• 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.

• Journal of the Korean Electrochemical Society
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• v.10 no.1
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• pp.7-13
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• 2007

We synthesized and investigated $La_{0.75}Sr_{0.25}FeO_3$ by Glycine Nitrate Process(GNP) method used as cathode materials for SOFC(solid oxide fuel cell). Optimized amount of glycine is 3.17 mol. ICP elemental composition analysis indicated that the stoichiometry of the synthesized powders have nearly nominal values. SEM images and XRD patterns reveal that the synthesized powder has uniform size distribution and high degree of crystallinity. The sample powders were isostatically pressed to form a pellet. The green body was sintered at $1200^{\circ}C$ and the relative density of the sintered specimens were measured by Archimedes mettled. We measured electrochemical performance of LSF by AC impedance spectroscopy. Resistance of LSF shows lower value than that of LSM throughout all temperature region. The anode-supported solid oxide fuel cell showed a performance of $342mW/cm^2(0.7V,\;488mA/cm^2)$ at $750^{\circ}C$. The electrochemical characteristics of the single cell were examined by at impedance method.

• The Journal of Korean Academy of Prosthodontics
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• v.49 no.2
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• pp.120-127
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• 2011

Purpose: The purpose of this study was to examine the effects of chromium chloride addition on coloration, mechanical property and microstructure of 3Y-TZP. Materials and methods: Chromium chloride was weighed as 0.06, 0.12, and 0.25 wt% and each measured amount was dissolved in alcohol. $ZrO_2$ powder was mixed with each of the individual slurry to prepare chromium doped zirconia specimen. The color, physical properties and microstructure were observed after the zirconia specimen were sintered at $1450^{\circ}C$. In order to evaluate the color, spectrophotometer was used to analyze the value of $L^*$, $C^*$, $a^*$ and $b^*$, after placing the specimen on a white plate, and measured according to the International Commission on Illumination (CIE) standard, Illuminant D65 and SCE system. The density was measured in the Archimedes method, while microstructures were evaluated by using the scanning electron microscopy (SEM) and XRD. Fracture toughness was calculated Vickers indentation method and indentation size was measured by using the optical microscope. The data were analyzed with 1-way ANOVA test (${\alpha}$ = 0.05). The Tukey multiple comparison test was used for post hocanalysis. Results: 1. Chromium chloride rendered zirconia a brownish color. While chromium chloride content was increased, the color of zirconia was changed from brownish to brownish-red. 2. Chromium chloride content was increased; density of the specimen was decreased. 3. More chromium chloride in the ratio showed increase size of grains. 4. But the addition of chromium chloride did not affect the crystal phase of zirconia, and all specimens showed tetragonal phase. 5. The chromium chloride in zirconia did not showed statistically significant difference in fracture toughness, but addition of 0.25 wt% showed a statistically significant difference (P<.05). Conclusion: Based on the above results, this study suggests that chromium chlorides can make colored zirconia while adding in a liquid form. The new colored zirconia showed a slight difference in color to that of the natural tooth, nevertheless this material can be used as an all ceramic core material.