• Proceedings of the Korean Information Science Society Conference
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• 2004.10a
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• pp.724-726
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• 2004

본 논문에서는 L$_1$평면상에 도로망이 주어져 있어서 여행자들이 그 도로들을 이용하여 더욱 빠르게 이동할 수 있는 가정 하에서 가장 기초적인 기하문제 중에 하나인 두 점 사이의 최단 경로를 찾는 문제를 다룬다. 이 때, 두 점 사이의 거리는 L$_1$ 거리가 아닌 주어진 도로들을 이용하여 두 점 사이를 이동할 때 필요한 최소시간으로 측정한다. 단순한 평면상에서의 최단경로와는 달리 도로망이 설치되어 있는 경우는 그것을 해결하기가 일반적으로 쉽지 않다. 본 논문에서는 도로망이 있는 평면에 대한 깊은 관찰과 이해를 통해 도로망이 설치되어 있는 L$_1$ 평면상에서의 최단경로 문제를 해결하는 효율적인 알고리즘을 제시한다. 덧붙여, 본 논문에서 제시하는 문제 해결 방법은 L$_1$ 평면뿐만 아니라 유클리드 평면에도 어렵지 않게 적용할 수 있으며 보로노이 다이어그램으로의 일반화도 간단하다.

• Proceedings of the Korea Information Processing Society Conference
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• 2021.11a
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• pp.948-951
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• 2021

본 논문에서는 직육면체 형태의 실내 공간에서 다중 개체 영역을 검출하는 방법을 제안한다. 평면 검출 알고리즘은 평면성을 띄지 않거나 관측이 미흡한 영역에 대해 기하 정보를 검출할 수 없다. 이로 인해 장애물과 같은 개체의 영역을 파악할 수 없는 한계점이 있다. 제안 방법은 유클리드 클러스터링을 기반으로 군집화를 수행하고, 클러스터의 간소화를 통해 다중 개체 영역을 검출한다. 제안 방법은 직육면체 공간의 내부표면을 활용해 직육면체 공간과 좌표계를 공유하는 주요 개체들의 영역을 다량으로 검출한다. 제안 방법은 실험을 통해 다중 개체 영역이 적합하게 검출되었음을 보인다.

• The Journal of the Institute of Internet, Broadcasting and Communication
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• v.16 no.1
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• pp.291-299
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• 2016

This paper raises a question of whether a simple periodic phenomenon is associated with the topology and provides the convincing answers to it. A variety of music instrumental sound signals are used to prove our assertion, which are embedded in Euclidean space to analyze their topologies by computing the homology groups. A commute time embedding is employed to transform segments of waveforms into the corresponding geometries, which is implemented by organizing patches according to the graph-based metric. It is shown that commute time embedding generates the intrinsic topological complexities although their geometries are varied according to the spectrums of the signals. This paper employs a persistent homology to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, and discusses their applications.

• Education of Primary School Mathematics
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• v.14 no.1
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• pp.27-41
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• 2011

This study is the consideration to 'The Data' and 'On Divisions' of Euclid which is the historical start of analysis and synthesis. 'The Data' and 'On Divisions' compared to Euclid's Elements is not interested. In this study, analysis and synthesis were examined for significance. In this study, means for 'analysis' and 'synthesis' were examined through an analysis of 'The Data' and 'On Divisions'. First, the various terms including analysis and synthesis were examined and the concepts of the terms were analyzed. Then, analysis was divided into 'external analysis' and 'internal analysis'. And synthesis was divided into 'theoretical synthesis' and 'empirical synthesis'. On the basis of this classification problem presented in elementary textbooks and the practical applications were explored.

• Journal of Broadcast Engineering
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• v.23 no.2
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• pp.227-234
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• 2018

Recently, stitching techniques are used for obtaining wide FOV, e.g., panorama contents, from normal cameras. Despite many proposed algorithms, the no objective quality evaluation method is developed, so the comparison of algorithms are performed only in subjective way. The paper proposes a 'Delaunay-triangulation based objective assessment method' for evaluating the geometric and photometric distortions of stitched or warped images. The reference and target images are segmented by Delaunay-triangulation based on matched points between two images, the average Euclidian distance is used for geometric distortion measure, and the average or histogram of PSNR for photometric measure. We shows preliminary results with several test images and stitching methods for demonstrate the benefits and application.

• Journal for History of Mathematics
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• v.19 no.1
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• pp.43-54
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• 2006

The purpose of this paper, followed by 'Nature$\cdot$Human, and Golden Section I ', is to study aesthetic consciousness, mentality model and body proportion of human, and the golden section applied to architecture and hand axe of stone age. In particular, handaxes of one million years ago have shown that they had critical competency to the basis of art and mathematics in the future. Furthermore, without pen, paper and ruler, the existence of mentality model made fundamental conversion of mathematics possible. Different sizes of handaxes were made by maintaining the equal golden section. This was the first example in relation to the principle mentioned in 'Stoicheia' by Euclid which was published hundred thousands of years later.

• Korean Journal of Child Studies
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• v.12 no.2
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• pp.51-66
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• 1991

The purpose of study I was to investigate developmental processes and sex differences in the acquisition of topological seriation and Euclidean horizontal/vertical concepts. The purpose of Study II was to investigate the effects of basic geometric activity on the acquisition of space concepts. The subjects of Study I were 164 five- and six-year-old children. The children were grouped by age in 6 month units. The subjects of Study II were 45 children who showed immature space concepts. The data were analyzed by two-way ANOVA, $Scheff{\acute{e}}^{\prime}s$ posthoc test, and paired comparison t-test. On Study I, significant differences were found among the age groups in each of the dependent variables. Sex differences were found on all tasks except cued Euclidean tasks. In Study II, basic geometric activity of 3 weeks duration was found to be effective in the acquisition of the horizontal/vertical concepts in children whose space concept had been immature.

• Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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• v.24 no.1
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• pp.124-129
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• 2010

When a phenolic resin is carbonized by the leakage current flowing along its surface, the carbonization pattern is one of the most important factors to determine its carbonization characteristics. However, the typical carbonization pattern of a phenolic resin is too complicated to be analyzed by conventional Euclidean geometry. In most cases, such a complicated shape shows a fractal structure. It is possible, therefore, to examine the characteristics of the carbonization pattern regarding a given phenolic resin. In order to quantitatively investigate the carbonization pattern of the phenolic resin carbonized by a leakage current, in this paper, the fractal dimension of the carbonization pattern has been calculated as a function of the magnitude of a leakage current and the distance between two electrodes. For reliability of calculation, the correlation function as well as the box counting method has been used to calculate the fractal dimension. According to the result of calculation, the fractal dimension increases as the current increases at the constant electrode gap distance. However, there is no significant relation between the fractal dimension and the electrode gap distance at a constant current.

• Journal of Broadcast Engineering
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• v.4 no.2
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• pp.87-102
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• 1999

We propose an algorithm for augmenting a real video sequence with views of graphics ojbects without metric calibration of the video camera by representing the motion of the video camera in projective space. We define a virtual camera, through which views of graphics objects are generated. attached to the real camera by specifying image locations of the world coordinate system of the virtual world. The virtual camera is decomposed into calibration and motion components in order to make full use of graphics tools. The projective motion of the real camera recovered from image matches has a function of transferring the virtual camera and makes the virtual camera move according to the motion of the real camera. The virtual camera also follows the change of the internal parameters of the real camera. This paper shows theoretical and experimental results of our application of non-metric vision to augmented reality.

• Communications of Mathematical Education
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• v.37 no.4
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• pp.635-652
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• 2023

This study conducts a comprehensive analysis of the curricular progression of the concepts and learning sequences of 'lines', specifically, 'line segments', 'straight lines', and 'rays', at the elementary school level. By examining mathematics curricula and textbooks, spanning from 2nd to 7th and 2007, 2009, 2015, and up to 2022 revised version, the study investigates the timing and methods of introducing these essential geometric concepts. It also explores the sequential delivery of instruction and the key focal points of pedagogy. Through the analysis of shifts in the timing and definitions, it becomes evident that these concepts of lines have predominantly been integrated as integral components of two-dimensional plane figures. This includes their role in defining the sides of polygons and the angles formed by lines. This perspective underscores the importance of providing ample opportunities for students to explore these basic geometric entities. Furthermore, the definitions of line segments, straight lines, and rays, their interrelations with points, and the relationships established between different types of lines significantly influence the development of these core concepts. Lastly, the study emphasizes the significance of introducing fundamental mathematical concepts, such as the notion of straight lines as the shortest distance in line segments and the concept of lines extending infinitely (infiniteness) in straight lines and rays. These ideas serve as foundational elements of mathematical thinking, emphasizing the necessity for students to grasp concretely these concepts through visualization and experiences in their daily surroundings. This progression aligns with a shift towards the comprehension of Euclidean geometry. This research suggests a comprehensive reassessment of how line concepts are introduced and taught, with a particular focus on connecting real-life exploratory experiences to the foundational principles of geometry, thereby enhancing the quality of mathematics education.