• Title/Summary/Keyword: alternate angles

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Teachers' & Students' Concepts of the Measurement of the Size of the Earth

  • Chae, Donghyun;Han, Jejun
    • Journal of The Korean Association For Science Education
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    • v.33 no.3
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    • pp.639-649
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    • 2013
  • The purpose of this study is to figure out how teachers conduct an experiment in measuring the size of the Earth and how students recognize it. For this study, an in-depth interview was conducted one week after the lesson on the experiment about measuring the size of the Earth. The participants were five secondary school teachers and five secondary school students. The in-depth interview was recorded and transcribed. The result of the interview was drawn through an inductive categorized analysis method. As a conclusion of this study, the teachers taught the students the lesson using alternate angles instead of using the altitude of the Sun. Their lessons were based on Eratosthene's story or some related illustrations suggested in the textbook and not based on an explanation of the principle. Also, students measured the Earth's size only by using alternate angles and didn't understand the meaning of the shadow in the experiment. The results of this study show that teachers need to reconstruct the textbook and understand the accurate experimental principle for the students to have a meaningful experience of the experiment on measuring the size of the Earth.

A Note on Dealing with Some Contents of Geometry in the Middle School Mathematics (중학교 수학에서 기하 내용 취급에 관한 연구)

  • 김흥기
    • Journal of Educational Research in Mathematics
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    • v.14 no.1
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    • pp.111-127
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    • 2004
  • In this note we examined some terms, parallel lines and angles in elementary school mathematics and middle school mathematics respectively. Since some terms are represented early in elementary school mathematics and not repeated after, some students are not easy to apply the terms to their lesson. Also, since the relation between parallel lines and angles are treated intuitively in 7-th grade, applying the relation for a proof in 8-th grade would be meaningless. For the variety of mathematics education, it is desirable that the relation between parallel lines and angles are treated as postulate. Also, for out standing students, it is desirable that we use deductive reasoning to prove the relation between parallel lines and angles as a theorem. In particular, the treatments of vertical angles and the relation between parallel lines and angles in 7-th grade text books must be reconsidered. Proof is very important in mathematics, and the deductive reasoning is necessary for proof. It would be efficient if some properties such as congruence of vertical angles and the relation between parallel lines and angles are dealt in 8-th grade for proof.

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The relation of the angle sum of a triangle and the property of parallel lines in Elementary school mathematics (초등학교 수학에서 삼각형 내각의 합과 평행선의 성질의 연계성)

  • Hong, Gap Ju;Song, Myeong Seon
    • Education of Primary School Mathematics
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    • v.16 no.2
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    • pp.183-192
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    • 2013
  • This study points out that the angle sum of a triangle and the property of parallel lines are taught without showing any relations between them on elementary school mathematics textbooks. This study looks into the structure of Euclid Elements so that it discusses about the contents of current Korean textbooks. The property of the alternate angles and the corresponding angles of parallel lines are inherent in many subjects in Elementary school mathematics, and have meaning that must be thought with the angle sum of triangles in the structure of Euclid Elements. With this consideration, this study makes a conclusion that these two subjects should be taught by presenting relations between them.

Comparison between Subjective and Objective Angle of Deviation Using by Synoptophore and Prism Bar in Strabismus Patients (사시환자에서 Synoptophore와 Prism bar를 이용한 자각적 사시각과 타각적 사시각의 비교)

  • Wi, Dae-Gwang;Joo, Seok-Hee;Lee, Koon-Ja;Leem, Hyun-Sung
    • Journal of Korean Ophthalmic Optics Society
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    • v.15 no.1
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    • pp.79-85
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    • 2010
  • Purpose: We studied the relationship between subjective and objective deviating angle. Methods: Those who were diagnosed with strabismus among the patients who had no systemic diseases that fifty-one subjects (Male; 21, Female; 30) were measured between seven to sixty three years, evaluated to alternate cover test after AR/K (Canon RK-FI, Japan) and retinoscope measured refractive errors. Objective deviating angle was measured using prism bar; and subjective and objective deviating angles were measured and compared using the synoptophore. Results: For the correlation between subjective and objective deviating angles. The differences were $2.6{\pm}2.5{\Delta}$, between subjective deviating angle measured using synoptophore and objective deviating angles measured using synoptophore were $0.7{\pm}1.4{\Delta}$, the average with each other were $1.7{\pm}1.8{\Delta}$, with all the differences highly significant. Conclusions: We thought not only reduced angle of deviating errors and identified the significance in the correlation between subjective and objective deviating angles but also considered to be useful in determining deviating angle of patient with strabismus.

Revisiting Tangram and Similar Tangrams based on Mathematics Curriculums (수학과 교육과정에 비추어 본 탱그램과 유사탱그램의 재조명)

  • Song, Sang-Hun
    • Journal of Educational Research in Mathematics
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    • v.18 no.3
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    • pp.391-405
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    • 2008
  • There are some studies on tangram a kind of jigsaw(silhouette or dissection) puzzle. And Korean national curriculums mention about tangram. But the past studies and the textbooks are not so related to curriculums. So this study is focused on some problems and limitations of tangram activities related to curriculum. This study gives some educational suggestions using tangram: (1) alternate drawing of tangram (2) making mathematical figures instead of shapes (3) proper activities related to the national curriculum (especially, polygons and angles) and mathematical thinking (4) examples of exploring mathematical figures and angles coming in and out of national curriculum In addition to, this study suggests some mathematical activities of using similar tangrams (especially sphinx puzzle).

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Taxonomic Reassessment of the Genus Polysiphonia (Rhodomelaceae, Rhodophyta): Morphology and Reproduction of Neosiphonia decumbens and N. harlandii (홍조 붉은실속 식물의 분류학적 재검토: 누은새붉은실과 가시새붉은실의 형태와 생식)

  • Kim, Myeong-Suk
    • ALGAE
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    • v.18 no.2
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    • pp.107-119
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    • 2003
  • Neosiphonia is separated from the traditionally well known genus Polysiphonia (Rhodomelaceae, Rhodophyta) and 12 species includes in Korea. In this study, the vegetative and reproductive developments of two Neosiphonia species, N. decumbens (Segi) M.S. Kim et I.K. Lee and N. harlandii (Harvey) M.S. Kim et I.K. Lee, are reinvestigated. N. decumbens is diagnosed by following combination of the characters: plants 1-3 cm high, dwarf, decumbent, main axes indistinct, irregularly branched in dichotomous manner, and alternately or secundly ramified with wide angles above. N. harlandii is distinguished by the features: plants 4-8 cm high, usually solitary and saxicolous, erect, densely corticated at base of distinct main axes, rather irregularly alternate in branch, and with cicatrigenous branchlets developed numerously on every part of frond. The two species share typical characteristics of the genus Neosiphonia, such as a base attached by unicellular rhizoids, cut off by cross wall, pericentral cells in 4, trichoblasts moderately developed near the apex of branches, leaving persistent scar-cells, tetrasporangia arranged in a spiral series, procarps with 3-celled carpogonial branch, and spermatangial branches arising as a primary branch of trichoblast. Taxonomy of the two Neosiphonia in regard to Polysiphonia is discussed.

Single-Stage Quasi Resonant Type PSR(Primary Side Regulation) PWM Converter for the LED Drive in TRIAC Phase Controlled Dimmer (TRIAC위상 제어 조광기에서의 LED구동을 위한 Single-Stage 준 공진형 PSR(Primary Side Regulation) PWM 컨버터)

  • Han, Jae-Hyun;Lim, Young-Cheol;Jung, Young-Gook
    • Journal of the Korean Institute of Illuminating and Electrical Installation Engineers
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    • v.27 no.2
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    • pp.84-94
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    • 2013
  • In case when the existing TRIAC phase controlled dimmer is drove for the LED lighting equipments, there are many problems such as the LED flicker in low phase-angles, the acoustic noise and elements damage by increase of the peak voltage in the input filter capacitor, mulfunction by insufficiency of the TRIAC holding current, and the abnormal oscillation by LC resonant. In this paper, we proposes the single-stage quasi-resonant PSR(Primary Side Regulation) PWM converter, and the design, the simulation and experiment are performed. As a result, it could confirm that the proposed PWM converter is the lighting equipments for LED drive which can alternate the existing 60W class incandescent bulbs and it has the high drive performance of the efficiency 80% and over, the power factor 0.95 and over under the normal voltage 220V. Finally, total harmonic distortion(THD) is gratified with a standard[1] of the lighting equipments and the durability is evaluated as the high reliablilty of 150,000 hours and over.

The Crystal and Molecular Structure of 25,26,27,28-Tetrnacetoxy[4]Arene${\cdot}$Monohydrate (25,26,27,28-테트라아세트오키시[4]에렌${\cdot}$일수화물의 결정 및 분자구조)

  • Choong Tai Ahn;Kwanghyun No
    • Journal of the Korean Chemical Society
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    • v.37 no.3
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    • pp.344-350
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    • 1993
  • 25,26,27,28-Tetraacetoxycalix[4]arene·monohydrate is orthorhombic, space group Pbca with a = 14.979(4), b = 15.154(4), c = 27.890(3) ${\AA}$, Z = 8, V = 6330.6 ${\AA}^{-3}$, D$_c$ = 1.28 $g{\cdot}cm^{-3}$, (Mo K${\alpha}$) = 0.71069 ${\AA}$, ${\mu}$ = 0.86 cm$^{-1}$, F(000) = 2600, and R = 0.069 for 3376 unique observed reflections with I > 1.0 ${\sigma}$(I). The structure was solved by direct methods and refined by cascade diagonal least-squares refinement. All the C-H bond lengths(= 0.96 ${\AA}$), the methyl groups and the methylene groups are fixed and refined as the rigid groups with ideal geometry. The macrocycle exists in the 1,3 alternate conformation (by Conforth) making the angles of 110.7, 684, 113.7 and 68.8$^{\circ}$ between the benzene rings and the methylenic mean plane, and four each acetoxy groups are twisted away from their own benzene rings with the angles of 68.2, 97.6, 78.9 and 71.3$^{\circ}$, respectively. The relative dihedral angles between two opposite side of the benzene rings are 135.6$^{\circ}$ for the rings (1) and (3) and 135.2$^{\circ}$ for (2) and (4). A water molecule which has nearly the same height of the methylenic plane of the macrocycle in the c-axis, is located within the distances of 2.942(5) ${\AA}$ from the O(8) atom of the carbonyl group and 2.901 ${\AA}$ from, another O(2)(1/2-x, -1/2+y, z). The shortest contact between the molecule is 3.193 ${\AA}$ from the O(4) to the C(3)(1/2+x, 1/2-y,-z).

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FACTORS INFLUENCING STUDENTS' PREFERENCES ON EMPIRICAL AND DEDUCTIVE PROOFS IN GEOMETRY (중학생의 경험적 증명과 연역적 증명에 대한 선호 요인 분석)

  • Park, Gwi-Hee;Yoon, Hyun-Kyoung;Cho, Ji-Young;Jung, Jae-Hoon;Kwon, Oh-Nam
    • Communications of Mathematical Education
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    • v.24 no.2
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    • pp.325-344
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    • 2010
  • The purpose of this study is to investigate what influences students' preferences on empirical and deductive proofs and find their relations. Although empirical and deductive proofs have been seen as a significant aspect of school mathematics, literatures have indicated that students tend to have a preference for empirical proof when they are convinced a mathematical statement. Several studies highlighted students'views about empirical and deductive proof. However, there are few attempts to find the relations of their views about these two proofs. The study was conducted to 47 students in 7~9 grades in the transition from empirical proof to deductive proof according to their mathematics curriculum. The data was collected on the written questionnaire asking students to choose one between empirical and deductive proofs in verifying that the sum of angles in any triangles is $180^{\circ}$. Further, they were asked to provide explanations for their preferences. Students' responses were coded and these codes were categorized to find the relations. As a result, students' responses could be categorized by 3 factors; accuracy of measurement, representative of triangles, and mathematics principles. First, the preferences on empirical proof were derived from considering the measurement as an accurate method, while conceiving the possibility of errors in measurement derived the preferences on deductive proof. Second, a number of students thought that verifying the statement for three different types of triangles -acute, right, obtuse triangles - in empirical proof was enough to convince the statement, while other students regarded these different types of triangles merely as partial examples of triangles and so they preferred deductive proof. Finally, students preferring empirical proof thought that using mathematical principles such as the properties of alternate or corresponding angles made proof more difficult to understand. Students preferring deductive proof, on the other hand, explained roles of these mathematical principles as verification, explanation, and application to other problems. The results indicated that students' preferences were due to their different perceptions of these common factors.

An Optimal Adaptation Framework for Transmission of Multiple Visual Objects (다중 시각 객체 전송을 위한 최적화 적응 프래임워크)

  • Lim, Jeong-Yeon;Kim, Mun-Churl
    • Journal of KIISE:Software and Applications
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    • v.35 no.4
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    • pp.207-218
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    • 2008
  • With the growth of the Internet, multimedia streaming becomes an important means to deliver video contents over the Internet and the amount of the streaming multimedia contents is also getting increased. However, it becomes difficult to guarantee the quality of service in real-time over the IP network environment with instantaneously varying bandwidth. In this paper, we propose an optimal adaptation framework for streaming contents over the Internet in the sense that the perceptual quality of the multi-angie content with multiple visual objects is maximized given the constraints such as available bandwidth and transcoding cost. In the multi-angle video service framework, the user can select his/her preferred alternate views among the given multiple video streams captured at different view angles for a same event. This enhanced experience often entails streaming problems in real-time over the network, such as instantaneous bandwidth changes in the Internet. In order to cope with this problem, we assume that multi-angle video contents are encoded at different bitrates and the appropriate video streams are then selected or transcoded for delivery to meet such bandwidth constraints. For the user selective consumption of the various bitstreams in the multi-angle video service, the bitstream in each angle can be encoded in various bitrate, and the user can select a sub-bitrstream in the given bitrstreams or transcode the corresponding content in order to deliver the optimally adapted video contents to the instantaneously changing network condition. Therefore, we define the transcoding cost which means the time taken for transcoding the video stream and formulate a unified optimization framework which maximizes the perceptual quality of the multiple video objects in the given constraints such as the transcoding cost and the network bandwidth. Finally, we present plenty of the experimental results to show the effectiveness of the proposed method.