• 제목/요약/키워드: tangent line

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Isotomic and Isogonal Conjugates Tangent Lines of Lines at Vertices of Triangle

  • Seo, Min Young;Ahn, Young Joon
    • 통합자연과학논문집
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    • 제10권1호
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    • pp.27-32
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    • 2017
  • In this paper we consider the two tangent lines of isogonal and isotomic conjugates of the line at both vertices of a given triangle. We find the necessary and sufficient condition for the two tangent lines of isogonal or isotomic conjugates of the line at both vertices and the median line to be concurrent. We also prove that every line whose isogonal conjugate tangent lines at both vertices are concurrent with the median line intersects at a unique point. Moreover, we show that the three intersection points correspond to the vertices of triangle are collinear.

Lakatos 이론과 GSP를 활용한 접선지도연구 (On effective way of teaching concept of tangent line using Lakatos theory and GSP)

  • 안병국;김병학;박윤근
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제24권3호
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    • pp.627-658
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    • 2010
  • 접선의 개념은 수학에서 매우 중요하다. 그러나 대학생들조차 미분가능과 접선의 존재를 동일시하는 등 접선의 중요성과 개념에 대해 혼란스러워하고 있다. 이런 관점에서 본 논문에서는 선행연구를 창조하고 초, 중, 고교의 교과서와 교육과정을 분석하여 접선개념의 도입 등을 분석하고 Lakatos 이론과 GSP를 이용한 접선지도방법과 실제 학교현장에서 사용할 수 있는 학습지도안을 제시하고, 현장적용 및 교수실험결과를 소개한다.

수학적 모델링 과정에서 접선 개념의 재구성을 통한 미분계수의 재발명과 수학적 개념 변화 (Students' Reinvention of Derivative Concept through Construction of Tangent Lines in the Context of Mathematical Modeling)

  • 강향임
    • 대한수학교육학회지:학교수학
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    • 제14권4호
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    • pp.409-429
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    • 2012
  • 본 연구의 목적은 학생들이 수학적 모델링 활동을 통해 미분계수를 재발명하는 과정을 분석하여 학교현장의 미분계수 지도에 의미 있는 시사점을 제공하는 것이다. 이를 위해 고등학교 2학년 문과 학생 2명을 대상으로 모델링 과정과 그 과정을 통해 나타나는 수학적 개념 변화를 분석하였다. 그 결과, 학생들은 할선의 극한으로 접선을 재구성하고 접선의 기울기와 순간속도를 연결하기 위해 미분계수를 재발명하였다. 이 과정을 통해 학생들의 접선 개념과 시간-속도 그래프에 대한 개념이 변화되었음을 확인하였다. 본 연구의 모델링 과정에서는 학생들의 시각적인 이해를 돕고, 수학적인 개념을 탐구하는 본질적인 사고에 집중할 수 있도록 테크놀로지를 활용하였다.

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The maxillary incisor labial face tangent: clinical evaluation of maxillary incisor inclination in profile smiling view and idealized aesthetics

  • Naini, Farhad B.;Manouchehri, Shaadi;Al-Bitar, Zaid B.;Gill, Daljit S.;Garagiola, Umberto;Wertheim, David
    • Maxillofacial Plastic and Reconstructive Surgery
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    • 제41권
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    • pp.31.1-31.7
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    • 2019
  • Background: To test the hypothesis that in profile smiling view, for ideal aesthetics, a tangent to the labial face of the maxillary central incisor crowns should be approximately parallel to the true vertical line and thereby perpendicular to the true horizontal line. Methods: An idealized female image was created with computer software and manipulated using the same software to construct an "ideal" female profile image with proportions, and linear and angular soft tissue measurements, based on currently accepted criteria for idealized Caucasian profiles. The maxillary incisor labial face tangent was altered in 5° increments from 70 to 120°, creating a range of images, shown in random order to 70 observers (56 lay people and 14 clinicians), who ranked the images from the most to the least attractive. The main outcome was the preference ranks of image attractiveness given by the observers. Results: The most attractive inclination of a tangent to the labial face of the maxillary incisor crowns in profile view in relation to the true horizontal line was 85°, i.e. 5° retroclined from a perpendicular 90° inclination. The most attractive range appears to be between 80 and 90°. Excessive proclination appeared to be less desirable than retroclination. Beyond 105° most observers recommend treatment. Conclusion: In natural head position, the ideal inclination of the maxillary incisor crown labial face tangent in profile view will be approximately parallel to the true vertical line and thereby approximately perpendicular to the true horizontal line.

한국 젊은이의 안면미 선호경향에 관한 연구 : 얼굴의 측모평가를 중심으로 (A STUDY ON THE FACIAL ESTHETIC PREFERENCES AMONG KOREAN YOUTHS: ASSESSMENT OF PROFILE PREFERENCES)

  • 송세진;최익찬
    • 대한치과교정학회지
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    • 제22권4호
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    • pp.881-920
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    • 1992
  • This study was designed to assess profile preferences among Korean youths in the year 1992. Facial esthetics was evaluated by means of silhouette profiles, eliminating the influence of a number of aspects that may affect judgment when normal lateral photographs are used. The main points of preference to be clarified here are as follows. First, on facial convexity, Second, on nasion depth, Third, on mentolabial sulcus depth, Fourth, on the position of upper and lower lips, Fifth, on facial type according to Angle's classification of malocclusion, Sixth, on Song's tangents. The 54 subjects printed in questionnaire as black and white silhouettes were selected from 300 tracings from cephalometric radiographs of people whose age ranging from 11 to 20 years. Photographs of six female subjects were retouched by computer graphic software and printed in color and black/white photographs which were used for adaptation of eyes of participants in selecting profiles in silhouette. They constitute 2 questions. The 54 subjects were grouped as 22 questions, each of them composed of 6 subjects, according to the aspects to be clarified. Twenty four questions in total were asked to assess profile preferences. For the assessment, the profile line, the facial esthetic triangle, Song's tangents, and Angle's classification of malocclusion were introduced. The profile line is composed of 11 component points which are Trichion, Glabella, Nasion, Pronasale, Subnasale, Labrale superius, Stomion, Labrale inferius, Supramentale, Pogonion, and Gnathion. The facial esthetic triangle is composed of 3 tangents: A-tangent which is the tangent of dorsum of nose, B-tangent which is the line passing through Sn and Ls, and C-tangent which is drawn on the turning point of the curve which lies between mentolabial sulcus (Sm) and pogonion (Pg). Angle's classification has 3 types of malocclusion which are Class I, Class II, and Class III. Class II malocclusion is subdivided into Division 1 and Division 2. The participants of the survey were composed of 861 college students (448 male students, 413 female students) whose majors grouped as Fine Arts. Liberal Arts, and Natural Sciences, and whose mean age 21.8 years. The statistics program SPSS/PC + of SPSS Inc. was used to analyze answers of participants. Crosstabulation, Chi-square test, and Kendall test were done. The conclusions are as follows: First, Korean youths have a tendency to prefer the slightly convex face to the flat or concave face. Second, they prefer a moderately deep nasion. Third, they prefer a moderately deep mentolabial sulcus. Fourth, they prefer the position of lips which are near to Ricketts' E-line. The position of the upper lip which is slightly posterior to E-line is preferred. The upper lip which lies too far anterior or posterior to the lower lip is not perferred. Fifth, they prefer most, according to Angle's Classification of Malocclusion, Class I facial profile which has a slight inclination to Class II division 2. The order of preference is Class I, Class II division 2, Class III, and Class II division 1. Sixth, they prefer the type 2 and 3 of Song's tangents. The facial profile within which A-and B-tangent meet is preferred. The facial profile which has Cotangent that .meets with A-tangent slightly posterior to the crossing point of A-and B-tangent or that parallels with B-tangent is preferred.

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FDM에서 곡면부의 접선기울기가 제품의 표면에 미치는 영향 (Influence of Tangent Line Angle on Surface Roughness at Fused Deposition)

  • 하만경;전재억
    • 한국기계가공학회지
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    • 제1권1호
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    • pp.23-28
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    • 2002
  • Fused deposition modelling(FDM) is a rapid prototyping(RP) process that fabricates part layer by layer by deposition of molte thermoplastic material extrude from a nozzle. RP system has benefits. Benefit would be the ability to experiment with physical objects of any complexity m a relatively short period of time. But it has a matter of surface roughness and geometric accuracy. We study on Influence of tangent line angle on surface roughness at fused deposition.

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초고주파 대역에서의 기판의 유전상수 및 손실계수 측정 (Measurements of Dielectric constant and Loss tangent of Microwave Substrates)

  • 이선하;한상민;김영식
    • 한국전자파학회:학술대회논문집
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    • 한국전자파학회 2000년도 종합학술발표회 논문집 Vol.10 No.1
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    • pp.238-242
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    • 2000
  • In this paper, the method for dielectric constant and less tangent measurements of microwave substrates using a microstrip line is presented. The two samples of an open-ended line and a short-ended tine are made and complex propagation constant is evaluated from the one-port scattering parameter measurements. This method has been automated fully using a personal computer and a vector network analyzer.

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근사개념 지도를 위한 관련 지식의 교수학적 고찰 (A study on the pedagogical consideration of the related knowledge for teaching 'Approximation' conception)

  • 정영우;이목화;김부윤
    • 한국수학교육학회지시리즈E:수학교육논문집
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    • 제26권1호
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    • pp.137-154
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    • 2012
  • 미적분학에서 '근사(approximation)'는 핵심 개념 가운데 하나인데, 이를 설명하기 위한 기본 개념은 '접선(tangent)'이며, 접선은 특별한 조건을 가지는 '직선(line)'이다. 본 연구에서는 미적분학의 이론적 기초가 되는 이들 수학적 지식에 대해 중등학교 기하지도 관점에 기초하여 교수학적 고찰을 하고, 이와 관련하여 개연성 있는 지도를 위한 주안점과 지도 방안을 제안한다. 이를 위해 유클리드 기하학에서의 점, 선, 원, 직선, 접선, 근사에 대해 알아보고, 이를 해석 기하학으로 번역하는 과정을 통해 대수적 조작을 위한 수학적 지식들을 유의미하게 유도한다. 그리고 현대수학의 관점으로 이를 발전시켜 근사를 위한 수학적 지식들의 유선(流線, stream line)을 구성한다. 또한 이를 바탕으로 직선, 접선 그리고 근사에 관한 학교수학의 내용을 고찰하여 지도의 주안점과 지도 방안을 모색한다. 이러한 연구는 교사들에게 교수학적 내용지식을 주며, 이들 수학적 지식을 개연성 있게 지도할 수 있는 수업모델 개발에 대한 기초를 제공한다. 나아가 학생들에게 수학이 계통적 학문이라는 것과 학교수학이 뚜렷한 목적성 아래 구성된 활동이라는 것을 인식하게 한다.