• Proceedings of the KSME Conference
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• 2002.08a
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• pp.83-86
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• 2002

Numerical simulations are conducted for laminar flow past a sphere rotating In the transverse direction, in order to investigate the effect of the rotation on the characteristics of flow over a sphere. The Reynolds numbers considered are Re=100, 250 and 300 based on the free-stream velocity and the sphere diameter, and the rotational speeds are in the range of $0{\leq}{\omega}{\leq}1$, where ${\omega}^{\ast}$ is the maximum velocity on the sphere surface normalized by the free-stream velocity. At ${\omega}^{\ast}=0$ (without rotation), the flow past the sphere experiences steady axisymmeoy, steady planar-symmetry and unsteady planar-symmetry, respectively, at Re=100, 250 and 300. However, with rotation, the flow becomes planar-symmetric for all the cases investigated and the symmetry plane is orthogonal to the axis of the rotation. The flow is also steady or unsteady depending on both the Reynolds number and the rotational speed, and the vortical structures behind the sphere are significantly modified by the rotation. For example, at Re=300, hairpin vortices completely disappear in the wake at ${\omega}^{\ast}=0.4\;and\;0.6$, and at ${\omega}^{\ast}=1$ vortical structures of a high frequency are newly generated due to the shear layer instability. It is also shown that with increasing rotational speed, the time-averaged drag and lift coefficients increase monotonically.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.21 no.9
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• pp.829-834
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• 2008

Two-dimensional photonic quasicrystal (PQCs) template patterns have been fabricated on a 1.1 ${\mu}m$-thick DMI-150 photoresist using a multiple-exposure holographic method. A 442-nm HeCd laser was utilized as a light source and the holographic exposure was carried out at a fixed angle of ${\theta}$ = 6$^{\circ}$. After the first holographic exposure, the sample was rotated to a proper angle and the second exposure was performed to the same manner. This exposure process was repeated n/2 times to obtain n-fold symmetric PQC patterns and then the sample was developed. The diffraction patterns of the fabricated PQC template were observed using a 632.8-nm HeNe laser. The fabricated PQCs exhibited 8, 10 and 12-fold rotational symmetry, which was in a good agreement with the interference simulation results. In addition, the diffraction patterns with n-rotation symmetry were observed for the corresponding n-fold PQCs. We believe that the multiple-exposure holography is a good method to fabricate the mesoscale PQCs with a high rotational symmetry.

• Education of Primary School Mathematics
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• v.5 no.1
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• pp.1-11
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• 2001

The purpose of the study is to introduce how tessellation can be used and integrated to connect geometry to pattern in elementary mathematics educations. Tessellation examples include transformations such as translational symmetry, rotational symmetry, reflection symmetry, and glide reflection symmetry. In addition, many examples of tessellation using softwares such as Escher, TesselMania!, and LOGO programs. Further, future study will continue to foster students and teachers to try to construct their alive mathematics knowledge. The study of geometry and patterns require a rich teaching and learning environment provided by in-depth understanding of thinking connections to objects in real world.

• Journal of Korea Game Society
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• v.14 no.6
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• pp.109-118
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• 2014

We studied the creation of fractal images with polygonal rotation symmetry. As in Loocke's method[13] we start with IFS of affine functions that create polygonal fractals and extends the IFS by adding functions that create Julia sets instead of adding square root functions. The resulting images are rotationally symmetric and Julia set shaped. Also we can improve fractal images by modifying probabilistic IFS algorithm, and we suggest a method of deforming Julia set by changing exponent value.

• Journal of Fashion Business
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• v.20 no.6
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• pp.79-93
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• 2016

Since the development of patterns using tessellation is applied to a wide range of fields such as clothing, architecture, environment, and products, etc. and its expression principle is also found in various fields such as mathematics and science, etc. However, this pattern is mostly used as a math material with little studies on fashion and culture. In addition, it is thought that Korean traditional culture products need more various and modern design development methods and pattern through preliminary investigation which is simple copy of traditional items, simple copy of Korean Alphabet, Chinese character, and folk paintings. Therefore, it will present the method to make more design cases using Tessellation. Tessellation that combines mathematics and art will be the infinite form of designing of designers as well as creative training way to understand the composition principles of old culture and to raise sense of modern design. Tessellation of regular triangle, regular square, and regular hexagon was performed on the patterns which have meaning of wealth and prosperity of Korean traditional patterns. As the concrete method, first, each side of the regular triangle is developed symmetrically with patterns of fish, turtle, and cicadas. Second, rotational movement after symmetry movement about middle point of one side ${\times}$ 1 symmetry movement about middle point ${\times}$ 1 using crane and cloud, of the regular triangle was performed. Third, the regular square was tessellated parallel movement ${\times}$ 2 with "Da(multi)" and dragon pattern as the source image. Fourth, the sitting tiger was tessellated with symmetry movement about middle point ${\times}$ 2 and parallel movement ${\times}$ 1. Fifth, three bat patterns are tessellated by again rotational movement of two sides after rotational movement of one side and rotational movement of the other side. In addition, It developed traditional culture product design of the scarf, umbrella, aprons, neckties.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.458-461
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• 1995

A new type of rotational motor which is developed has a resolution smaller than 10 $^{-4}$ radian and can be accessed for full rotational angles. The operation principle of the motor is based on inchworm motion of two belt driving mechanism. Flexure hinge mechanism, which is pertinent to symmetry construction of the motor, is designed to minimze the effort to frame and is analyzed by using finite element method. Depending on input signal amplitude, rotational angle by one cycle is varied form 0.2*10 $^{-4}$ rad to 9.76* $^{-4}$ rad. This shows that it has the capability of getting very small rotational angle by considering radius of rotor and amplitude of input signal.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2008.06a
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• pp.8-8
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• 2008

Two-dimensional photonic quasicrystal (PQCs) template patterns have been fabricated on a $1.1{\mu}m$-thick DMI-150 photoresist using a multiple-exposure holographic method. A 442-nm HeCd laser was utilized as a light source and the holographic exposure was carried out at a fixed angle of $\theta=6^{\circ}$. After the first holographic exposure, the sample was rotated to a proper angle and the second exposure was performed to the same manner. This exposure process was repeated n/2 times to obtain n-fold symmetric PQC patterns and then the sample was developed. The fabricated PQCs exhibited 8, 10 and 12-fold rotational symmetry and the diffraction patterns using a 632.8-nm HeNe laser were observed for n-rotation symmetry corresponding n-fold PQCs. The fabricated PQC template patterns were examined using scanning electron microscopy(SEM). Transmission spectra were measured fourier transform infrared(FTIR) spectrometer.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2001.05a
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• pp.115-120
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• 2001

A gyroscope is a rotating body possessing one axis of symmetry and whose rotation about the symmetry axis is relatively large compared with the rotation about any other axis. Tuning fork is this type of structure that various modem gyro-sensors are based on. In this paper, dynamic behavior of a cantilevered beam subjected ta a base rotation with respect to the eccentric axis that is parallel to the beam axis is analyzed. The final equations of motion in terms of generalized coordinates can be solved with numerical scheme with various values of angular velocities and angular accelerations of the rotating axis. In contrast to the case of rotating cantilever beam like helicopter blade, the rotational motion with respect to the beam axis has effect to decrease the stiffness of the beam and has unstable region depending on the magnitude of the rotational angular velocity and angular acceleration.

• The Mathematical Education
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• v.56 no.3
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• pp.235-255
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• 2017

This study compared and contrasted the topics related to congruence and symmetry in the elementary mathematics textbooks series of Korea, Japan, Hong Kong, Finland, and Singapore in three aspects: (a) when to teach, (b) what to teach, and (c) how to teach. Firstly, the results of when to teach showed differences across the countries with a variation of teaching the topics among grades from 3 to 6. Secondly, the results of what to teach revealed subtle but significant differences. Regarding congruence, Korea and Japan deal with congruence in a systematic manner, while Finland tends to address the brief definition of congruence, and Hong Kong and Singapore focus on teaching tessellation which implies congruence. Regarding symmetry, Korea and Japan deal only with a symmetric figure for a line and that for a point, while Hong Kong includes a rotational symmetry and Finland extends further to cover the figures positioned in a symmetry both for a line and for a point. Lastly, the results of how to teach demonstrated that Korea tends to focus on the procedure of drawing both triangles to be congruent and symmetric figures. This implies that we need to consider alternative methods such as using various instructional materials and making an explicit connection among mathematical concepts in teaching congruence and symmetry.

• Applied Microscopy
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• v.40 no.1
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• pp.21-28
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• 2010

In a simulation study of atomic resolution transmission electron microscope images of single layer and bilayer graphene, it is demonstrated that the conventional Bloch wave formulations can be used when high-order Laue zone reflections are properly taken into account in the theory. The simulated images for bilayer graphene show 3-fold rotational lattice symmetry rather than the 6-fold one under certain conditions. This result can be understood as revealed the 3-fold rotational lattice symmetry of bilayer graphene in three dimensions along [0001]. For single layer graphene the observed phase images showing 3-fold rotational lattice symmetry were particularly noted. This phenomenon has been explained by an assumption of the re-configuration of electron density on the surface of graphene. And the matching images have been obtained as simulated with up to the second order Laue zone reflections only, reflecting the re-configuration of electrons on the surface.