• Bulletin of the Korean Mathematical Society
• /
• v.46 no.6
• /
• pp.1099-1133
• /
• 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
• /
• v.22 no.6
• /
• pp.43-49
• /
• 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
• /
• v.67 no.3
• /
• pp.291-300
• /
• 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.

• Journal of Educational Research in Mathematics
• /
• v.8 no.2
• /
• pp.541-551
• /
• 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.

• School Mathematics
• /
• v.1 no.2
• /
• pp.483-512
• /
• 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.

• Proceedings of the KIEE Conference
• /
• 2001.07d
• /
• pp.2326-2328
• /
• 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
• /
• v.38 no.4
• /
• pp.517-532
• /
• 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.

• Journal of the Korea Academia-Industrial cooperation Society
• /
• v.20 no.6
• /
• pp.598-603
• /
• 2019

Three-dimensional shape measurement technology is used in various industries. Among them, optical three-dimensional shape measurement techniques based on the optical trigonometry are mainly used in the field of semiconductor product inspection, where large quantities of three-dimensional shape measurements are made daily in factories and fine measurements are also required. The light source and the drive circuit, which are components of three-dimensional measurement equipment based on this optical trigonometry, produce heat generated by prolonged operation, and may be exposed to conditions where the ambient temperature is not constant, resulting in temperature-induced measurement errors. In this study, the compensation method of the Thermal Errors for Phase Measuring Profilometry is proposed. Three-Dimensional Shape Measurement Equipment based on Phase Measuring Profilometry is implemented to measure the height of an object and ambient temperature for 10 Hours, and a regression line was obtained line by making simple linear regression using measured temperature and height values. This regression line was used to correct the error of the height measurement according to the temperature, and thermal error was from 139.88 um(Micrometer) to 13.12 um.

• Research in Mathematical Education
• /
• v.12 no.4
• /
• pp.283-291
• /
• 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.

• Journal for History of Mathematics
• /
• v.23 no.1
• /
• pp.41-52
• /
• 2010

Ancient Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sturas in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. And rules or problems of the mathematics were transmitted both orally and in manuscript form.Indian mathematicians made early contributions to the study of the decimal number system, arithmetic, equations, algebra, geometry and trigonometry. And many Indian mathematicians were appearing one after another in Ancient. This paper is a comparative study of mathematics developments in ancient India and the other ancient civilizations. We have found that the Indian mathematics is quantitative, computational and algorithmic by the principles, but the ancient Greece is axiomatic and deductive mathematics in character. Ancient India and the other ancient civilizations mathematics should be unified to give impetus to further development of mathematics education in future times.