• Title/Summary/Keyword: 정10각형

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A Study on the Construction of Regular Polygons in 'Method of Ruler and Compass' (`자와 컴퍼스의 방법`에 제시된 정다각형의 작도 방법 연구)

  • Han, In-Ki
    • Journal for History of Mathematics
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    • v.21 no.2
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    • pp.119-134
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    • 2008
  • In this paper we study a book 'Method of Ruler and Compass' written in Russia three hundreds years ago. In this book many construction problems related with plane figures and solid figures are solved. In this study we analyze construction method of some regular polygon(square, regular pentagon, regular octagon, regular decagon) suggested in 'Method of Ruler and Compass', give mathematical proofs of these construction.

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Simulation of Small Clusters(II) -Geometries and Energies of$C_6-C_10$- (탄소 클러스터들에 관한 시뮬레이션(II) -$C_6-C_10$의 구조와 에너지-)

  • Lee, Jong-Mu
    • Korean Journal of Materials Research
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    • v.2 no.2
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    • pp.95-100
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    • 1992
  • The bond lengths, bond angles and energies of $C_6$ clusters are calculated by using the simulation technique based on some semiempirical potential energy functions, with the result that the equilibrium configuration of $C_6$ is a regular equilateral hexagon. The same simulations have been performed for linear and cyclic forms of $C_7-C_10$ clusters and the results show that the regular heptagonal, octagonal, nonagonal and decagonal forms are more stable than the linear forms of the respective clusters. Comparison of this result with the present author's previous result that the most stable configurations of $C_2-C_5$ are linear implies that the most stable configuration of the cluster changes from one-dimension al to two-dimensional one as the cluster size increases and that the critical cluster size is $C_6$.

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Object tracking algorithm of Swarm Robot System for using SVM and Dodecagon based Q-learning (12각형 기반의 Q-learning과 SVM을 이용한 군집로봇의 목표물 추적 알고리즘)

  • Seo, Sang-Wook;Yang, Hyun-Chang;Sim, Kwee-Bo
    • Journal of the Korean Institute of Intelligent Systems
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    • v.18 no.3
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    • pp.291-296
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    • 2008
  • This paper presents the dodecagon-based Q-leaning and SVM algorithm for object search with multiple robots. We organized an experimental environment with several mobile robots, obstacles, and an object. Then we sent the robots to a hallway, where some obstacles were tying about, to search for a hidden object. In experiment, we used four different control methods: a random search, a fusion model with Distance-based action making(DBAM) and Area-based action making(ABAM) process to determine the next action of the robots, and hexagon-based Q-learning and dodecagon-based Q-learning and SVM to enhance the fusion model with Distance-based action making(DBAM) and Area-based action making(ABAM) process.

Integrated Analytical-Numerical Approach to Compute the Energy on Rock-fall Protection Fence (해석적-수치해석적 방법을 통한 낙석방지울타리에 작용하는 에너지 분석)

  • Kim, Hee Su;Hwang, Youngcheol;Jang, Hyun-Ick;Ban, Hoki
    • Journal of the Korean GEO-environmental Society
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    • v.20 no.12
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    • pp.57-64
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    • 2019
  • A man-made slope has been increased due to the construction of road. This slope lies at risk of rock falling, induced mostly by heavy rainfall. The MOLIT (Ministry of Land, Infrastructure and Transport) recommends the specific dimension of rockfall protection fence (post, wire-rope, and mesh) which should resist 48~61 kJ. However, the energy absorption capacity of each component of rockfall protection fence is not clearly presented. Hence, this study made an effort to compute the energy absorption capacity of each component in analytical and numerical method, and compared with each other.

Axial Compression of Stub Columns for Concrete-filled Square Steel Tubes (일축 압축력을 받는 콘크리트충전 각형강관 단주의 구조적 거동)

  • Yoo, Yeong-Chan
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.22 no.2
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    • pp.617-624
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    • 2021
  • Concrete-filled steel tubular columns can improve the strength and deformation capacity of structures, thereby enabling the development of efficient structures. The Korean design standard (KDS41) regarding concrete-filled steel tubular structures, established by the architectural institute of Korea in 2005, was revised in 2009 and 2016. The objective was to understand the compressive strengths and deformation capacity of stub columns for concrete-filled square steel tubes under uniaxial compression and validate the KDS41's standard code for necessary corrections. Experiments were conducted on 26 specimens with parameters, such as the width-thickness ratio of cold-formed square tubes. The following values of the stub columns for concrete-filled square steel tubes were obtained: compressive strengths, relationship between the axial load and axial displacement, and failure modes. An analysis of these results enabled an understanding of the concrete-filled effect and the influence of the wide-thickness ratio. The compressive strengths of filled concrete saw a 9% increase compared to a state of uniaxial stress, which must be noted in a future edition of KDS41. After benchmarking the results regarding square steel tubes generated by cold forming to the guidelines provided by the KDS41, the KDS41's value of 2.26 for the limiting width-to-thickness ratio for the compact section was found to be inflated. With a safety concern, this paper proposes a more conservative value of 1.35.

A Boundary Integral Approximation For the Stress Intensity Factors in Elastic Plate Bending (강성평판굽힘 문제의 응력확대계수를 위한 경계적분수치해법)

  • Kim, J. W.
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.6 no.3
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    • pp.282-288
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    • 1982
  • 크랙탄성평판의 굽힘문제가 경계적분방정식으로 구성되었다. 자연변수인 변위, 수직기울기, 굽힘 모우멘트, 등가전단적과 크랙끝에서 응력의 성장율로 정의되는 응력확대계수들이 주변수로 포함 된다. 이 적분방정식들은 가역에너지 적분이론(Green-Rayleigh)을 기초로 크랙응력분포특성에 맞 게 발전되었으며 해당되는 핵함수들이 유도되었다. 등분석 모우멘트를 받는 중앙크랙이 있는 정 4각형 모형에 대한 응력확대계수가 계산되어 기존의 유한요소법의 해와 비교되었다.

Analysis of the hydraulic structure of geometric shape according to sediment transportation and bed change characteristic (수공구조물 설치에 따른 유사확산 및 하상변동 특성에 관한 분석)

  • Ahn, Seung-Seop;Song, In-Ryul;Lee, Hyo-Jung;Lee, Nam-Hun
    • Proceedings of the Korea Water Resources Association Conference
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    • 2008.05a
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    • pp.963-966
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    • 2008
  • 본 연구에서는 최근까지 유사관측을 수행하고 있는 금강본류 하도구간의 금남$\sim$공주 지점을 대상으로 하였다. 분석을 위하여 이 지점의 총유사량 산정에 영향을 미치는 부유사량 관측 및 수위, 유량과 같은 하천 흐름 등에 관한 과거의 자료를 수집 정리 하였다. 본 연구에서 적용하고자 하는 교량의 교각에 대한 기하학적 형상은 원형, 정사각형, 정팔각형, 장방형으로 하였으며 분석 모형은 SED2D-WES 모형을 이용하여 유역에 대한 교각의 형상이 미치는 영향에 대하여 연구 하였다. 그 결과 지름이 6m, 경간장 57m인 원형교각의 경우 교각에서 약 14.3m 떨어진 곳에서 최고 유속 0.75m/s가 발생되었으며, $6{\sim}6m$의 정사각형교각의 경우 교각으로부터 약 15.8m떨어진 곳에서 0.68m/s의 최대 유속이 발생하고 $6{\sim}6m$ 정팔각형교각의 경우 교각으로부터 약 16.2m떨어진 곳에서 0.65m/s의 최대유속이 발생하고, 마지막으로 $3{\sim}6m$ 장방형교각의 경우 교각으로부터 약 21m 떨어진 구간에서 0.63m/s의 최고 유속이 발생하는 것으로 나타났다. 대상유역의 길이가 길고, 유속이 낮으므로 유출지점까지 흘러내려가는 유사량보다 하천내에 유입된 유사가 그대로 퇴적되는 경우가 많아 24시간 분석결과 하상변동량은 퇴적량과 침식량을 합하여 약 0.22%정도 변동되는 것으로 나타났으며, 교각형상에 따른 하상변동특성으로 원형교각의 경우 세굴이 일어나는 지점은 교각에서 약 16.88m떨어진 지점까지 하상변동이 일어났으며, 정사각형 교각의 경우 교각에서 약 10.96m떨어진 지점까지, 정팔각형 교각의 경우 교각에서 약 6.32m떨어진 지점까지, 장방형 교각의 경우 교각에서 약 18.23m떨어진 지점까지 하상변동이 나타남을 알 수 있었다.

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Oscillatory Motion of Natural Convective Flow in Partially Divided Square Enclosure (수평격판을 갖는 4각형 밀폐공간내에서 자연대류의 진동유동)

  • 김점수;정인기;송동주
    • Transactions of the Korean Society of Mechanical Engineers
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    • v.16 no.10
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    • pp.1963-1970
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    • 1992
  • An oscillatory motion of the natural convection in a two dimensional, partially divided square enclosure heated from below, and fitted with a partition is investigated numerically. The enclosure was composed of the lower hot and the upper cold horizontal walls and the adiabatic vertical walls, and a partition was situated perpendicularly at the mid-height of the one vertical insulated wall. The governing equations are solved by using the finite element method with Galerkin method. The computations were performed with the variation of the length and the thermal conductivity of the partition, and Rayleigh number based on the temperature difference between horizontal walls and the enclosure height with water(Pr=4.95). also, the effect of the inclination angles was studied for the transition to the oscillating flow. As the results, it was found that the intensity and frequency of oscillatory motion were affected significantly by the Rayleigh number and the length of partition. The effect of oscillatory motion was weaken with the increase of the thermal conductivity of partition. The inclination angle for the transition was raised with the increase of Rayleigh number and the length of partition.

Wetting Characteristics of Water Droplet on the Solid Surfaces with Variable Pillar-Type Nanostructures (다양한 기둥 타입을 가지는 나노 구조물 고체 표면에서의 물 액적 젖음 특성)

  • Yoo, Min Jung;Kwon, Tae Woo;Ha, Man Yeong
    • Transactions of the Korean Society of Mechanical Engineers B
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    • v.40 no.10
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    • pp.659-666
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    • 2016
  • A numerical study, using the molecular dynamics simulation method, was carried out to investigate the wetting characteristics of water droplets on a solid square pillar surface with variable periodic edge length patterns at the nanoscale. In this study, the pillar plane was supposed to be rectangular or square shaped. In addition, the surface area was increased while the shape of the pillar plane was kept fixed. In the case of the square pillar, the edge length increased from $4.24{\AA}$ to $12.72{\AA}$. Also, the rectangular pillar had two types of length edges. In this case, one edge length was fixed at $8.48{\AA}$ and the other edge length was increased from $4.24{\AA}$ to $12.72{\AA}$. Through these length changes, the hydrophobicity and hydrophilicity of a water droplet on the variable pillar surfaces were analyzed.

An analysis on concept definition and concept image on quadrangle of middle and high school students (중·고등학생의 사각형에 대한 개념 정의 이해와 개념 이미지 분석)

  • Chang, Hyun Suk;Kim, Myung Chang;Lee, Bongju
    • The Mathematical Education
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    • v.61 no.2
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    • pp.323-338
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    • 2022
  • The purpose of this study are to analyze how well middle and high school students understand the concept definition of quadrangle and to explore the phenomenon about their concept image. A test tool was developed and 60 8th graders, 63 9th graders and 65 10th graders were tested, and some students who needed in-depth analysis were interviewed. The results are as follows. First, it cannot be said that understanding level of the concept definition of the quadrangle naturally improves as the grade level goes up. Particularly, it was found that the understanding of the definition of the rhombus is the lowest in all three grades compared to other quadrangle. Second, although female students understood the definition of square better than male students, the understanding level of the definition of trapezoid, parallelogram, rhombus, and rectangle did not differ by gender. Third, it was found that the students who did not understand the concept definition of the quadrangle were more and more influenced by the concept image as the grade level went up. Fourth, it showed that a tendency to be less influenced by the concept definition and more influenced by textbooks and teachers as the grades go up when students form a concept image.