• Journal for History of Mathematics
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• v.20 no.3
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• pp.147-166
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• 2007

This study is about the law of cosines. It dealt with its historical origin and the developmental process of the age of Greece, Islam and Modern age. Especially, we tried to find out how the extension of the law of cosines for spherical triangles and tetrahedron from the law of cosines for plane was done. On the basis of this analysis, we investigated how the law of cosines was generated and proved it through the logical demonstration and mathematical induction. This made us find out the mathematical meaning of mathematical concepts.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.22 no.4
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• pp.691-699
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• 2018

Astronomical positioning has been carried out from the past by using Sextant. The St. Hilaire method was mainly used by Nautical Almanac and Sight Reduction Tables For Marine Navigation. In modern times, it has been able to use the LOP(Line of Position) method smoothly by combining with IT technology. However, in comparison with the past method, the LOP method always shows two positions, True Position and False Position, which must be distinguished by the navigator. Therefore, in this paper, we proposed a method of using the azimuth to remove the false position generated by the LOP method. In particular, the theoretical considerations using azimuth are presented in various ways, and the validity of the theoretical considerations is confirmed. Simulations are presented to confirm that the theoretical basis of the thesis is valid.

• Journal of the Institute of Electronics Engineers of Korea CI
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• v.45 no.3
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• pp.160-174
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• 2008

In this paper, we propose new coding techniques for photometry data of three-dimensional(3-D) mesh models. We make a good use of geometry and connectivity information to improve coding efficiency of color, normal vector, and texture data. First of all, we determine the coding order of photometry data exploiting connectivity information. Then, we exploit the obtained geometry information of neighboring vortices through the previous process to predict the photometry data. For color coding, the predicted color of the current vertex is computed by a weighted sum of colors for adjacent vortices considering geometrical characteristics between the current vortex and the adjacent vortices at the geometry predictor. For normal vector coding, the normal vector of the current vertex is equal to one of the optimal plane produced by the optimal plane generator with distance equalizer owing to the property of an isosceles triangle. For texture coding, our proposed method removes discontinuity in the texture coordinates and reallocates texture image segments according to the coding order. Simulation results show that the proposed compression schemes provide improved performance over previous works for various 3-D mesh models.