• Journal for History of Mathematics
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• v.33 no.3
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• pp.155-165
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• 2020

Pythagorean theorem is a proposition on the relationship between the lengths of three sides of a right triangle. It is well known that Pythagorean theorem for Euclidean geometry deforms into an interesting form in non-Euclidean geometry. In this paper, we investigate a new perspective that replaces right triangles with 'proper triangles' so that Pythagorean theorem extends to non-Euclidean geometries without any modification. This is seen from the perspective that a rectangle is an equiangular quadrilateral, and a right triangle is a half of a rectangle. Surprisingly, a proper triangle (defined by Paolo Maraner), which is a half of an equiangular quadrilateral, satisfies Pythagorean theorem in many geometries, including hyperbolic geometry and spherical geometry.

• Honam Mathematical Journal
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• v.34 no.1
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• pp.103-111
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• 2012

Wetzel[5] proved if ${\Gamma}$ is a closed curve of length L in $E^n$, then ${\Gamma}$ lies in some ball of radius [L/4]. In this paper, we generalize Wetzel's result to the non-Euclidean plane with much stronger version. That is to develop a lower bound of length of a triangle inscribed in a circle in non-Euclidean plane in terms of a chord of the circle.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1998.10a
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• pp.251-257
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• 1998

Spherical space frame structure with triangular network pattern, which has the various characteristics for the mechanic property, a funtional property, an aesthetic property and so on, has often been used as one of the most efficient space structures. It is expected that this type will be used widely in large-span structural roofs. But because this structure is made of network by combination of line elements there me many nodes therefore, the structure behavior is very complicated and there can be an overall collapse of structure by buckling phenomenon if the external force reaches a limitation. This kind of buckling is due to geometric shape, network pattern, the number of layer and so on, of structure. Therefore spherical space frame with triangle network pattern have attracted many designers and researchers attention all over the world. The number of layer of space frame is divided in to the simgle, double, multi layer. That is important element which is considered deeply in the beginning of structural design. The buckling characteristics of single-layer model and double-layer model for the spherical space frame structure with triangular network pattern are evaluated and the buckling loads of these types are compared with investigation their structural efficiency in this study.

• Journal of the Institute of Electronics Engineers of Korea SP
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• v.40 no.6
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• pp.41-50
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• 2003

For copyright protection of digital contents, we employ watermarking techniques to embed watermark signals into digital host data. In this paper we propose an adaptive watermarking algorithm for three-dimensional (3-D) mesh models. Watermark signals are inserted into vertex coordinates adaptively according to changes of their position values. While we embed strong watermarks in the areas of large variations, watermarks are weakly inserted in other areas. After we generate triangle strips by traversing the 3-D model and convert the Cartesian coordinates to the spherical coordinate system, we calculate variations of vertex positions along the traversed strips. Then, we insert watermark signals into the vertex coordinates adaptively according to the calculated variations. We demonstrate that imperceptibility of the inserted watermark is significantly improved and show the bit error rate (BER) for robustness.

• Journal of the Korean Society for Precision Engineering
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• v.24 no.11
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• pp.134-143
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• 2007

A new approach based on mean value coordinate combined with Laplacian coordinate is proposed for shape deformation of a large polygon model composed of triangular net. In the method, the spherical mean value coordinates for closed control meshes is introduced to describe a vertex in the triangle meshes to be deformed. Furthermore, the well known quardratic least square method for the Laplacian coordinates is employed in order to deform the control meshes. Because the mean value coordinates are continuous and smooth on the interior of control meshes, deforming operation of control meshes change the shape of polygon model while preserving the intrinsic surface detail. The effectiveness and validity of this novel approach was demonstrated by using it to deform large and complex polygon models with arbitrary topologies.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1069-1105
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• 2001

Regular maps and hypermaps are cellular decompositions of closed surfaces exhibiting the highest possible number of symmetries. The five Platonic solids present the most familar examples of regular maps. The gret dodecahedron, a 5-valent pentagonal regular map on the surface of genus 5 discovered by Kepler, is probably the first known non-spherical regular map. Modern history of regular maps goes back at least to Klein (1878) who described in [59] a regular map of type (3, 7) on the orientable surface of genus 3. In its early times, the study of regular maps was closely connected with group theory as one can see in Burnside’s famous monograph [19], and more recently in Coxeter’s and Moser’s book [25] (Chapter 8). The present-time interest in regular maps extends to their connection to Dyck\`s triangle groups, Riemann surfaces, algebraic curves, Galois groups and other areas, Many of these links are nicely surveyed in the recent papers of Jones [55] and Jones and Singerman [54]. The presented survey paper is based on the talk given by the author at the conference “Mathematics in the New Millenium”held in Seoul, October 2000. The idea was, on one hand side, to show the relationship of (regular) maps and hypermaps to the above mentioned fields of mathematics. On the other hand, we wanted to stress some ideas and results that are important for understanding of the nature of these interesting mathematical objects.

• Journal of Korea Game Society
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• v.8 no.3
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• pp.69-76
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• 2008

This paper presents a novel rendering algorithm based on sperical coordinate representation of the object. The vertices of the object are transformed into the sperical coordinate system, and we construct additional maps: the centroid and index of the triangle, the memory access table. While OpenGL rendering pipeline touches all vertices of an object, the proposed method takes account of the only visible vertices by examining the visible triangles of the object. Simulation results demonstrated that the proposed method achieve an efficient rendering performace.

• 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 Biosystems Engineering
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• v.12 no.3
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• pp.30-41
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• 1987

The geometrical shape of a plow bottom may be the most important factor affecting the performance of a plow for a given soil and operating conditions. There are various designs of the Jaenggi (Korean plow) available commercially, which may be different from each other and from the plow (Western plow) in respect to the shape and performance. This study was intended to investigate the geometrical characteristics of Jaenggi. The coordinate digitizer equipped with 3 potentiometers was designed and manufactured for measurement of the shape of curved plane of moldboard and share. The digitizer was connected to a microcomputer having the data acquisition system. This device was used to analyze the plow bottoms of 5 differently-made Jaenggis and one cylindrical plow. The results of the study are summarized as follows: 1. It was possible to measure easily and quickly the curved plane of plow bottom and to plot the view on three major plans using the coordinate digitizer electrically connected to a microcomputer system. 2. The shape of five Jaenggi bottoms analyzed could be characterized by the cutting angle having the range of $33-42^{\circ}$, the maximum share-lift angle of $41-50^{\circ}$, and the setting angle of moldboard wing of $46-70^{\circ}$. The most critical difference of the shape factors between the Jaenggi and the plow was found in the maximum share-lift angle, the former was more than twice as much as the latter. 3. The analysis of the shape of Jaenggi bottoms showed that the share projections on 3 major plans had a varied triangle, which was quite different from that of plow bottom. Especially, it was analyzed that the shape of furrow slice for the Jaenggi had a skewed rectangle, leaving a considerable height of the ridge at the furrow bottom. 4. The dihedral angle was similar range of $30-85^{\circ}$ for the all bodies investigated, but the directional angle was somewhat different from each other. The difference in directional angle was $5^{\circ}$ for the plow, $20^{\circ}$ for the Jaenggi A and $30^{\circ}$ for the Jaenggi B. 5. Area of the spherical representation region was 0.0328 for the plow, 0.1194 for the Jaenggi A and 0.1716 for the Jaenggi B. This may indicate that the plow came close to a working surface and the Jaenggi A and the Jaenggi B departed from a working surface to a somewhat greater extent.