• 대한수학회보
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• 제46권6호
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• pp.1099-1133
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• 2009

We study the hyperbolic cosine and sine laws in the extended hyperbolic space which contains hyperbolic space as a subset and is an analytic continuation of the hyperbolic space. And we also study the spherical cosine and sine laws in the extended de Sitter space which contains de Sitter space S$^n_1$ as a subset and is also an analytic continuation of de Sitter space. In fact, the extended hyperbolic space and extended de Sitter space are the same space only differ by -1 multiple in the metric. Hence these two extended spaces clearly show and apparently explain that why many corresponding formulas in hyperbolic and spherical space are very similar each other. From these extended trigonometry laws, we can give a coherent and geometrically simple explanation for the various relations between the lengths and angles of hyperbolic polygons, and relations on de Sitter polygons which lie on S$^2_1$, and tangent laws for various polyhedra.

• Journal of Welding and Joining
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• 제22권6호
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• pp.43-49
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• 2004

In this study, a visual sensor system which can detect I-butt weld joint with height variation and includes a seam tracking algorithm was investigated. Three-dimensional position of an object can be acquired by using the method of distance measurement, i.e., an optical trigonometry which results from the spatial relations between the camera, the object and the structured light by a visible laser. Effects of laser intensity and iris number for the image quality as well as object material were investigated for the optical system design. For the image processing, a region of interest is defined from the whole image and a line image of laser is drew by using the gray level difference in the image. From the drew laser line, the weld joint can be recognized in searching the biggest point position calculated from the central difference method. Through a series of welding experiments, a good tracking performance was confirmed under GMA welding.

• Structural Engineering and Mechanics
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• 제67권3호
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• pp.291-300
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• 2018

In this work, a new trigonometry theory of shear deformation is developed for the static analysis of thick isotropic beams. The number of variables used in this theory is identical to that required in the theory of Euler-Bernoulli, sine function is used in the displacement field in terms of the coordinates of the thickness to represent the effects of shear deformation. The advantage of this theory is that shear stresses can be obtained directly from the relationships constitute, while respecting the boundary conditions at the free surface level of the beam. Therefore, this theory avoids the use of shear correction coefficients. The differential equilibrium equations are obtained using the principle of virtual works. A thick isotropic beam is considered, whose numerical study to show the effectiveness of this theory.

• 대한수학교육학회지:수학교육학연구
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• 제8권2호
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• pp.541-551
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• 1998

Recently, the importance of participating in classes activity and cultivating student's thinking ability is emphasized in the mathematics education society. Teachers are demanded to change their teaching style centered pencile-and paper into using the variety instructional aids, such as calculator, video tape, computer, ohp, and projector, etc. In this paper, we search for the mathematica's function and the method that apply mathematical to the secondary school mathematics. Mathematical has many functions: calculator, algebra, graphics, animations, programing, notebook. We find that mathematica can be applied to the graph of function, the understand of simultaneous equations, the graph of trigonometry function, the calculation of limit, the computation of areas as limits, the derivative of a function and tangent line, a solid figure, and others in secondary school mathematics.

• 대한수학교육학회지:학교수학
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• 제1권2호
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• pp.483-512
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• 1999

The purpose of the research was to investigate the patterns of student's mathematical thinking and behavior and describe the nature of difficulties the student underwent in trigonometry as the student conducted independent explorations within the interactive technology environment. Also, the research identified the connections among multiple representations and merits and shortcomings in using a graphic calculator as a tool. A take-based clinical interview procedure as the method for qualitative research was used to find the cognitive actions of the participant and his interactions with the graphic calculator. A case study report was written for the student. The researcher found that the student moved from operative stage, to constructive stage, to applicable stage of thinking. From Colgan; Graphing has significance both to mathematics and mathematics education in at least three ways since: * graphing represents an important technique, instrument and process in mathematics; * through ‘graphing’, per se, students can be said to be using one symbolic system to extend and acquire an understanding of another(e. g., trigonometric functions and their graphs). * graphing is propaedeutic to other, more advanced topics and concepts in mathematics.

• 대한전기학회:학술대회논문집
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• 대한전기학회 2001년도 하계학술대회 논문집 D
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• pp.2326-2328
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• 2001

This paper's purpose is to obtain 3-Dimension information by using a monocular camera. This system embodies to obtain the height of object by using trigonometry method between a reference point of circumstance and an object. It is possible to build up system regardless of operating system, and then set it up. An comfortable USB port camera is used everywhere without the capture board. The internet can be used by using the applet and JMF everywhere. We regard the camera as a fixed. And we have developed a Real-Time JPEG/RTP Network Camera system using UDP/IP on Ethernet.

• East Asian mathematical journal
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• 제38권4호
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• pp.517-532
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• 2022

This study looked at how content reviews with mathematical games in class would influence the mathematical disposition of middle school students. In doing so, three games adapted from prior research were used as a supplementary instruction after school hours over three months. The mathematical topics of the games involved concepts of probability and trigonometry at the middle school level. The results of the pre- and post-survey on mathematical disposition indicate that incorporating mathematical games appeared to have some positive impacts on whether students might be more eager to learn mathematics and actually put more effort in learning materials.

• 한국산학기술학회논문지
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• 제20권6호
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• pp.598-603
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• 2019

삼차원 형상 측정 기술은 다양한 산업에서 활용하고 있는 기술이다. 그 중, 광 삼각법에 기초한 광학식 삼차원 형상 측정 기술들은 매일 공장에서 오랜 시간 동안 대량의 삼차원 형상 측정을 하고, 미세한 측정 또한 요구되는 반도체 생산품 검사 분야에서 주로 사용된다. 이러한 광 삼각법 기반의 삼차원 측정 장비들의 구성 요소인 광원과 구동 회로는 장시간 작동하게 되면 발열이 나타나게 되고 장시간 작동하며 주변의 온도가 일정하지 않은 상황에 노출되기도 하여 온도로 인한 측정 오차가 발생하게 된다. 본 논문에서는 장시간 반복해서 사용하는 PMP(Phase Measuring Profilometry) 형상 측정법에서의 열 변위 보정에 관한 방법을 제안하였다. PMP 형상 측정법 기반의 삼차원 형상 측정 장치를 구현하여 10시간에 걸쳐 물체의 높이와 주변 온도를 측정하는 실험을 진행하였고, 측정된 온도와 높이 값을 이용하여 단순 선형 회귀 분석을 하여 회귀직선을 얻었다. 이 회귀직선을 이용하여 온도에 따른 높이 측정값의 오차를 보정하게 되면 정상적인 측정값에서의 오차 값이 139.88 um(Micrometer) 에서 13.12 um로 보정되는 것을 확인하였다.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제12권4호
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• pp.283-291
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• 2008

The extension to a wide population of secondary education in many advanced countries seems to have led to a weakening of the mathematics curriculum. In response, many students have been classified as "gifted" so that they can access a stronger program. Apart from the difficulties that might arise in actually determining which students are gifted (Is it always clear what the term means?), there are dangers inherent in programs that might be devised even for those that are truly talented. Sometimes students are moved ahead to more advanced mathematics. Elementary students might be taught algebra or even subjects like trigonometry and vectors, and secondary students might be taught calculus, differential equations and linear algebra. It is my experience over thirty-five years of contact with bright students that acceleration to higher level mathematics is often not a good idea. In this paper, I will articulate some of the factors that have led me to this opinion and suggest alternatives. First, I would like to emphasize that in matters of education, almost every statement that can be made to admit counterexamples; my opinion on acceleration is no exception. Occasionally, a young Gauss or Euler walks in the door, and one has no choice but to offer the maximum encouragement and allow the student to go to the limit of his capabilities. A young genius can demonstrate an incredible amount of mathematical insight, maturity and mastery of technique. A classical example is probably the teen-age Euler, who in the 1720s was allowed regular audiences with Jean Bernoulli, the foremost mathematician of his day.

• 한국수학사학회지
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• 제23권1호
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• pp.41-52
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• 2010

고대의 인도수학은 산스크리트어로 쓰여 있고, 수학의 법칙이나 문제들은 구전되었거나 필사본의 형태로 경전 속에 포함되어 있으며, 학생들이 암기를 쉽게 할 수 있도록 아주 간결하게 정리되어 있다. 고대 인도의 많은 수학자들은 일찍이 십진법, 계산법, 방정식, 대수학, 기하학, 삼각법 등의 연구에 공헌하였다. 이 논문은 고대 인도수학과 다른 문명권의 수학발전을 비교하였다. 고대 그리스 수학이 공리적이고 연역적이라면, 인도수학은 양적이며 계산적이지만 원리를 가지고 문제를 해결하는 특성이 있다. 고대 인도와 타 문명권의 수학을 비교하는 것은 오늘날 수학교육과 수학사 연구에 의미가 있는 것으로 사료된다.