• East Asian mathematical journal
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• v.31 no.1
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• pp.119-126
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• 2015

The aim of this paper is to research certain properties of conic regular functions of conic quaternion variables in $\mathbb{C}^2$. We generalize the properties of conic regular functions and the Cauchy theorem of conic regular functions in conic quaternion analysis.

• East Asian mathematical journal
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• v.31 no.1
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• pp.127-134
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• 2015

We give a rth conic regular functions with conic quaternion variables in $\mathbb{C}^2$ and obtain a hyper-conjugate harmonic function of conic regular function in conic quaternions in the sense of Clifford analysis.

• School Mathematics
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• v.9 no.1
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• pp.119-139
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• 2007

The purpose of this study is to analyze students' misconception in the teaming of the conic sections with the cognitive and pedagogical point of view. The conics sections is very important concept in the high school geometry. High school students approach the conic sections only with algebraic perspective or analytic geometry perspective. So they have various misconception in the conic sections. To achieve the purpose of this study, the research on the following questions is conducted: First, what types of misconceptions do the students have in the loaming of conic sections? Second, what types of errors appear in the problem-solving process related to the conic sections? With the preliminary research, the testing worksheet and the student interviews, the cause of error and the misconception of conic sections were analyzed: First, students lacked the experience in the constructing and manipulating of the conic sections. Second, students didn't link the process of constructing and the application of conic sections with the equation of tangent line of the conic sections. The conclusion of this study ls: First, students should have the experience to manipulate and construct the conic sections to understand mathematical formula instead of rote memorization. Second, as the process of mathematising about the conic sections, students should use the dynamic geometry and the process of constructing in learning conic sections. And the process of constructing should be linked with the equation of tangent line of the conic sections. Third, the mathematical misconception is not the conception to be corrected but the basic conception to be developed toward the precise one.

• Journal of Integrative Natural Science
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• v.9 no.1
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• pp.10-15
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• 2016

In this paper the approximation methods of offset curve of conic with explicit error bound are considered. The quadratic approximation of conic(QAC) method, the method based on quadratic circle approximation(BQC) and the Pythagorean hodograph cubic(PHC) approximation have the explicit error bound for approximation of offset curve of conic. We present the explicit upper bound of the Hausdorff distance between the offset curve of conic and its PHC approximation. Also we show that the PHC approximation of any symmetric conic is closer to the line passing through both endpoints of the conic than the QAC.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.335-340
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• 2011

We study some properties of tangent lines of conic sections. As a result, we establish a characterization of conic sections.

• East Asian mathematical journal
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• v.28 no.4
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• pp.453-474
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• 2012

The conic sections is an important topic in the current high school geometry. It has been recognized by many researchers that high school students often have difficulty or misconception in the learning of the conic sections because they are taught the conic sections only with algebraic perspective or analytic geometry perspective. In this research, we suggest a way of teaching the conic sections using a dynamic geometry software based on some mathematics teaching and learning theories such as Freudenthal's and Dienes'. Students have various experience of constructing and manipulating the conic sections for themselves and the experience of deriving the equations of the quadratic curves under the teacher's careful guidance. We identified this approach was a feasible way to improve the teaching and learning methods of the conic sections.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.69-82
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• 2002

The purpose of this study is to explore historical development of conic sections and analyze formal aspects, application aspects and intuitive aspects in conic sections. We suggest implication for learning-teaching conic sections.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.1597-1600
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• 1997

Most autonomous mobile robots view things only in front of them. As a result they may collide against objects moving from the side or behind. To overcome the problem we have built an Active Omni-directional Range Sensor that can obtain omni-directional depth data by a laser conic plane and a conic mirror. Also we proposed a self-localization algorithm of mobile robot in unknown environment by fusion of Odometer and Active Omn-directional Range Sensor.

• Communications of the Korean Mathematical Society
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• v.17 no.2
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• pp.331-347
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• 2002

We characterize the best geometric conic approximation to regular plane curve and verify its uniqueness. Our characterization for the best geometric conic approximation can be applied to degree reduction, offset curve approximation or convolution curve approximation which are very frequently occurred in CAGD (Computer Aided Geometric Design). We also present the numerical results for these applications.

• Journal of Korean Ophthalmic Optics Society
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• v.8 no.2
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• pp.77-83
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• 2003

To investigate the influence of the variation of conic coefficient of the front surface on the RMS SD(Root Mean Square Spot Diameter) in a back focal plane, we use programs which are Cove V and LOSA 2.0. We consider a spectacle lens with back vertex power of -4.00D, diameter of 70 mm, the front surface powers which are 2.00D, 4.00D, 6.00D, and 8.00D, and the indices which are $n_d$=1.498, 1.523, 1.586, and 1.660, respectively. The RMS SD in the back focal plane and the thickness of an aspherical tens having the optimized conic constant are smaller than those of a spherical lens. The RMS SD in the back focal plane decreases as the front surface power decreases. From these results, we determine the optimized conic constant to improve the optical image quality and decrease RMS SD in the back focal plane.