• 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.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 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 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 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.