• Journal of the Korean School Mathematics Society
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• v.20 no.4
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• pp.445-464
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• 2017

This study targeting 10 high school 3rd grade students who have studied space figures in natural sciences track analyzes the process of analogical discovery from the construction of inscribed and circumscribed circles of a triangle to that of inscribed and circumscribed spheres of a tetrahedron through the analytical method using Geogebra. The subjects are divided into two groups of five, the experimental group consisting of those who have experienced analytical method and the comparative group consisting of those who haven't. This research analyzing the process of constructing inscribed and circumscribed spheres of a tetrahedron. Although students of both groups all have an accurate preliminary knowledge of inscribed and circumscribed circles of a triangle, they have difficulty in constructing inscribed and circumscribed spheres of a tetrahedron. However, the students of experimental group who have studied the constructing process of inscribed and circumscribed circles of a triangle in reverse using analytical method and Geogebra can perform analogical discovery finding out the way to construct inscribed and circumscribed spheres of a tetrahedron using analogy by themselves. They can control and explore space figures by visualization. Also, they can immediately examine and provide feedback on the analogizing process of their own. In addition, the process affects the attitude of students toward mathematics positively as well as gives validity to the result of analogy.

• Journal of the Korean School Mathematics Society
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• v.12 no.4
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• pp.365-388
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• 2009

In this paper we solve various triangle construction problems given by three points(a midpoint of side and other two points). We investigate relation between these construction problems, draw out a base problem, and make hierarchy of solved construction problems. In detail we describe analysis for searching solving method, and construction procedure of required triangle.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• Journal for History of Mathematics
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• v.18 no.1
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• pp.1-10
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• 2005

Sea Mirror, reflecting the heaven of the circles circumscribed or inscribed, by Li Zhi of Yuan Dynasy(1271-1368) was resolved by Li Rui(1773-1817) and added by the new four rules not solved. In the Chosun Dynasty, Nam Byung Churl resolved the problems of the Sea Mirror of the circle measurement and the preface was written by his younger brother Nam Byung Gil(1820-1869). In this paper, the concepts of the problems in the Sea Mirror and its three problems will be introduced.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 2006.05a
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• pp.377-378
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• 2006

The knuckle crane mainly consists of six parts such as swing, main boom, outer boom, extension boom, hydraulic rotor and knuckle. And the hydraulic rotor is connected at the end of extension boom has rotor block, rotor body, rotor vane. In this study, we carried out kinematics analysis of the hydraulic rotor block curvature for a knuckle crane. Then, we showed the formula to establish the radius of a circumscribed circle to form the rotor block curvature. Third, we analyzed the stress at each point of the rotor block curvature according to the contact angle. From the result of this study, we designed the rotor block curvature with a proper contact angle for a knuckle crane to guarantee the stability of hydraulic rotor.

• Journal of the Institute of Electronics and Information Engineers
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• v.50 no.10
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• pp.171-180
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• 2013

Generally, when we apply zernike moments value for matching, we can use those moments value obtained from projecting image information under circumscribed circle to zernike basis function. However, the problem is that the power of discrimination can be reduced because hand images include lots of overlapped information due to its special characteristic. On the other hand, when distinguishing hand poses, information in specific area of image information except for overlapped information can increase the power of discrimination. In this paper, in order to solve problems like those, we design R3 ring mask by combining image obtained from R2 ring mask, which can weight information of the power of discrimination and image obtained from R1 ring mask, which eliminate the overlapped information. The moments which are obtained by R3 ring mask decrease operational time by reducing dimension through principle component analysis. In order to confirm the superiority of the suggested method, we conducted some experiments by comparing our method to other method using seven different hand poses.

• Restorative Dentistry and Endodontics
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• v.31 no.2
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• pp.96-102
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• 2006

There are various factors affecting the fracture of NiTi rotary files. This study was performed to evaluate the effect of cross sectional area, pecking motion and pecking distance on the cyclic fatigue fracture of different NiTi files. Five different NiTi $files-Profile^{(R)}$ (Maillefer, Ballaigue, Switzerland), $ProTaper^{TM}$(Maillefer, Ballaigue, Switzerland), $K3^{(R)}$ (SybronEndo. Orange, CA) , Hero $642^{(R)}$ (Micro-mega, Besancon, France), Hero $Shaper^{(R)}$ (Micro-mega, Besancon, France)-were used. Each file was embedded in temporary resin, sectioned horizontally and observed with scanning electron microscope. The ratio of cross-sectional area to the circumscribed circle was calculated. Special device was fabricated to simulate the cyclic fatigue fracture of NiTi file in the curved canal,. On this device, NiTi files were rotated (300rpm) with different pecking distances (3 mm or 6 mm) and with different motions (static motion or dynamic pecking motion) . Time until fracture occurs was measured. The results demonstrated that cross-sectional area didn't have any effect on the time of file fracture. Among the files, $Profile^{(R)}$ took the longest time to be fractured. Between the pecking motions, dynamic motion took the longer time to be fractured than static motion. There was no significant difference between the pecking distances with dynamic motion, however with static motion, the longer time was taken at 3mm distance. In this study, we could suggest that dynamic pecking motion would lengthen the time for NiTi file to be fractured from cyclic fatigue.

• Journal of Cadastre & Land InformatiX
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• v.48 no.1
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• pp.123-138
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• 2018

To sustainably monitor air pollution in Seoul, the number of Air Pollution Monitoring Station has been gradually increased by Korea's Ministry of Environment. Although particulate matters(PM), one of the pollutants measured at the stations, have an significant influence on human body, the concentration of PM in Korea came in second among 35 OECD member countries. In this study, using the data of PM concentration from the stations, distribution maps of PM10 and PM2.5 concentrations over Seoul were generated, and spatial factors potentially related to PM distribution were investigated. Based on a circumscribed hexagon about a circle in radius of 500 meters created as a basic unit, Seoul was sectionalized and PM concentration map was generated using the interpolation technique of 'inverse distance weighting'. The distributions of PM concentrations were investigated with commuting time by administrative district and the outcome was related with land-use type and volume of traffic. Results from this analysis indicated distribution pattern of PM10 concentration was different from that of PM2.5 by administrative district and time. The distribution of PM concentration was strongly related to not only the size of business and trafficked areas among the land-use type, but also the existence of urban green. Further analysis of the relationship between the PM concentration and detailed land-use and urban green maps can be helpful to identify spatial factors which have an impact on the PM concentration on the regional scale.