• Proceedings of the Korea Society of Mathematical Education Conference
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• 2010.04a
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• pp.151-163
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• 2010

This study is to provide improved teaching methods on classical geometric construction education by a straightedge and compass in school mathematics. In this paper, justifications of construction methods of Korean textbooks, for perpendicular bisector of an segment and angle bisector are discussed, which can be directly applicable to teaching geometric construction meaningfully. Based on these considerations, several implications for desirable teaching methods concerning geometric construction were suggested.

• East Asian mathematical journal
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• v.26 no.2
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• pp.151-164
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• 2010

This study is to provide improved teaching methods on classical geometric construction education by a straightedge and compass in school mathematics. In this paper, justifications of construction methods of Korean textbooks, for perpendicular bisector of an segment and angle bisector are discussed, which can be directly applicable to teaching geometric construction meaningfully. Based on these considerations, several implications for desirable teaching methods concerning geometric construction were suggested.

• Journal of IKEEE
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• v.11 no.4
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• pp.297-306
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• 2007

A sensor network is composed of a large number of sensor nodes that are densely deployed in a field. Each sensor performs a sensing task for detection specific events. After detecting this event, location information of the sensor node is very important. Range-based scheme of the proposed approaches typically achieve high accuracy on either node-to-node distances or angles, but this scheme have a drawback because all sensor nodes have the special hardware. On the other hand, range-free scheme provides economic advantage because of no needed hardware even if that leads to coarse positioning accuracy. In this paper, we propose a range-free localization algorithm without range information in wireless sensor networks. This is a range-free approach and uses a small number of anchor nodes and known sensor nodes. This paper develops a localization mechanism using the geometry conjecture (perpendicular bisector of a chord). The conjecture states that a perpendicular bisector of a chord passes through the center of the circle.

• Journal of Digital Convergence
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• v.11 no.2
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• pp.215-220
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• 2013

They are well-known geometric properties of a circle that the perpendicular bisector of a chord passes through the center of a circle, and the intersection of the perpendicular bisectors of any two chords is its center. This paper is related to a fast pupil detection method capable of detecting the center and the radius of a pupil using these geometric properties at high speed when detecting the pupil region for iris segmentation. The proposed method is characterized as rapidly detecting the center and the radius of the pupil, extracting the candidate points of the circle in human eye images using morphological operations, and finding two chords using four points on the circular edge, and taking the intersection of the perpendicular bisectors of these two chords for its center. The proposed method can not only detect the center and the radius of a pupil rapidly but also find partially occluded pupils in human eye images.

• Journal of Korean Academy of Oral and Maxillofacial Radiology
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• v.11 no.1
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• pp.23-32
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• 1981

The purpose of this study was to assess temporomandibular joint subluxation by means of cephalometry using two lateral cephalograms from each person with in centric occlusion and wide-open mouth position, and to compare patient group with subluxation to normal control group in the measurements and correlation coefficient. The 200 cephalograms of 100 Korean adults, patient group consisted of 24 females and 26 males ranged from 17 to 63 years age and the normal control group consisted of 20 females and 30 males ranged from 18 to 56 years age, were studied and analyzed statistically. The results were as follows; 1. In the comparison of patient group vs normal control group in the measurements, statistically significant differences were found in C-C', C'-PTM, K-FH, K-PTM, Gn-Gn', C-S-C', Gn-S-Gn', Gn-K-Gn', GoGn-SN, and GoGn-Go'Gn'. K-point* of patient group was located antero - superiorly than of normal control group, and the significance level was higher in K-PTM than in K-FH. There was no statistically significant difference found in local relationship of C-point between patient group and normal control group. The values of correlation coefficient among all measurements were in 0.958≥r≥-0.760, and the highest value was in Gn-Gn' to GoGn-Go'Gn' and Gn-K-Gn' to Gn-Gn', and the lowest value was in C'-PTM to Gn-K-Gn' of normal control group. K was determined as a point of intersection by a perpendicular bisector of Gn-Gn' and a perpendicular bisector of C-C'.

• The Mathematical Education
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• v.60 no.1
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• pp.61-76
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• 2021

The purpose of this study is to analyze the errors and difficulties which pre-service secondary teachers shows during the task modification in consideration of the cognitive demand and to provide significant implications to the pre-service teacher education program related to the modification of the mathematical tasks. In the pursuit of this purpose, tasks were selected from perpendicular bisector units and 24 pre-service teachers were asked to modify the tasks to higher and lower level tasks. After the modification activities, opportunities for reflection and modification were provided. The findings from analysis are as follows. Pre-service teachers had a difficulty to distinguish between PNC tasks and PWC tasks. Also, We identified the interference phenomena that pre-service teachers depended on the apparent elements of the task. Pre-service teachers showed a tendency to overlook the learning objectives and learning hierarchy during the task modification, and to focus on some types of task modification. However, pre-service teachers were able to have meaningful learning opportunities and extend the category of tools to technology including Geogebra through self-reflection and correction activities on task modification. The above results were summed up and we presented the implications to the task modification program in the pre-service secondary teacher education.

• Journal of the Korea Society of Computer and Information
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• v.20 no.9
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• pp.31-37
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• 2015

Symmetry is easily found in animals and plants as well as in artificial structures. It is useful not only for human cognitive process but also for image understanding by computer. Application areas include face detection and recognition, indexing of image database, image segmentation and detection, and analysis of medical images. The method used in this paper extracts edges, and the perpendicular bisector of any pair of selected edge points is considered to be a candidate axis of symmetry. The coefficients of the perpendicular bisectors are accumulated in the coefficient space. Axis of symmetry is determined to be the line for which the histogram has maximum value. This method shows good results, but the usefulness of the method is restricted because the amount of computation increases proportional to the square of the number of edges. In this paper, an acceleration method is proposed which performs $2^{2n}$ times faster than the original one. Experiment on 20 test images shows that the proposed method using level-3 image segmentation performs 63.9 times faster than the original method.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.27-39
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• 2008

In this paper we study triangle's properties related with angle bisectors, perpendiculars, circumcenter using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to investigate intersection of segments, how to prove equalities and inequalities using the principle of the lever in triangle.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.8
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• pp.750-757
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• 2011

Wireless Sensor Network is composed of a lot of sensor nodes that are densely deployed in a field. So generally this sensor nodes are spreaded using Helicopter or Fixed wing. Each node delivers own location and acquired information to user when it detects specific events. In this paper, we propose localization algorithm without range information in wireless sensor network using helicopter. Helicopter broadcasts periodically beacon signal for sensor nodes. Sensor nodes stored own memory this beacon signal until to find another beacon point(satisfied special condition). This paper develops a localization mechanism using the geometry conjecture(perpendicular bisector of a chord) to know own location. And the simulation results demonstrate that our localization scheme outperforms Centroid, APIT in terms of a higher location accuracy.

• Journal of the Korea Society of Computer and Information
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• v.21 no.4
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• pp.9-15
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• 2016

Symmetry is everywhere in the world around us from galaxy to microbes. From ancient times symmetry is considered to be a reflection of the harmony of universe. Symmetry is not only a significant clue for human cognitive process, but also useful information for computer vision such as image understanding system. Application areas include face detection and recognition, indexing of image database, image segmentation and detection, analysis of medical images, and so on. The technique used in this paper extracts edges, and the perpendicular bisector of any two edge points is considered to be a candidate axis of symmetry. The coefficients of candidate axis are accumulated in the coefficient space. Then the axis of symmetry is determined to be the line for which the coefficient histogram has maximum value. In this paper, an improved method is proposed that utilizes the directional information of edges, which is a byproduct of the edge detection process. Experiment on 20 test images shows that the proposed method performs 22.7 times faster than the original method. In another test on 5 images with 4% salt-and-pepper noise, the proposed method detects the symmetry successfully, while the original method fails. This result reveals that the proposed method enhances the speed and accuracy of detection process at the same time.