• 한국공간정보시스템학회:학술대회논문집
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• 2003.11a
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• pp.159-162
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• 2003

In this paper, to find probable collision positions between moving object and terrain in 3D space efficiently, we use a model, similar to Ray Tracing, which finds the triangles intersected by a directed line segment from a large amount of triangles. We try to reduce dead space as much as possible to find candidate triangles intersected by a directed line segment than previous work's. A new modified octree, LBV-Octree(Least Bounding Voxel Octree), is proposed, and we have a ray tracing with it. In the experiment, ray tracing with LBV-Octree provides $5%{\sim}11%$ better performance than with classical octree.

• Communications of Mathematical Education
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• v.24 no.2
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• pp.325-344
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• 2010

The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.39-48
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• 2005

A convex region covers a family of curves if it contains a congruent copy of each curve in the family, and a 'worm problem' for that family is to find the convex region of smallest area. In this paper, we find the smallest triangular cover of any prescribed shape for the family S of all triangles of diameter 1.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.259-267
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• 2005

In 2000 a general conjecture was proposed: a special polygon cannot be cut into an odd number of triangles of equal areas. It has been proved that the conjecture holds for polygons with at most six sides. In this paper we prove the existence of special n-polygon for any integer n > 6 and discuss the conjecture for special polygons with seven sides.

• Journal for History of Mathematics
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• v.16 no.3
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• pp.1-26
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• 2003

Gougu Rule for the right triangles is the Chinese Pythagorean theorem. In the late age of the Chosun Dynasty, mathematicians of Chosun pioneered the study of the Chinese Nine Chapters and other advanced mathematical problems as well as the Easternism in spite of the various difficulties after the Imchinoeran(임진왜란), Chungyuchairan(정유재란) and Byungchahoran(병자호란) The technologies of the addition and addition twice are the methods of the solution of the problems in the right triangles. This paper is intended to introduce some problems using these methods of solution.

• Korean Journal of Computational Design and Engineering
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• v.10 no.6
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• pp.455-464
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• 2005

This paper discusses the methods of computing tool-paths for machining free-form surfaces on 3-axis CNC machines in die and mould making. In computational view this paper describes the characteristics and issues of the geometric information and the shape, which make computing tool-paths difficult. Important points that should be considered in devising a computing method are also discussed. A newly implemented method is explained and compared with an old method for a commercial CAM system. The implemented method is used in a commercial CAM system and the computing time for an example is presented.

• Communications of Mathematical Education
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• v.29 no.3
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• pp.313-330
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• 2015

The classification is an important activity that is directly related to concept formation. Thus it will need to be made meaningful learning to classification through learner-centered teaching. But we doubts weather teaching and learning to the classification are reflected in the constructivist philosophy of 'learner-centered' well or not. The purpose of this study was to analyze critically the content of elementary textbooks and guidebook for teachers relating to the classification of angles and triangles in terms of constructivism. As a result, there is a problem in the classification of angles that are not provided a reasonable chance to set criteria by agreement of the communities. There is a problem in the classification of triangles that has the characteristics of radical development in terms of diversity. In addition, response of students was predicted like anyone who already acquired knowledge. And it has the shortcomings that the opportunity to have a choice and a discussion to hierarchical and partition classification are not provided. The followings are proposed based on such features; faithful reflection of 'Learner-centered' principle, careful prediction of student response, teaching that focus on process than results.

• Education of Primary School Mathematics
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• v.20 no.4
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• pp.305-319
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• 2017

In the process of finding the triangle height, 26 students in the 6th grade were surveyed to understand the students' triangle height through the eye movement data and to investigate the cognitive load of the students. As a result, the correctness rate of the pre-test was significantly increased in the post-test, and the frequency and retention of gaze data were smaller in the post-test than in the AOI of each question. The Participants's subjective cognitive load indicated that it was more difficult to understand the concept of rotated triangles compared with upright triangles that were parallel to the ground. More frequent and more retentions in the eye-tracking data were detected in the right triangles and acute triangles by rotating configuration. Eye movement data show that eye tracking technology can provide an objective measure of students' cognitive load for feedback on instructional design.

• Journal of the Korean School Mathematics Society
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• v.13 no.1
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• pp.143-161
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• 2010

The purpose of this paper was to analyze the example spaces related with the concepts of triangles in the 2nd grade Korean elementary mathematics textbooks, investigate the meaning of example spaces, and suggest the implications to teaching and learning geometrical concepts in the elementary schools. Mathematics textbooks are usually major materials in teaching and learning mathematics in Korea, and the content of the textbooks affects the quality of teaching and learning in the classroom. The results of the study showed that the Korean elementary textbooks provided examples with limited example spaces concerning the concepts of triangles. The researcher suggested that we should provide rich examples spaces, encourage learner-generated example spaces, and strengthen the connections of examples between in textbooks and in the classroom.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.5 no.4
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• pp.763-781
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• 2011

We present a texture-based hatching technique for color images and video. Whereas existing approaches produce monochrome hatching effects in considering of triangular mesh models by applying strokes of uniform size, our scheme produces color hatching effects from photographs and video using strokes with a range of sizes. We use a Delaunay triangulation to create a mesh of triangles with sizes that reflect the structure of an input image. At each vertex of this triangulation, the flow of the image is analyzed and a hatching texture is then created with the same alignment, based on real pencil strokes. This texture is given a modified version of a color sampled from the image, and then it is used to fill all the triangles adjoining the vertex. The three hatching textures that accumulate in each triangle are averaged and the result of this process across all the triangles forms the output image. We can also add a paper texture effect and enhance feature lines in the image. Our algorithm can also be applied to video. The results are visually pleasing hatching effects similar to those seen in color pencil drawings and oil paintings.