• The Mathematical Education
• /
• v.38 no.2
• /
• pp.179-187
• /
• 1999

Math teachers are very short of computer tools and manipulatives to use in geometry classes of middle schools for the development of spatial abilities. At most they can ask student to make regular polyhedrons for helping the students to understand by concrete experience, but this experience is not enough to develop spatial abilities in spatial figures including the regular polyhedrons. This article is to introduce instructional materials for development of spatical ability in the regular polyhedrons using computer software, Geometer's Sketchpad. In this article, students can imagine the whole figure through the parts of a plane figure and think of the parts from the solid figure by free movement from 2 dimensions to 3 dimensions, or from 3 dimensions to 2 dimensions. Also, the instructional materials devised in this article will be good to enhance spatial abilities because the relation of 1-1 correspondence in the movement of the parts can be conserved and observed precisely, which is very hard to demonstrate and visualize by paper-and-pencil. It is recommended that this kind of materials should be developed in various ways for teachers to use them directly in their geometry classes.

• The Mathematical Education
• /
• v.6 no.2
• /
• pp.1-9
• /
• 1968

In mathematics, a definition must have authentic reasons to be defined so. On defining geometric figures, there must be adequencies in sequel and consistency in the concepts of figures, though the dimensions of them are different. So we can avoid complicated thoughts from the study of geometric property. From the texts of SMSG, UICSM and others, we can find easily that the same concepts are not kept up on defining some figures such as ray and segment on a line, angle and polygon on a plane, and polyhedral angle and polyhedron on a 3-dimensionl space. And the measure of angle is not well-defined on basis of measure theory. Moreover, the concepts for interior, exterior, and frontier of each figure used in these texts are different from those of general topology and algebraic topology. To avoid such absurdness, I myself made new terms and their definitions, such as 'gan' instead of angle, 'polygonal region' instead of polygon, and 'polyhedral solid' instead of polyhedron, where each new figure contains its interior. The scope of this work is hmited to the fundamental idea, and it merely has dealt with on the concepts of measure, dimension, and topological property. In this case, the measure of a figure is a set function of it, so the concepts of measure is coincided with that of measure theory, and we can deduce the topological property for it from abstract stage. It also presents appropriate concepts required in much clearer fashion than traditional method.

• The Mathematical Education
• /
• v.58 no.2
• /
• pp.283-298
• /
• 2019

Among the measurement attributes included in the elementary school mathematics curriculum, perimeter, area, volume and surface area are intensively covered in fifth and sixth graders. However, not much is known about the level of student performance and difficulties in this area. The purpose of this study is to examine the understanding and performance of sixth-grade elementary school students on some ideas of measurement and ultimately to give some suggestions for teaching measurement and the development of mathematics textbooks. For this, diagnosis questions were developed in relation to the following parts: measurement of perimeter and area of plane figure, measurement of surface area and volume of solid figure, and the relationships between perimeter and area, and the relationships between surface area and volume. The performances of 95 sixth graders were analyzed for this study. The results showed children's low performance in the measurement area, especially measurement of perimeter and surface area, and relationship of the measurement concepts. Finally, we proposed the introduction order of the measurement concepts and what should be put more emphasis on teaching measurement. Specifically, it suggested that we consider placing a less demanding concept first, such as the area and volume, and dealing more heavily with burdensome tasks such as the perimeter and surface area.

• Proceedings of the KSME Conference
• /
• 2007.05a
• /
• pp.1383-1388
• /
• 2007

Accuracy and processing time are very important factors when the desired shape is fabricated with Selective Laser Sintering (SLS), one of Solid Freeform Fabrication (SFF) systems. In a conventional SLS process, laser spot size is fixed during laser exposing on the sliced figure. Therefore, it is difficult to accurately and rapidly fabricate the desired shape. In this paper, to deal with those problems an SFF system having ability of changing spot size is developed. The system provides high accuracy and optimal processing time. Specifically, a variable beam expander is employed to adjust spot size for different figures on a sliced shape. Finally, Design and performance estimation of the SFF system employing a variable beam expander are achieved and the mechanism will be addressed to measure the real spot size generated from the variable beam expander.

• Journal of Powder Materials
• /
• v.3 no.4
• /
• pp.253-259
• /
• 1996

The efficiency of thermoelectric devices for different applications is known to depend on the thermoelectric effectiveness of the material which tends to grow with the increase of its chemical homogeneity. Thus an important goal for thermal devices is to obtain chemically homogeneous solid solutions. In this work, the new process with rapid solidification (melt spinning method) followed by hot pressing was investigated to produce homogeneous material. Characteristics of the material were examined with HRD, SEM, EPMA-line scan and bending test. Property variations of the materials were investigated as a function of variables, such as dopant ${CdCl}_{2}$ quantity and hot pressing temperature. Quenched ribbons are very brittle and consist of homogeneous $Bi_2Te_3$, ${Bi}_{2}{Se}_{3}$ solid solutions. When the process parameters were optimized, the maximum figure of merit was 2.038$\times$$10^{-3}K^{-4}. The bending strength of the material hot pressed at 50$0^{\circ}C$ was 8.2 kgf/${mm}^2$.

• Proceedings of the KSME Conference
• /
• 2000.04b
• /
• pp.637-643
• /
• 2000

The shrouded corotating disk flow has a simple figure on geometric basis, but has various and complicated forms of flow. this complicated flows can be variously applied to not only information storage device, but also turbomachinery which is greatly influenced by centrifugal force. This study measured its velocity to measure inner flow field with unique flow field univluenced, using LDV and subminiature hot-wire. The result of experiment shows that distribution limits of solid body rotation region, dimensionless velocity gradient and distribution limits of disk surface boundary layer(Ekman layer) are changed by the gap of disks and rotating speed. Circulating vortex which is near the shroud is effected by the gap of disks and rotating speed.

• The Journal of The Korea Institute of Intelligent Transport Systems
• /
• v.5 no.1 s.9
• /
• pp.13-19
• /
• 2006

In this paper, a broadband Microwave Power Module(MPM) operating at 7 - 11 GHz is designed and fabricated. The MPM consists of a SSA (Solid State Amplifier) and a conventional TWT (traveling Wave Tube). This combined module takes advantage of a low noise and high gain of SSA. The computer modeling and simulation of the SSA are designed by the use of the ADS (Advanced Design System) software. The SSA is designed by configurating the CSSDA (Cascaded Single Stage Distributed Amplifier). The broadband MPM is measured to be noise figure 8.3 - 10.02 dB at 7 - 11 GHz bandwidth, output power of 38.12 dBm at 9 GHz.

• Journal of Powder Materials
• /
• v.3 no.4
• /
• pp.246-252
• /
• 1996

$Bi_{2}Te_{3}-Sb_{2}Te_{3}$, $Bi_{2}Te_{3}-Bi_{2}Se_{3}$ solid solutions are of great interest as materials for thermoelectric energy conversion. One of the key technologies to ensure the efficiency of thermoelectric device is to obtain chemically homogeneous solid solutions. In this work, the new process with rapid solidification followed by hot pressing was investigated to produce homogeneous thermoelectric materials. Characteristics of the materials were examined with XRD, SEM, EPMA-line scan and bending test. Property variations of the materials were investigated as a function of variables, such as excess Te quantity and hot pressing temperature. Quenched ribbons are very brittle and consisted of homogeneous $Bi_{2}Te_{3}$, $Sb_{2}Te_{3}$ solid solutions. When the process parameters were optimized, the maximum figure of merit was 3.073$\times$$10^{-3}K^{-4}$. The bending strength of the material, hot pressed at 45$0^{\circ}C$, was 5.87 kgf/${mm}^2$.

• Journal of Educational Research in Mathematics
• /
• v.18 no.1
• /
• pp.81-101
• /
• 2008

This study points out that the way of teaching varies according to the kinds of figures in explaining the volume and the surface area of solid figures in the seventh grade curriculum. Especially, the study discusses the limitation of the explanation depending on the experimental method using physical objects. Considering the study of Archimedes' research about measuring sphere, we investigate its educational implications and, based on this result, suggest the complementary approach and the considerations for applying to current school mathematics curriculum.

• Journal of Elementary Mathematics Education in Korea
• /
• v.22 no.2
• /
• pp.199-220
• /
• 2018

This is a traditional education content that has been consistently handled in elementary school mathematics textbooks since the first curriculum in Korea. It has been mainly used to find out the properties of the solid figure or to save the surface area. However, as the importance of spatial ability is increasingly emphasized, the nets of solids can be a very suitable learning material for dealing with the spatial ability. Therefore, in this study, we examined how the nets of solids were taught in elementary school mathematics curriculum and textbooks in Korea, and based on the analysis, we analyzed the contents of the nets of solids covered in textbooks of Japan, Singapore, Finland and Hong Kong. Through this study, we suggested the enhancement of activities to find the right nets, the presentation of solid figure from various angles, and the nets of solids with patterns for improvement of spatial visualization and spatial orientation.