• 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.

• Proceedings of the KSRS Conference
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• 2004.10a
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• pp.590-593
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• 2004

Extraction of ocean surface current velocity offers important physical oceanographic parameters especially on understanding ocean environment. Although Remote Sensing techniques were highly developed, the investigation of ocean surface current using Synthetic Aperture Radar (SAR) is not an easy task. This paper presents the results of ocean surface current observation using Doppler Centroid of ERS-1 SAR data obtained off the coast of Korea peninsula. We employed the concept, in which Doppler frequency shift and the ocean surface current are closely related, to evaluate ocean surface current. Moving targets cause Doppler frequency shift of the back scattered radar waves of SAR, thus the line-of-sight velocity component of the scatters can be evaluated. The Doppler frequency shift can be measured by estimating the difference between Doppler Centroid of raw SAR data and reference Doppler Centroid. Theoretically, the Doppler Centroid is zero; however, squinted antenna which is affected by several physical factors causes Doppler Centroid to be nonzero. The reference Doppler Centroid can be obtained from measurements of sensor trajectory, attitude and Earth model. The estimated Doppler Centroid was compensated by considering the accurate attitude estimation of ERS-1 SAR. We could verify the correspondence between the estimated ocean surface current and observed in-situ data in the error bound.

• 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 $G_1=G_2$.

• Honam Mathematical Journal
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• v.39 no.1
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• pp.127-136
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• 2017

For a quadrangle P, we consider the centroid $G_0$ of the vertices of P, the perimeter centroid $G_1$ of the edges of P and the centroid $G_2$ of the interior of P, respectively. If $G_0$ is equal to $G_1$ or $G_2$, then the quadrangle P is a parallelogram. We denote by M the intersection point of two diagonals of P. In this note, first of all, we show that if M is equal to $G_0$ or $G_2$, then the quadrangle P is a parallelogram. Next, we investigate various quadrangles whose perimeter centroid coincides with the intersection point M of diagonals. As a result, for an example, we show that among circumscribed quadrangles rhombi are the only ones whose perimeter centroid coincides with the intersection point M of diagonals.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.429-444
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• 2020

For a quadrilateral P, we consider the centroid G0 of the vertices of P, the perimeter centroid G1 of the edges of P and the centroid G2 of the interior of P, respectively. It is well known that P satisfies G0 = G1 or G0 = G2 if and only if it is a parallelogram. In this paper, we investigate various quadrilaterals satisfying G1 = G2. As a result, we establish some characterization theorems. One of them asserts the existence of convex quadrilaterals satisfying G1 = G2 without symmetry.

• Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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• v.15 no.2
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• pp.245-252
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• 1997

The development of digital camera and advancement of computer processor could simplify the acquisition and the analysis of digial image, and be the real-time processing by the digital photogrammetry. This study is about to enhancement of the image measuring accuracy by the centroid methods. We were able to determine more effective centroid measuring methods and suitable target shape as the development of analysis system and actualize semi-automatic measuring of digital image. And we can supply the weakness of non-metric camera for the geometric internal accuracy of digital image as the correct of Kodak DCS200 camera 8008s lens distortion.

• The Korean Journal of Ecology
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• v.26 no.3
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• pp.123-127
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• 2003

Cubic-meter volumes estimated from two proxy taper functions were compared to observed volumes of Japanese red cedar trees (Cryptomeria japonica D. Don) to evaluate accuracy and precision in the centroid method. Centroid volume estimates were also compared to volume estimates from existing whole-tree volume equations developed for another geographic region. This study found that one proxy function produced unbiased volume estimates while the other was biased. Volume estimates from the whole-tree equations were also biased. However, the volume estimates from the whole-tree equations were more precise than those from the centroid method. These results support previous studies that the centroid method can produce reliable volumes of trees when no other reliable volume equations exist.

• Journal of Broadcast Engineering
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• v.7 no.2
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• pp.126-135
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• 2002

An image contains various features such as color, shape, texture and location information. When only one of those features is used to retrieve an image, it is difficult to acquire satisfactory retrieval efficiency. Especially, in the database with huge capacity, such phenomenon happens frequently. Therefore, by using moi·e features, efficiency of the contents-based image retrieval (CBIR) system can be improved. This paper proposes a technique to consider location information about specific color as well as color information in image using centroid situation vector. Centroid situation vectors are calculated for specific color of the query image. Then, location similarity is determined through comparing distances between extracted centroid situation vectors of query image and target image in the database. Simulation results show that the proposed method is robust in zoom-in or zoom-out processed images and improves discrimination ability in fliped or rotated images. In addition, the suggested method reduced computational complexity by overlapping information extraction, and that improved the retrieval speed using an efficient index file.

• Bulletin of the Korean Mathematical Society
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• v.55 no.1
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• pp.139-148
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• 2018

In this paper, we prove a stability result for p-centroid bodies with respect to the Hausdorff distance. As its application, we show that the symmetric convex body is determined by its p-centroid body.

• East Asian mathematical journal
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• v.16 no.2
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• pp.363-370
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• 2000

We evaluate the dual quermassintegrals of $\gamma$-equichordal bodies and obtain the lower bound for the volume product of p-centroid body in $E^2$.