• 한국수학교육학회지시리즈A:수학교육
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• 제45권3호
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• pp.367-373
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• 2006

This study suggests that it is necessary to prove that the values of three areas of a triangle, which are obtained by the multiplication of the respective base and its corresponding height, are the same. It also seeks to deeply understand the meaning of Area formula of triangles by exploring some questions raised in the analysis of the proof. Area formula of triangles expresses the invariance of congruence and additivity on one hand, and the uniqueness of parallel line, one of the characteristics of Euclidean geometry, on the other. This discussion can be applied to introducing and developing exploratory learning on area in that it revisits the ordinary thinking on area.

• KCI Concrete Journal
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• 제14권1호
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• 콘크리트학회논문집
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• 제13권2호
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• pp.146-152
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• 2001

프랙탈 기하는 재료의 파괴거동과 같은 자연계에 존재하는 불규칙한 현상을 비정수의 프랙탈 차원으로 정량화할 수 있다. 이런. 프랙탈 차원에 기초하면 프랙탈 도형은 도형의 일부를 확대하면 전체와 같아지는 자기상사성 특성을 지닌다. 프랙탈적 해석방법을 시멘트 복합체의 파괴시의 균열성장거동에 적용하여 복합체의 미세구조와 파괴거동과의 관계를 알아볼 수 있다. 본 연구의 목적은 시멘트 복합체의 파괴시 소산되는 에너지와 균열의 프랙탈 차원과의 관계를 알아보는데 있다. 시멘트 복합체의 파괴실험을 실시하여 파괴에너지를 측정한 후, 파괴시 형성된 균열형상의 프랙탈 차원을 박스계수법을 통해 산정하고 그 관계를 알아보았다. 실험결과 프랙탈 차원과 파괴에너지의 관계는 비례관계를 나타냈으며 파괴에너지에 대한 프랙탈 차원의 정량적 평가가 가능하다고 사료된다.