• 한국수학교육학회지시리즈A:수학교육
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• 제50권2호
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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.

• 한국수학교육학회지시리즈A:수학교육
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• 제52권1호
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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.

• East Asian mathematical journal
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• 제35권2호
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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.

• 대한수학회논문집
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• 제39권1호
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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.

• 대한수학회지
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• 제57권1호
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• pp.1-19
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• 2020

Using the complex parabolic rotations of holomorphic null curves in ℂ⁴ we transform minimal surfaces in Euclidean space ℝ³ to a family of degenerate minimal surfaces in Euclidean space ℝ⁴. Applying our deformation to holomorphic null curves in ℂ³ induced by helicoids in ℝ³, we discover new minimal surfaces in ℝ⁴ foliated by hyperbolas or straight lines. Applying our deformation to holomorphic null curves in ℂ³ induced by catenoids in ℝ³, we rediscover the Hoffman-Osserman catenoids in ℝ⁴ foliated by ellipses or circles.

• 한국수학교육학회지시리즈E:수학교육논문집
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• 제24권3호
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• pp.731-744
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• 2010

현행 교과서에서는 원, 타원, 포물선, 쌍곡선 등의 이차곡선이 원뿔을 잘랐을 때 나타나는 단면 곡선이라고 통합적으로 소개하면서도 실제로는 각각 2차식으로 표현된다는 점 외에 그 곡선들 사이의 어떤 연관성도 언급되어 있지 않다 '이차곡선'이라는 단원명에서 알 수 있듯이 기하학적 작도에 의해 도입된 원뿔곡선이 이차방정식으로 표현되고 이 방정식을 통해 초점, 꼭짓점, 준선 등을 찾는 기계적 활동만이 주를 이루고 있다. 본 논문에서는 원뿔곡선의 발견 이후부터 현재에 이르는 역사적 발달 과정 속에서 이루어진 다양한 논의를 통하여 이차곡선의 본질을 분석하고 이를 바탕으로 이차곡선의 교수 학습 방법 개선을 위한 시사점을 얻고자 한다.

• 한국광학회지
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• 제1권2호
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• pp.217-222
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• 1990

A general ray tracing scheme has been developed for using a personal computer which trace finite rays through any non-rotationally symmetric system. This scheme may be used for the surface type such as conic section with or without aspherics, toric surfaces, sagittal and tangential cylindrical sections and axicons. Specially, any combinational of decentered, tilted and rotated surfaces has been considered. Before transfering to the next surfaces, the local coordinates are refered back to an initial reference coordinate system. We can get a mathmtical model of a non-rotationally symmetrical finite ray trace running on an inexpensive personal computer.

• East Asian mathematical journal
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• 제37권4호
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• pp.499-521
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• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• East Asian mathematical journal
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• 제37권4호
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• pp.401-426
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• 2021

In order to propose ways to implement mathematical connection between algebra and geometry, this study reinterpreted and visualized the Khayyam's geometric method solving the cubic equations using two conic sections and the Al-Kāshi's method of constructing of angle trisection using a cubic equation. Khayyam's method is an example of a geometric solution to an algebraic problem, while Al-Kāshi's method is an example of an algebraic a solution to a geometric problem. The construction and property of conics were presented deductively by the theorem of "Stoicheia" and the Apollonius' symptoms contained in "Conics". In addition, I consider connections that emerged in the alternating process of algebra and geometry and present meaningful Implications for instruction method on mathematical connection.

• East Asian mathematical journal
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• 제39권4호
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• pp.419-436
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• 2023

In this study, we aimed to develop a teacher-adaptive platform model that enhances teachers' instructional activities and teaching capabilities, allowing them to conduct intended lessons effectively. The platform is designed to support various teaching and learning activities based on the instructional situation, and additionally provides teaching and learning materials, assessment questions, and results. The developed teaching and learning platform utilized Moodle, an open-source-based LMS solution that provides various tools for online learning. The platform was specifically designed for teaching conic sections in high school geometry, and it was constructed to enable teachers to deliver their intended lessons effectively.