• School Mathematics
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• v.4 no.1
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• pp.1-13
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• 2002

The purpose of this study is to investigate the reasons and backgrounds of drawing auxiliary lines in the proof of geometry. In most of proofs in geometry, drawing auxiliary lines provide important clues, thus they play a key role in deductive proof. However, many student tend to have difficulties of drawing auxiliary lines because there seems to be no general rule to produce auxiliary lines. To alleviate such difficulties, informal activities need to be encouraged prior to draw auxiliary lines in rigorous deductive proof. Informal activities are considered to be contrasting to deductive proof, but at the same time they are connected to deductive proof because each in formal activity can be mathematically represented. For example, the informal activities such as fliping and superimposing can be mathematically translated into bisecting line and congruence. To elaborate this idea, some examples from the middle school mathematics were chosen to corroborate the relation between informal activities and deductive proof. This attempt could be a stepping stone to the discussion of how to teach auxiliary lines and deductive reasoning.

• Journal of Industrial Technology
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• v.15
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• pp.153-168
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• 1995

The purpose of this study is to develop a method for predicting the aerodynamic performance of the subsonic airfoils in the 2-dimensional, steady and viscous flow. For this study, the airfoil geometry is specified by adopting the longest chord line system and by considering local surface curvature. In case of the inviscid-incompressible flow, the analysis is accomplished by the linearly varying strength vortex panel method and the Karman-Tsien correction law is applied for the inviscid-compressible flow analysis. The Goradia's integral method and the Truckenbrodt integral method are adopted for the boundary layer analysis of the laminar flow and the turbulent flow respectively. Viscous and inviscid solutions are converged by the Lockheed iterative calculating method using the equivalent airfoil geometry. And the analysis of the seperated flow is performed using the Dvorak and Maskew's method as the basic method. The wake effect is also considered and its geometry expressed by the formula of Summey & Smith when no seperation occurs. A computational efficiency is verified by the comparison of the computational results with experimental data and by the shorter execution time.

• The KSFM Journal of Fluid Machinery
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• v.12 no.6
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• pp.7-12
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• 2009

This paper presents a numerical study on the design of side-suction inlet geometry which is used for multi stage centrifugal pumps or inline centrifugal pumps. In order to achieve an optimum inlet geometry and to explain the interactions between the different geometric configurations, the three dimensional computational fluid dynamics and the design of experiment methods have been applied. Geometric design variables describing the cross sectional area distribution through the inlet were selected. The objective functions are defined as the non-uniformity of the velocity distribution at the passage exit which is just in front of the impeller eyes. From the 2k factorial design results, the most important design variable was found and the performance of the side suction inlet was improved compared to the base line shape.

• Journal of the Korean Institute of Telematics and Electronics D
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• v.34D no.11
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• pp.9-19
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• 1997

By noticing that most waveguide devices were connected to power source through coaxial line, three dimentional finite element analysis using TEM mode incident was tried. When tEM mode was used, being dissimilar to TE$_{10}$ mode incident, analysis model of TEM mode incident has almost the same geometry with real products. Therefore, the degree of trust about analysis result is improved. Reflection coefficients of coaxial line, W/G adaptor, magnetron obtained by simulation was compared with experimental results.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.67-74
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• 2024

Maximal surfaces have a prominent place in the field of differential geometry, captivating researchers with their intriguing properties. Bearing a direct analogy to the minimal surfaces in Euclidean space, investigating both their similarities and differences has long been an important issue. This paper is aimed to give a local characterization of maximal surfaces in 𝕃³ in terms of their geodesic curvatures, which is analogous to the minimal surface case presented in [8]. We present a classification of the maximal surfaces under some simple condition on the geodesic curvatures of the parameter curves in the line of curvature coordinates.

• Journal for History of Mathematics
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• v.26 no.1
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• pp.33-56
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• 2013

This is a literature study about the concept of 'Division into Equal Parts' in middle school geometry. First, we notice that the concept of the division into equal parts in middle school geometry is given in four themes, which are those of line segments, angles, arches and areas. Second, we investigate and analyse the historical backgrounds of these four kinds of divisions into equal parts. Third, the possibility of extension in terms of method and concept was researched. Through the result of this study, we suggest that it is desirable to use effective utility of history in mathematical teaching and learning in middle school.

• Communications of Mathematical Education
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• v.27 no.3
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• pp.179-203
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• 2013

The purpose of this study was to discuss the example that developed geometry model textbook based on storytelling using real-life context. To achieve this purpose, we first elaborated the meaning of the textbook based on storytelling with real-life context, and then we discussed the outline of the story and the summary of each lesson. This study defined the storytelling textbook with real-life context as the textbook consisting of activities that explored and organized mathematical concepts by using real-life situations as materials of stories. The geometry textbook we developed employed two real-life materials, a map and a set square: we used a map for the coordinate geometry and a set square for the equation of a line. To attract students' interest, we introduced confrontation between a teacher and two students and a villain. We implemented experimentation with the textbook based on storytelling in order to verify its validity. The participants were 25 students that were enrolled in a high school in Seoul. Among them, 17 participants were surveyed. Students' answers from the survey questionnaire suggested that the geometry textbook we developed based on storytelling helped them learn mathematics and that the instruments such as a map and a set square helped them understand mathematical concepts. However, their opinion implied that the story of the textbook needed to be improved so that the story reflected more realistic contexts that were familiar with students.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.6 no.3
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• pp.247-254
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• 2006

Biometrics are getting more and more attention in recent years for security and other concerns. So far, only fingerprint recognition has seen limited success for on-line security check, since other biometrics verification and identification systems require more complicated and expensive acquisition interfaces and recognition processes. Hand-Geometry can be used for biometric verification and identification because of its acquisition convenience and good performance for verification and identification performance. It could also be a good candidate for online checks. Therefore, this paper proposes a Hand-Geometry recognition system based on geometrical features of hand. From anatomical point of view, human hand can be characterized by its length, width, thickness, geometrical composition, shapes of the palm, and shape and geometry of the fingers. This paper proposes thirty relevant features for a Hand-Geometry recognition system. This system presents verification results based on hand measurements of 20 individuals. The verification process has been tested on a size of $320{\times}240$ image, and result of the verification process have hit rate of 95% and FAR of 0.020.

• Proceedings of the KSR Conference
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• 2002.05a
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• pp.213-218
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• 2002

A new German high speed railway slab track was investigated. The construction objective was to provide a durable and maintenance free track system consisting of precast concretepanels of consistently high quality and highest achievable accuracy in track geometry. The System on the basis of precast panels similar to the slab track system constructed on the line Dachau- Karlsfeld in 1997.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.795-800
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• 2001

In this study, a program to design a multi-stage axial compressor is developed wi th mean-line analysis and vortex methods. In a preliminary design stage, a method. to design in a short time is needed and mean-line analysis is usually used for this purpose. Arbitrary pressure ratio and reaction can be assigned to generate overall geometry and several vortex methods are adopted to consider the radial distribution of velocity and reaction. The variation of performance, when we use free vortex, forced vortex, and exponential method, is compared and discussed.