• Journal for History of Mathematics
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• v.21 no.4
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• pp.105-126
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• 2008

This article summarizes the historical changes of the secondary school geometry to give insights into the new direction of geometry education for the 21th century. Geometry has been considered as an essential subject in high school since mid-nineteen century in accordance with the social changes. Since the development of computer softwares such as CAD effects on the role of geometry in work and professional societies, the knowledge and skills the contemporary world require to school geometry have being changed. More focus on applications and modeling aspects, expansion of reasoning and problem solving, emphasis on design-related elements are features of the school geometry for the new century.

• The Mathematical Education
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• v.44 no.1 s.108
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• pp.1-14
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• 2005

This study analyzed the differences in the contents as well as in the methods of development and presentation of learning contents in Korean and German mathematics textbooks for middle school students. For the research we investigated only the area of geometry, and in particular this study performed in-depth analysis concerning 4 subjects; namely congruences of triangles, special points in a triangle, similarity of figures and the theorem of Pythagoras.

• Journal of the Korean Magnetic Resonance Society
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• v.19 no.3
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• pp.119-123
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• 2015

The thermodynamic properties and structural geometry of $KMgCl_3{\cdot}6H_2O$ were investigated using thermogravimetric analysis, differential scanning calorimetry, and nuclear magnetic resonance. The initial mass loss occurs around 351 K ($=T_d$), which is interpreted as the onset of partial thermal decomposition. Phase transition temperatures were found at 435 K ($=T_{C1}$) and 481 K ($=T_{C2}$). The temperature dependences of the spin-lattice relaxation time $T_1$ for the $^1H$ nucleus changes abruptly near $T_{C1}$. These changes are associated with changes in the geometry of the arrangement of octahedral water molecules.

• Research in Mathematical Education
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• v.9 no.3 s.23
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• pp.285-294
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• 2005

The author has been teaching with an instructional module consisting of many mathematical concepts, based on designs formed by personal names or words to arouse students' interesting in learning mathematics. This module has been growing since it was first used as a supplementary lesson for calculus students. Now it consists of concepts that connect with mathematical topics such as number sense, algebraic thinking, geometry, and statistical reasoning, as well as other subjects such as art and quilt design. With its content we can provide our students the basic mathematical knowledge needed for further study in their own fields. In this article, we will demonstrate the latest development of this instructional module, which makes connections between mathematical knowledge and the design of personal quilt patterns. We will exhibit a 'Quilt of Nations' which consists of the designed quilt blocks of different countries, such as USA, Japan, Taiwan, Korea and others, as well as a quilt design using the abbreviation of this seminar. Then we will talk about how the connections are built, and how to design these mathematically rich, uniquely created, beautifully designed, and personalized quilt block patterns.

• The Mathematical Education
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• v.40 no.1
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• pp.93-102
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• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• The Mathematical Education
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• v.53 no.3
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• pp.383-397
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• 2014

This study aims to explore secondary students' thinking while doing proof in geometry. Two secondary students were interviewed and the interview data were analyzed. The results of the analysis suggest that the two students similarly showed as follows: a) tendencies to use the rules of congruent and similar triangles to solve a given problem, b) being confused about the rules of similar and congruent triangles, and c) being confused about the definitions, partition and hierarchical classification of quadrilaterals. Also, the results revealed that a relatively low achieving student has tendency to rely on intuitive information such as visual representations.

• Geomechanics and Engineering
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• v.35 no.2
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• pp.181-194
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• 2023

The primary objective of this study is to examine the influence of geometry on the stability characteristics of cylindrical microstructures. This investigation entails a stability analysis of a bi-directional functionally graded (BD-FG) cylindrical imperfect concrete beam, focusing on the impact of geometry. Both the first-order shear deformation beam theory and the modified coupled stress theory are employed to explore the buckling and dynamic behaviors of the structure. The cylinder-shaped imperfect beam is constructed using a porosity-dependent functionally graded (FG) concrete material, wherein diverse porosity voids and material distributions are incorporated along the radial axis of the beam. The radius functions are considered in both uniform and nonuniform variations, reflecting their alterations along the length of the beam. The combination of these characteristics leads to the creation of BD-FG configurations. In order to enable the assessment of stability using energy principles, a numerical technique is utilized to formulate the equations for partial derivatives (PDEs).

• Education of Primary School Mathematics
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• v.18 no.1
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• pp.17-30
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• 2015

The purpose of this study is to identify how developed program influence students' creativity by analyzing creative thinking and creative attitude which is appeared when mathematically gifted students get the program expected to improve their creativity. For the study, the 'dimension based geometry exploring program' was developed that consist of twelve lessons. The main idea of it, is implication of the novel . Through a pre and post-test, students's creativity were measured and compared. The results show significant changes on the scores of creative thinking skills and creative attitudes. As the result, mathematically gifted students' creative thinking skills and creative attitudes were improved by applying the of dimension based geometry exploring program.

• Journal of Educational Research in Mathematics
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• v.11 no.2
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• pp.403-419
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• 2001

The axiomatic geometry unit of the space figure in Mathematics II in the expository book of high school math curriculum (published by Ministry of Education, June 20, 1995) suggests some teaching points to bear in mind, so as not to make use of the system of axiom. However, it doesn't take the axiom about the space geometry as a starting point of argument, and so many textbooks can be found, in which intuitively true propositions are proved acceptable by the logical ambiguous statements. Thus, this study analyzes the contents of axiomatic geometry in high school math II textbooks and draws their problems. As an alternative improvement, 3 kinds of axiom on the space geometry and some important propositions, which are basic to proofs of proposition, will be presented here in this paper.

• Journal of the Korean Chemical Society
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• v.36 no.2
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• pp.169-173
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• 1992

The surface geometry of o-diiodobenzene (ODIB) adsorbed on silver colloid surfaces has been studied. This molecule is standing up on 1 day old colloid surfaces, while it is lying down or standing up on 1 month old colloid surfaces. The surface geometry of ODIB is affected by the atomic scale surface roughness of colloid used. The SERS intensity of ODIB for lying down geometry is much more strong than that for standing up. This may be mainly due to that the distance from surface to the center of the molecule in lying down geometry is shorter than that in standing up.