• Research in Mathematical Education
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• v.18 no.2
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• pp.103-128
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• 2014

This paper presents the Global van Hiele (GVH) questionnaire as a tool for mapping knowledge and understanding of plane and solid geometry. The questionnaire facilitates identification of the respondents' mastery of the first three levels of thinking according to van Hiele theory with regard to key geometrical topics. Teacher-educators can apply this questionnaire for checking preliminary knowledge of mathematics teaching candidates or pre-service teachers. Moreover, it can be used when planning a course or granting exemption from studying in basic geometry courses. The questionnaire can also serve high school mathematics teachers who are interested in exposing their students to multiple-choice questions in geometry.

• Proceedings of the KSME Conference
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• 2007.05a
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• pp.1836-1841
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• 2007

Based on three-dimensional (3-D) FE limit analyses, this paper provides plastic limit and TES(Twice-Elastic-Slope) loads for pipe bends under combined pressure and out-of-plane bending. The plastic limit loads are determined from FE limit analyses based on elastic-perfectly-plastic materials using the small geometry change option, and the FE limit analyses using the large geometry change option provide TES plastic loads. A wide range of parameters related to the bend geometry is considered. Based on the FE results, closed-form approximations of plastic limit and TES plastic load solutions for pipe bends under out-of-plane bending are proposed.

• Journal for History of Mathematics
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• v.29 no.5
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• pp.295-314
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• 2016

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. We learned that dynamic programming in tropical algebraic geometry can be used to find the shortest path in graphs. We have also learned about the Bezout's Theorem, which is a theorem concerning the intersections of tropical plane curves, and the stable intersection principle.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1996.10a
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• pp.38-47
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• 1996

Sectional analysis program for plane strain or axisymmetric geometry of aluminum alloy sheet metals was developed. For modeling the anomalous behavior of aluminum alloy, Barlat's strain rate potential and Hill's 1990 non-quadratic yield theory arranged under the plane stress assumption were employed. 2-D rigid-viscoplastic FEM formulation based on the bending-augmented membrane theory was derived, solving simultaneously force equilibrium as well as non-penetration condition. Isotropic hardening law was also assumed for yielding behavior. To verify the validity and availability of the developed program, 2-D stretch/draw forming process for plane strain geometry and cylindrical cup deep drawing process for axisymmetric geometry were simulated.

• Proceedings of the Korean Society for Technology of Plasticity Conference
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• 1997.10a
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• pp.158-163
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• 1997

In this paper the tool geometry of the PSS test were optimized in order to assure the reliability of the test. Considering many factors for optimization of the tool geometry, computer-simulation technique using three-dimensional finite element method(FEM) was used. Three design variables -the punch length, punch crown and punch corner radius- are chosen to be optimized according to the Taguchi's experiment technique with the L9 orthogonal array. The optimum condition to ensure the plane strain mode over the overall area of the specimen was clarified. Moreover the simulation results are confirmed by experiment.

• The Mathematical Education
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• v.40 no.1
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• Korean Journal of Computational Design and Engineering
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• v.6 no.1
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• pp.31-39
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• 2001

Presented in this paper are algorithms to compute the positions of vertices and equations of edges of the Voronoi diagram of a circle set. The circles are located in a Euclidean plane, the radii of the circles are not necessarily equal and the circles are not necessarily disjoint. The algorithms correctly and efficiently work when the correct topology of the Voronoi diagram was given. Given three circle generators, the position of the Voronoi vertex is computed by treating the plane as a complex plane, the Z-plane, and transforming it into another complex plane, the W-plane, via the Mobius transformation. Then, the problem is formulated as a simple point location problem in regions defined by two lines and two circles in the W-plane. And the center of the inverse-transformed circle in Z-plane from the line in the W-plane becomes the position of the Voronoi vertex. After the correct topology is constructed with the geometry of the vertices, the equations of edge are computed in a rational quadratic Bezier curve farm.

• Publications of The Korean Astronomical Society
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• v.23 no.2
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• pp.31-35
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• 2008

We present analytical approximations for calculating the scattering and escape of non-ionizing photons from a plane-parallel medium with uniformly illuminated by external sources. We compare the results with the case of a spherical dust cloud. It is found that more scattering and absorption occur in the plane-parallel geometry than in the spherical geometry when the optical depth perpendicular to the plane and the radial optical depth of the sphere are the same. The results can provide an approximate way to estimate radiative transfer in a variety interstellar conditions and can be applied to the dust-scattered diffuse Galactic light.

• International Journal of Aeronautical and Space Sciences
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• v.14 no.2
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• pp.183-192
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• 2013

This paper presents formation reconfiguration using impulsive control input for spacecraft formation flying. Spacecraft in a formation should change the formation size and/or geometry according to the mission requirements and space environment. To modify the formation radius and geometry with respect to the leader spacecraft, the follower spacecraft generates additional control inputs; the two impulsive control inputs are general control type of the spacecraft system. For the impulsive control input, Lambert's problem is modified to construct the transfer orbit in relative motion, given two position vectors at the initial and final time. Moreover, the numerical simulation results show the transfer trajectories to resize the formation radius in the radial/along-track plane formation and in the along-track/cross-track plane formation. In addition, the maneuver characteristics are described by comparing the differential orbital elements between the reference orbit and transfer orbit in the radial/along-track plane formation and along-track/cross-track plane formation.

• Korean Journal of Optics and Photonics
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• v.5 no.3
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• pp.379-385
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• 1994

The sensitivity vector which depends on geometry of object illumination angles and distances of ESPI was analyzed. And the sensitivities of in-plane and out-of-plane displacements have been investigated. From these results, we have the conclusion that it is useful to use the diverging beam for object illumination. With diverging object illumination, only little errors are occurred when we approximate the sensitivity vector to constant all over the object surface.urface.