• Journal for History of Mathematics
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• 제26권5_6호
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• pp.371-388
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• 2013

In ${\ll}$The Method${\gg}$, Archimedes presented the famous heuristic technique for calculating areas, volumes and centers of gravity of various plane and solid figures, utilizing the law of the lever. In that treatise, Archimedes used the fact that the center of gravity of a cone lies one-quarter of the way from the center of the base to the vertex, but the proof of this is not extant in his works. This study analyzes the propositions and their relations of ${\ll}$The Method${\gg}$ focusing on the procedural characteristics of the 'method' of Archimedes. According to the result of that analysis, this study discusses the likely approach which was taken for Archimedes to find out the center of gravity of a cone.

• School Mathematics
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• 제7권4호
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• Korean Journal of Social Welfare
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• 제44권
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• pp.178-208
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• 2001

This study concerns the understanding of 'social exclusion' which is getting poplular in Europe as the new term or paradigm in order to resolve poverty problem. As case study on the France, the purpose of this study is to extract the consideration of welfare policy and suggestions as to us. In order to understand comprehensively the concept 'social exclusion' and the situation of the France, this study analyzes the existing researches on its concept and tries to realize a comparative study. Thus, this study indicates that the France is the state which has taken the most interest in 'social exclusion'. The second parti of this study concerns the change of the concept 'social exclusion' and its policies in the France. The concept 'social exclusion' which has used in the 1960's, has settled as the term of policies in the 1980's, thanks to seriousness of poverty and unemployment problem and change of social consciousness (opinion). As policy on the 'social exclusion', there are Revenu minimum d'insertion of the 1988 and law on the social exclusion of the 1998. Through analysis of policies on the 'social exclusion' in the France, we can get the following consideration of welfare policy and suggestions: on the macro level, the necessity to establish the comprehensive perspective on the poverty problem, invention and development of the term as regard to social new problem; on the micro lever, planning of welfare program according to clients needs, importance of perpetual assessing of the existing welfare program and institutions, the institutional establishment of 'reserve budget', the application of decentralization principle and the active participation of the private sector in order to promote the effectiveness and the efficiency of the program and institutions.