• Journal of Science Education
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• v.34 no.1
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• pp.175-184
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• 2010

We agree with Hanna and Jahnke's assertion on the use of arguments from physics in mathematical proofs and analyze their educational example of the use of arguments from physics in the proof of the center of gravity of a triangle. Moreover, we suggest practical models for the center of gravity of a triangle for the demonstration in a classroom. Comparing with the traditional mathematical arguments, the role of concepts and models from physics in arguments from physics will be clearly pointed out. Also, the necessity for arguments from physics in the classroom will be discussed in this paper.

• Journal for History of Mathematics
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• v.34 no.4
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• pp.137-149
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• 2021

The center of gravity of a triangle is the center of a physical shape. This is the content in the second grade of middle school, 'The Use of Similarity'. Unlike the cases of circumcenter and incenter, which are easily recognized visually, it is not easy for teachers to guide students with the visual meaning of center of gravity. According to the survey results, students, regardless of academic achievement, grade, and major, perceived the center of gravity of various plane figure as the center of their shape within a limited area through visual judgment. With reference to the results and contents of this process, it is hoped that the point of the three medians is meaningful not only in argumentative definition that the intersection of the triple line is the center of gravity of the triangle, but also in the center of a figure.

• Communications of the Korean Mathematical Society
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• v.31 no.3
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• pp.637-645
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• 2016

For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. When P is a triangle, the centroid $G_0$ always coincides with the centroid $G_2$. For the centroid $G_1$ of a triangle, it was proved that the centroid $G_1$ of a triangle coincides with the centroid $G_2$ of the triangle if and only if the triangle is equilateral. In this paper, we study the relationships between the centroids $G_0$, $G_1$ and $G_2$ of a quadrangle P. As a result, we show that parallelograms are the only quadrangles which satisfy either $G_0=G_1$ or $G_0=G_2$. Furthermore, we establish a characterization theorem for convex quadrangles satisfying $G_1=G_2$, and give some examples (convex or concave) which are not parallelograms but satisfy $G_1=G_2$.

• Communications of Mathematical Education
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• v.22 no.1
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• pp.27-39
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• 2008

In this paper we study triangle's properties related with angle bisectors, perpendiculars, circumcenter using the principle of the lever. We analyze proof method using the principle of the lever, and describe how to investigate intersection of segments, how to prove equalities and inequalities using the principle of the lever in triangle.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.6B
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• pp.1174-1182
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• 1999

Recently the shape information of the visual object in the scene is more important, as the completion of the MPEG-4 standard and the progress of the MPEG-7 standard. This paper represents the study of effective coding method of vertices that are used in the polygonal approximation to represent the feature of visual object. In the proposed method, we make the centers of gravity of triangles that are made using the vertices of polygonal approximation and encode them sequentially We can get a coding gain because the centers of the gravity of triangles have narrower dynamic ranges.

• Phonetics and Speech Sciences
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• v.12 no.3
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• pp.85-94
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• 2020

Vowel articulation in subjects related to speech disorders seems to be difficult. A chant method that properly reflects the characteristics of language could be used as an effective way of addressing the difficulties. The purpose of this study was to find out whether the chant method is effective as a means of enhancing vowel articulation. The subjects of this study were 60 normal adults (30 males and 30 females) in their 20s and 30s whose native language is Korean. Eight utterance conditions including chanting and reading conditions were recorded and their acoustic data were analyzed. The results of the analysis of the acoustic variables related to the formant confirmed that the F1 and F2 values of the vowel formants are increased and the direction of movement of the center of gravity of the vowel triangle is statistically significantly forwarded and lowered in the chant method in both the word and the phrase context. The results also proved that accent is the most influential musical factor in chant. There was no significant difference between four repeated tokens, which increased the reliability of the results. In other words, chanting is an effective way to shift the center of gravity of the vowel triangle, which suggests that it can help to improve speech intelligibility by forming a desirable place for articulation.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.135-145
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• 2017

For a polygon P, we consider the centroid $G_0$ of the vertices of P, the centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P. When P is a triangle, (1) we always have $G_0=G_2$ and (2) P satisfies $G_1=G_2$ if and only if it is equilateral. For a quadrangle P, one of $G_0=G_2$ and $G_0=G_1$ implies that P is a parallelogram. In this paper, we investigate the relationships between centroids of quadrangles. As a result, we establish some characterizations for rhombi and show that among convex quadrangles whose two diagonals are perpendicular to each other, rhombi and kites are the only ones satisfying $G_1=G_2$. Furthermore, we completely classify such quadrangles.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.25 no.3
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• pp.296-303
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• 2014

In this paper, we propose an algorithm to visualize radio wave environment based on the measured Received Signal Strength Indication( RSSI) and 3D geographic information. We estimate the source position using the circumcenter of the triangle and visualize the radio wave environment using the empirical propagation models. A mode seeking algorithm(mean-shift clustering) is used to seek the peak points and the center of gravity is utilized to reduce the estimation errors. Our approach finds its applications in the radio wave monitoring systems for the efficient utilization of radio resources.

• Journal of Sensor Science and Technology
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• v.18 no.6
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• pp.423-431
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• 2009

Standard uroflowmetry measures the urine weight using single load cell to evaluate the urinary flow rate. Impact noise should be introduced due to gravity when the urine stream falls down into the container upon the load cell. The present study placed three load cells on the three vertices of a regular triangle and the three signals were ensemble averaged to enhance the signal-to-noise ratio(SNR) regardless of how the urination was made. Simulated urination experiment was performed with three different urine collection methods. In all three methods, SNR of the averaged signal was much higher than each load cell signals. With no urine collection device, the present signal averaging technique resulted in SNR values higher by 10~15 dB than when dual funnels or upper funnel were used to guide the urine stream. Therefore, it was demonstrated that the three point measurement followed by with ensemble averaging could enable accurate uroflowmetric test without any specially made urine collection devices.