해석 결과를 비교하였다.

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