• East Asian mathematical journal
• /
• 제31권1호
• /
• pp.119-126
• /
• 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
• /
• 제31권1호
• /
• pp.127-134
• /
• 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.

• 대한수학교육학회지:학교수학
• /
• 제9권1호
• /
• pp.119-139
• /
• 2007

이차곡선은 고등학교 기하 내용의 중요한 개념의 하나이다. 그러나 교수-학습 상황에서 학생들은 단순히 대수적인 접근과 해석기하적인 접근만 시도하므로 그 본질적인 기하학적 의미를 파악하지 못하며 단순한 기계적인 계산만을 수행하여 문제를 풀어나가려 하기 때문에 여러 가지 오개념(misconception)을 가지게 된다. 이 논문은 효과적인 이차곡선 교수학습 연구의 일부로, 학생들의 오개념을 인지적 관점, 심리학적 관점, 교수학적 관점에서 분석하고 그 원인을 분석하였다. 연구 결과, 학생들의 직접적이고 다양한 작도 경험의 부재가 오개념의 주된 원인이 되었다. 이차곡선에 대한 교수-학습은 기하적인 관점으로 접근 한 후 대수적인 관점으로 연결시켜야 할 필요성과 오개념에 대한 정확한 진단은 효과적인 교수-학습의 기초가 됨을 확인 하였다.

• 통합자연과학논문집
• /
• 제9권1호
• /
• pp.10-15
• /
• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• 제28권1호
• /
• pp.22-32
• /
• 2024

In this paper we present a method of conic section approximation by hexic Bézier curves. The hexic Bézier approximants are G³ Hermite interpolations of conic sections. We show that there exists at least one hexic Bézier approximant for each weight of the conic section The hexic Bézier approximant depends one parameter and it can be obtained by solving a quartic polynomial, which is solvable algebraically. We present the explicit upper bound of the Hausdorff distance between the conic section and the hexic Bézier approximant. We also prove that our approximation method has the maximal order of approximation. The numerical examples for conic section approximation by hexic Bézier curves are given and illustrate our assertions.

• 호남수학학술지
• /
• 제33권3호
• /
• pp.335-340
• /
• 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
• /
• 제28권4호
• /
• pp.453-474
• /
• 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.

• 한국수학사학회지
• /
• 제15권1호
• /
• pp.69-82
• /
• 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
• /
• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
• /
• pp.1597-1600
• /
• 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.

• 대한수학회논문집
• /
• 제17권2호
• /
• pp.331-347
• /
• 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.