• Journal for History of Mathematics
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• v.17 no.3
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• pp.93-108
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• 2004

In this article we study on various proofs of the Steiner-Lehmus theorem(any triangle that has two equal angle bisectors is isosceles). We suggest 6 geometric proofs and 3 algebraic proofs of the theorem in detail, analyze these proofs, extract related theorems, proof ideas.

• 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.

• Proceedings of the Korea Water Resources Association Conference
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• 2004.05b
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• pp.376-380
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• 2004

측벽이 존재하는 개수로 난류흐름에 대한 DNS 자료를 이용하여 난류의 비등방성을 해석하였다. 측벽의 2등분선(sidewall bisector)에서 난류강도의 분포를 통해 바닥과 자유수면에서의 비등방성을 분석하고, AIM을 도입하여 흐름장 전반에 걸쳐 세부적인 비등방성 해석을 수행하였다. 측벽의 2등분선에서의 난류강도의 분포를 통해 바닥과 자유수면 근처에서 난류강도가 강한 비등방성을 갖는 것을 볼 수 있었다. 또한 3개의 다른 영역에서 AIM의 도입을 통해 측벽이나 바닥근처에서는 난류의 비등방성이 구형 관수로 흐름과 유사한 것으로 나타났으나, 개수로 난류흐름의 주된 특성이 velocity-dip phenomena가 존재하는 영역에서는 구형 관수로 흐름과는 달리 천이영역이 존재한다는 것을 알 수 있었다.

• International Journal of CAD/CAM
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• v.8 no.1
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• pp.11-20
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• 2009

The conventional methods of boundary-conformed 2D surfaces generation usually yield some problems. This paper deals with two boundary-conformed 2D surface generation methods, one conventional approach, the linear Coons method, and a new method, boundary-conformed interpolation. In this new method, unidirectional 2D surface has been generated using some of the geometric properties of the given boundary curves. A method of simultaneous displacement of the interpolated curves from the opposite boundaries has been adopted. The geometric properties considered for displacements include weighted combination of angle bisector and linear displacement vectors at all the data-points of the two opposite generating curves. The algorithm has one adjustable parameter that controls the characteristics of transformation of one set of curves from its parents. This unidirectional process has been extended to bi-directional parameterization by superimposing two sets of unidirectional curves generated from both boundary pairs. Case studies show that this algorithm gives reasonably smooth transformation of the boundaries. This algorithm is more robust than the linear Coons method and capable of resolving the 2D boundary-conformed parameterization problems.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.71.2-71.2
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• 2014

For better understanding of the physics of pores, we have investigated horizontal and vertical motions of plasma in a pore obtained on 2013 August 24 by using high time and spatial resolution data from the Fast Imaging Solar Spectrograph (FISS) of the 1.6 meter New Solar Telescope (NST). We infer the LOS velocity by applying the bisector method to the wings of Ca II 8542 ${\AA}$ profile, and inspect oscillations of the intensity and the LOS velocity in the pore. In this presentation, we discuss the physical implications of our results in view of a connection between LOS and horizontal plasma flows in a concentrated magnetic flux.

• Journal of The Korean Astronomical Society
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• v.19 no.1
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• pp.15-31
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• 1986

We have analyzed Gray's observed mean line bisectors of FS, G0, G2, and G5 normal dwarf stars and interpreted them by computing theoretical line bisectors based on a two stream model. A set of perturbed models has been derived, and their detailed structures on temperature fluctuations and velocity fields are presented as a function of depth, which account for the observed bisectors. From the present study, it is found that the degree of stellar convective overshootings and temperature fluctuations in the upper atmospheres increases towards earlier spectral types. The convection cell size inferred from these models is found to increase also with the advancing earlier type. We demonstrated the usefulness of line bisector analysis as a diagnostic probe for stellar convection.

• The Bulletin of The Korean Astronomical Society
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• v.37 no.2
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• pp.113.1-113.1
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• 2012

The characteristics of Doppler shifts in a quiet region of the Sun are investigated by comparing between the $H{\alpha}$ line and the Caii infrared line at 854.2 nm. A small area of $16^{\prime\prime}{\times}40^{\prime\prime}$ was observed for about half an hour with the Fast Imaging Solar Spectrograph (FISS) of the 1.6 meter New Solar Telescope (NST) at Big Bear Solar Observatory. The observed area contains a network region and an internetwork region, and identified in the network region are $H{\alpha}$ fibrils, Caii fibrils and bright points. We infer the Doppler velocity from each line profile at a point with the lambdameter method as a function of half wavelength separation ${\Delta}{\lambda}$. It is confirmed that the bisector of the spatially-averaged Caii line profile has an inverse C-shape of with a significant peak redshift of +1.8 km/s. In contrast, the bisector of the spatially-averaged $H{\alpha}$ line profile has a different shape; it is almost vertically straight or, if not, has a C-shape with a small peak blueshift of -0.5 km/s. In both the lines, the bisectors of bright network points are much different from those of other features in that they are significantly redshifted not only at the line centers, but also at the wings. We also find that the spatio-temporal fluctuation of Doppler shift inferred from the Caii line is correlated with those of the $H{\alpha}$ line. The strongest correlation occurs in the internework region, and when the inner wings rather than the line centers are used to determine Doppler shift. In this region, the RMS value of Doppler shift fluctuation is the largest at the line center, and monotonically decreases with ${\Delta}{\lambda}$. We discuss the physical implications of our results on the formation of the $H{\alpha}$ line and Caii 854.2 nm line in the quiet region chromosphere.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.88.1-88.1
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• 2013

We have investigated vertical motions of plasma in the pores and changes of the motions with height by using high time and spatial resolutions data obtained by the Fast Imaging Solar Spectrograph (FISS) of the 1.6 meter New Solar Telescope (NST). We infer the LOS velocity by applying the bisector method to the wings of CaII 854.2 nm line profile. We find that (1) upflow velocity in the pores decreases with height and turns into downward in the upper chromosphere; (2) 3 min and 5 min oscillations are found from the Doppler velocity in the pore at various wavelengths from the wing (${\pm}2.35{\AA}$) to the core (${\pm}1.25{\AA}$) of the CaII line; and (3) power of high (low) frequency oscillation obtained from the CaII intensity increases (decreases) with height. We discuss the physical implications of our results in view of the connection of LOS plasma flows in a concentrated magnetic flux (pore) between the photosphere and the low chromosphere.

• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.92.1-92.1
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• 2013

In this study, we examined chromospheric oscillation signatures in two solar active regions, a limb active region and a sunspot with a light bridge, observed by the Fast Imaging Solar Spectrograph (FISS) of the 1.6m New Solar Telescope (NST) at Big Bear Solar Observatory. The FISS is a slit spectrograph with a fast imaging capability and can observe the solar chromosphere in $H{\alpha}$ and Ca II $8542{\AA}$ bands simultaneously with high spectral resolutions. After dark and flat correction, we compensated for image rotation at the Coude focus and made image alignment. We estimated Doppler shifts over active regions using the bisector method and investigated the temporal and spatial fluctuations of Doppler shifts for some selected cases. And we obtain the power map by using the Lomb-Scargle periodogram technique to examine the oscillation power at different features. Finally, we will discuss our results and implications.

• Journal of the Korea Society of Computer and Information
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• v.21 no.4
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• pp.9-15
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• 2016

Symmetry is everywhere in the world around us from galaxy to microbes. From ancient times symmetry is considered to be a reflection of the harmony of universe. Symmetry is not only a significant clue for human cognitive process, but also useful information for computer vision such as image understanding system. Application areas include face detection and recognition, indexing of image database, image segmentation and detection, analysis of medical images, and so on. The technique used in this paper extracts edges, and the perpendicular bisector of any two edge points is considered to be a candidate axis of symmetry. The coefficients of candidate axis are accumulated in the coefficient space. Then the axis of symmetry is determined to be the line for which the coefficient histogram has maximum value. In this paper, an improved method is proposed that utilizes the directional information of edges, which is a byproduct of the edge detection process. Experiment on 20 test images shows that the proposed method performs 22.7 times faster than the original method. In another test on 5 images with 4% salt-and-pepper noise, the proposed method detects the symmetry successfully, while the original method fails. This result reveals that the proposed method enhances the speed and accuracy of detection process at the same time.