• Honam Mathematical Journal
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• v.29 no.3
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• pp.475-480
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• 2007

In this paper we find the point at which the rational B$\'{e}$zier curve has the given tangent direction. We also analyze the geometric properties of the point of quadratic rational B$\'{e}$zier curve.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.13 no.3
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• pp.217-224
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• 2009

In this paper we present an approximation method of quadric surface using quartic spline. Our method is based on the approximation of quadratic rational B$\acute{e}$zier patch using quartic B$\acute{e}$zier patch. We show that our approximation method yields $G^1$ (tangent plane) continuous quartic spline surface. We illustrate our results by the approximation of helicoid-like surface.

• Korean Journal of Optics and Photonics
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• v.1 no.2
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• pp.217-222
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• 1990

A general ray tracing scheme has been developed for using a personal computer which trace finite rays through any non-rotationally symmetric system. This scheme may be used for the surface type such as conic section with or without aspherics, toric surfaces, sagittal and tangential cylindrical sections and axicons. Specially, any combinational of decentered, tilted and rotated surfaces has been considered. Before transfering to the next surfaces, the local coordinates are refered back to an initial reference coordinate system. We can get a mathmtical model of a non-rotationally symmetrical finite ray trace running on an inexpensive personal computer.

• Journal of the Korean School Mathematics Society
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• v.17 no.1
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• pp.45-71
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• 2014

In learning the conic session, there is a gap between the curricula of the high school and the university level for the pre-service math teachers. So through the art of problem posing, 38 number of pre-service teachers worked in a pair to find fidelities in the environment of hand-held graphing calculator. We concluded that the cognitive fidelity showed three different properties using "what if not" strategy which the mathematical fidelity between the representations supported. Also, the exploration using a calculator in the pedagogical fidelity strongly helped them to apply and to expand their learning.

• School Mathematics
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• v.15 no.4
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• pp.995-1013
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• 2013

The purpose of this paper was to investigate mathematics teachers' mathematical content knowledge about quadratic curves. Three components of mathematical knowledge are needed for teaching: (i) knowing school mathematics, (ii) knowing process of school mathematics, (iii) making connections between school mathematics and advanced mathematics. 24 mathematics teachers were asked to perform 10 questions based on mathematics curriculum. The results showed that mathematics teachers had some difficulties in conic section definitions and eccentricity definitions of ellipse and hyperbola. And they also got difficulty in Dandellin sphere proof of the equivalence of conic section definitions and quadratic curve definitions. Especially, no one answered correctly to the question about the definition of eccentricity. The ratio of correct answer for the question about constructing tangent lines of quadratic curves is less than that for the question about the applications of the properties of tangent lines. These findings suggests that it is needed that to provide plenty of opportunities to learn mathematical content knowledge in teacher education programs.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2009.11a
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• pp.469-473
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• 2009

The supersonic gas ejector, as gas dynamic appliance, has been applied for a long time because of simplicity and reliability. However, for the prediction of ejector performances with given parameters, that is, working gas pressure and the nozzle shape, it is necessary to raise accuracy of modelling for properties of ejector gas flow. The purpose of the represented work is to compare one-dimensional modelling and numerical results with experimental results. The ejector with a conic nozzle has been designed and tested (Mach number at the nozzle exit section was 3.31, the nozzle throat diameter - 6 mm). Working gas - nitrogen, was brought from system of gas bottles. Diameter of the mixture chamber at the nozzle exit section was limited by condensation temperature of nitrogen and equaled 20 mm. The one-dimensional theory predicted the minimal starting pressure equaled 8.18 bar (absolute) and 0.051 bar in the vacuum chamber. Accordingly the minimal starting pressure was 9.055 bar and 0.057 in the vacuum chamber bar have been fixed in experiment.

• Korean journal of applied entomology
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• v.29 no.3
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• pp.157-164
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• 1990

The surface patterns and the structures of transverse section of the egg-shell of the sikmoth, Bombyx mandarina, have been described by scanning electron microscope. Three spatially differentiated cross section, called lamellar, conic pillar and cover layers, are found on the mature eg-shell. Silkmoth chorion proteins were detected more than 80 components from a single chorion by two-dimensional electrophoresis. Major protein components of the egg-shell have bee identified on the basis of their isoelectric points and molecular weights, pH 4-6 and 6-30 kd. Several protein components are found entirely or predominantly in th cover layers.

• Communications of Mathematical Education
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• v.36 no.1
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• pp.23-38
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• 2022

The study provided a perspective on which readers can see Newton's proof heuristically in order to overcome the difficulty of proof showing 'QT²/QR converges to the latus rectum of ellipse' in the proof of the inverse square law of Newton's Principia. The heuristic perspective is as follows: The starting point of the proof is the belief that if we transform the denominators and numerators of QT²/QR into expression with respect to segments related to diameter and conjugate diameter, we may obtain some constant, the desired value, by their relationship PV × VG/QV² = PC²/CD² in Apollonius' Conic sections. The heuristic perspective proposed in this study is meaningful because it can help readers understand Newton's proof more easily by presenting the direction of transformation of QT²/QR.

• Journal for History of Mathematics
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• v.21 no.2
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• pp.39-54
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• 2008

This paper investigate Descartes' , which is significant in the history of mathematics, from standpoint of problem-solving. Descartes has clarified the general principle of problem-solving. What is more important, he has found his own new method to solve confronting problem. It is said that those great achievements have exercised profound influence over following generation. Accordingly this article analyze Descartes' work focusing his method.

• Korean Institute of Interior Design Journal
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• no.13
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• pp.203-215
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• 1997

This Study typed the roof-design in analysis of structural design of the glulam architecture, developed worldwidely, nowaday. For this, it is studied the characters of glulam as the history of glulam architectures, manufacture of glulam, shapes and section of glulam, fireproof and combution of glulam. And it is studied roof-design according to structural type of glulam roof-structure. Conclusively, types of glulam roof design typied as 1)the Simple Beam str., 2)the Multi-Joints continous Beam str. 3)the Hinge str. 4)the Rahmen str. 5)the Archi str. 6)the Grid str. 7)etc str. (Folded-plate str., Radial str., Cylinder Shell str., Ring Dome str., Geodesic Dome str., Conic Coloid Shell str., H.P Shell str. Cantilever Shell str.)