• Title/Summary/Keyword: Conic

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The Indoor Position Detection Method using a Single Camera and a Parabolic Mirror (볼록 거울 및 단일 카메라를 이용한 실내에서의 전 방향 위치 검출 방법)

  • Kim, Jee-Hong;Kim, Hee-Sun;Lee, Chang-Goo
    • Journal of Institute of Control, Robotics and Systems
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    • v.14 no.2
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    • pp.161-167
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    • 2008
  • This article describes the methods of a decision of the location which user points to move by an optical device like a laser pointer and a moving to that location. Using a conic mirror and CCD camera sensor, a robot observes a spot of user wanted point among an initiative, computes the location and azimuth and moves to that position. This system offers the brief data to a processor with simple devices. In these reason, we can reduce the time of a calculation to process of images and find the target by user point for carrying a robot. User points a laser spot on a point to be moved so that this sensor system in the robot, detecting the laser spot point with a conic mirror, laid on the robot, showing a camera. The camera is attached on the robot upper body and fixed parallel to the ground and the conic mirror.

The Approximate Realization of Ab$\={u}$ Sahl's Geometric Construction about a Heptagon through GSP using Conic Sections (이차곡선을 활용한 정칠각형에 관한 Ab$\={u}$ Sahl의 작도법의 GSP를 통한 재조명)

  • Kim, Hyang-Sook;Pak, Jin-Suk;Ha, Hyoung-Soo
    • The Mathematical Education
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    • v.50 no.2
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    • pp.233-246
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    • 2011
  • The geometry field in the current high school curriculum deals mainly with analytic geometry and the reference to logic geometry leaves much to be desired. This study investigated the construction on a heptagon by using conic sections as one of measures for achieving harmony between analytic geometry and logic geometry in the high school curriculum with the Geometer's Sketchpad(GSP), which is a specialized software prevalent in mathematics education field and is intended to draw an educational suggestion on it.

The reinterpretation and the visualization of Apollonius' symptoms on conic sections (원뿔곡선에 관한 Apollonius의 Symptoms 재조명과 시각화)

  • Kim, Hyang Sook;Pak, Jin Suk;Ha, Hyoung Soo
    • The Mathematical Education
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    • v.52 no.1
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    • pp.83-95
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    • 2013
  • The purpose of this paper is to explain and reinterprets Apollonius' Symptoms on conic sections based on the current secondary curriculum of mathematics, present the historical background of Apollonius' Symptoms to teachers and students and introduce visualization proof of Apollonius' symptoms on a parabola, a hyperbola and an ellipse by a new method using dynamic geometry software(GSP) respectively.

The reinterpretation and visualization about trisecting general angle in Medieval Islam using conic sections (원뿔곡선을 이용한 중세 이슬람의 일반각의 3등분문제의 재조명과 시각화)

  • Kim, Hyang Sook;Kim, Mi Yeoun;Park, Jae Hyun
    • East Asian mathematical journal
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    • v.35 no.2
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    • pp.141-161
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    • 2019
  • The purpose of this paper is to reinterpret and visualize the trisection line construction of general angle in the Medieval Islam using conic sections. The geometry field in the current 2015 revised Mathematics curriculum deals mainly with the more contents of analytic geometry than logic geometry. This study investigated four trisecting problems shown by al-Haytham, Abu'l Jud, Al-Sijzī and Abū Sahl al-Kūhī in Medieval Islam as one of methods to achieve the harmony of analytic and logic geometry. In particular, we studied the above results by 3 steps(analysis, construction and proof) in order to reinterpret and visualize.

ANALYTIC FUNCTIONS RELATED WITH q-CONIC DOMAIN AND ASSOCIATED WITH A CONVOLUTION OPERATOR

  • BASEM AREF FRASIN;ALA AMOURAH;SYED GHOOS ALI SHAH;SAQIB HUSSAIN;SHAHBAZ KHAN;FETHIYE MUGE SAKAR
    • Journal of applied mathematics & informatics
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    • v.41 no.6
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    • pp.1209-1225
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    • 2023
  • In this paper, we defined some new classes of analytic functions in conic domains. We investigate some important properties such as necessary and sufficient conditions, coefficient estimates, convolution results, linear combination, weighted mean, arithmetic mean, radii of starlikeness and distortion for functions in these classes. It is important to mentioned that our results are generalization of number of existing results in the literature.

ANALYTIC FUNCTIONS WITH CONIC DOMAINS ASSOCIATED WITH CERTAIN GENERALIZED q-INTEGRAL OPERATOR

  • Om P. Ahuja;Asena Cetinkaya;Naveen Kumar Jain
    • Communications of the Korean Mathematical Society
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    • v.38 no.4
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    • pp.1111-1126
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    • 2023
  • In this paper, we define a new subclass of k-uniformly starlike functions of order γ (0 ≤ γ < 1) by using certain generalized q-integral operator. We explore geometric interpretation of the functions in this class by connecting it with conic domains. We also investigate q-sufficient coefficient condition, q-Fekete-Szegö inequalities, q-Bieberbach-De Branges type coefficient estimates and radius problem for functions in this class. We conclude this paper by introducing an analogous subclass of k-uniformly convex functions of order γ by using the generalized q-integral operator. We omit the results for this new class because they can be directly translated from the corresponding results of our main class.

FREE AND NEARLY FREE CURVES FROM CONIC PENCILS

  • Dimca, Alexandru
    • Journal of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.705-717
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    • 2018
  • We construct some infinite series of free and nearly free curves using pencils of conics with a base locus of cardinality at most two. These curves have an interesting topology, e.g. a high degree Alexander polynomial that can be explicitly determined, a Milnor fiber homotopy equivalent to a bouquet of circles, or an irreducible translated component in the characteristic variety of their complement. Monodromy eigenspaces in the first cohomology group of the corresponding Milnor fibers are also described in terms of explicit differential forms.

Confluent Hypergeometric Distribution and Its Applications on Certain Classes of Univalent Functions of Conic Regions

  • Porwal, Saurabh
    • Kyungpook Mathematical Journal
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    • v.58 no.3
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    • pp.495-505
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    • 2018
  • The purpose of the present paper is to investigate Confluent hypergeometric distribution. We obtain some basic properties of this distribution. It is worthy to note that the Poisson distribution is a particular case of this distribution. Finally, we give a nice application of this distribution on certain classes of univalent functions of the conic regions.

SOME CHARACTERIZATIONS OF CONICS AND HYPERSURFACES WITH CENTRALLY SYMMETRIC HYPERPLANE SECTIONS

  • Shin-Ok Bang;Dong Seo Kim;Dong-Soo Kim;Wonyong Kim
    • Communications of the Korean Mathematical Society
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    • v.39 no.1
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    • pp.211-221
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    • 2024
  • Parallel conics have interesting area and chord properties. In this paper, we study such properties of conics and conic hypersurfaces. First of all, we characterize conics in the plane with respect to the above mentioned properties. Finally, we establish some characterizations of hypersurfaces with centrally symmetric hyperplane sections.

A Case Study of Teaching Mathematics for Integrated Essay Education: Instruction of Conic Section using Concrete Materials and Technology (통합형 수리논술 지도 사례 - 구체물과 공학적 도구를 활용한 원뿔곡선 수업 -)

  • Ryu, Hyunah
    • Communications of Mathematical Education
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    • v.27 no.4
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    • pp.567-580
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    • 2013
  • As integrated essay writing is performed in university entrance examinations, teachers and students recognize the importance of integrated essay, but teachers have still difficulties of teaching methods. The purpose of this study is to derive educational implications through case of mathematics instruction for integrated essay education to pre-service mathematics teachers. The content knowledge of this class is a definition of conic section in mathematics and properties of conic section in an antenna reflector. The students have to discover them using the history of math, manipulative material, paper-folding and computer simulation. In this teaching and learning process the students can realize mathematical knowledge invented by humans through history of mathematics. The students can evaluate the validity of that as create and justify a mathematical proposition. Also, the students can explain the relation between them logically and descript cause or basis convincingly in the process of justifying. We should keep our study to instructional materials and teaching methods in integrated essay education.