• Journal for History of Mathematics
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• v.23 no.4
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• pp.47-58
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• 2010

This study suggests new interpretation about ancient mathematician Archimedes' 'method'. For this, we examined the core issue related to the interpretation of the 'method' and identified the unclear relation between the principle of the lever and the indivisibles, both of which have consisted of the main point of arguments. And by having conducted the exploratory historical guesswork about Archimedes' careful use of indivisibles, we make a hypothesis that the role of the principle of the lever in Archimedes' 'method' should be the control of ratio of change.

• Journal for History of Mathematics
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• v.23 no.3
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• pp.121-140
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• 2010

This study presents one universal mean formula of implicate quantity for speed, temperature, consistency, density, unit cost, and the national income per person in order to avoid the inconvenience of applying different formulas for each one of them. This work is done by using the principle of lever and was led to the formula of two implicate quantity, $M=\frac{x_1f_1+x_2f_2}{f_1+f_2}$, and to help the understanding of relationships in this formula. The value of ratio of fraction cannot be added but it shows that it can be calculated depending on the size of the ratio. It is intended to solve multiple additions with one formula which is the expansion of the mean formula of implicate quantity. $M=\frac{x_1f_1+x_2f_2+{\cdots}+x_nf_n}{N}$, where $f_1+f_2+{\cdots}+f_n=N$. For this reason, this mean formula will be able to help in physics as well as many other different fields in solving complication of structures.

• Journal of The Korean Association For Science Education
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• v.40 no.6
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• pp.583-594
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• 2020

In this study, the existing concept of density has a limitation in providing the cause of phenomena, and the concept of buoyancy poses a problem because it has many misconceptions and requires an overly difficult concept to understand quantitative calculation, so we suggest an explaining method as process viewpoint introducing the principle of lever. The new method of explanation has been proposed using the lever as visual tool to reveal the gravity as the fundamental principle and process viewpoint. As a result, teachers stayed on many alternative concepts and less than half of the teachers were aware that density was related to gravity. In addition, they recognized it as matter viewpoints, but there is a meaningful conceptual change after intervention(p<.000). Also, they evaluated that the new method is better able to recognize the principle and process viewpoint than the existing description method. Through this, we can confirm the educational value of explaining method as process viewpoint introducing the principle of lever.

• Journal of the Korean School Mathematics Society
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• v.9 no.1
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• pp.93-104
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• 2006

The centroid of triangle is physical property but almost mathematics teachers do not teach centroid by the help of experiments an so they have misconception on principle of centroid. In this paper we investigate whether teachers have made an experiment on centroid of triangle, and we check up on the level of understanding on centroid for mathematics teachers. We introduce the method of teaching centroid and study the process of generalization about centroid of triangle for gifted students.

• School Mathematics
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• v.7 no.4
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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.

• The Journal of Korean Philosophical History
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• no.29
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• pp.203-230
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• 2010

This article is aimed for to state the rationality of Mojia and reveal the scientific meaning in the theories related to the motion of objects in Mojing: the basic approach to the principle of gravitation in building castle, and comprehension and application of the principle in the lever devised for improving productivity as well as in an inclined plane. It is denied in this article that the technical advance and the positive influence on the people is achieved by Mojias only because they were occupied in the filed of craft. Mojia was one of the schools of Qin in the early stage who realized how important science wass for the better society focused on humanity. Furthermore, they were the frontiers who pursued the proper society through science. Therefore, the scientific theories claimed by Mojia is not emphasized only on the deducting regularity of nature. Instead, it could be theorized only by guaranteeing the welfare for common people and having close relation to it. The Chinese philosophy in the early Twentieth century had vigorous interest in the Mojia's opinions in science and set about conducting study in this part. Based on the study, it was revealed that the Mojia's opinion toward motion is superior to that of the West. Furthermore, it was proved to reflect the main idea in Mojia: the love for common people. Particularly, the theories from Mojia can be so applicable to today's life that some scholars regret the lack of interest in Mojia for the time and even scold themselves for the retarded progress in science of China.