• Journal of the Korean Data and Information Science Society
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• v.18 no.2
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• pp.543-552
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• 2007

We consider estimation of the right-tail probability in a half-triangle distribution, and also consider inference on reliability, and derive the k-th moment of ratio of two independent half-triangle distributions with different supports. As we define a skew-symmetric random variable from a symmetric triangle distribution about origin, we derive its k-th moment.

• Journal of the Korean Society of Costume
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• v.63 no.8
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• pp.76-89
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• 2013

This study is about 'asymmetry triangle-Mu' Jeoksam and Hansam in the early days of Joseon Dynasty. A study was done regarding the records of Jeoksam and Hansam in literature, the present state of the excavated 'asymmetry triangle-Mu' clothing Jeoksam and Hansam, and finally a deduction of the reason for the appearance of the 'asymmetry triangle-Mu' clothing Jeoksam and Hansam. The width of front length of 'asymmetry triangle-Mu' clothing in the early days of Joseon Dynasty is 29.5~35 cm and the width of one breath of the sleeve is 29.5~35 cm. The width of 'asymmetry triangle-Mu' is 9.5~16 cm and it is relatively big. Comparing to the width of one breath of the sleeve, it is almost 1:2.2~3.6 ratio. Therefore, when the sleeve was cut, the Mu was linked in order to save fabric the gusset of sleeve had to be folded and turned, and finally it became asymmetric. As a result of the above consideration, since the width of upper garments of $16{\sim}17^{th}$ century was big, the wearing of short tops of Jeoksam or Hansam without side vent as a small 'triangle-Mu' was uncomfortable. Because of this reason, the size had no option but to become bigger. So, during the $16^{th}$ and $17^{th}$ century, a period where mass production of fabric was difficult, the 'asymmetry triangle-Mu' type was considered to be a reasonable cutting method. After the middle of $17^{th}$ century, it can be estimated that 'asymmetry triangle-Mu' clothing disappeared according to the narrow aspect of clothing type.

• East Asian mathematical journal
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• v.26 no.2
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• pp.267-280
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• 2010

In this paper we study construction methods of $n^{th}$ line in triangle. Russian Mathematician Zetel suggested some construction methods of $n^{th}$ line in triangle 80 years ago. We find Zetel's papers, in detail explain the Zetel's construction methods, and suggest two elementary construction methods. Our results are received in the process of Research and Education program in science high school.

• The Mathematical Education
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• v.48 no.3
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• pp.287-302
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• 2009

This study investigated how 5th grade students found and understood triangle congruence conditions (SSS, SAS, ASA). In particular, this study focused on children's processes of discovering triangle congruence conditions and the obstacles which they encountered in the process of making sense of these conditions. Our data indicates that inquiring the cases in which less than three factors of triangle are given is helpful for children to guess triangle congruence conditions and understand the minimal characteristic of these conditions. And the degree of difficulty of discovering each congruence condition is different. Children discovered SAS condition and ASA condition easily, but it was hard for them to discover and understand that SSS was also a triangle congruence condition because they connected the length of a given side with the use of a scaled ruler not a compass.

• Journal of the Korean School Mathematics Society
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• v.13 no.2
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• pp.263-287
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• 2010

The purposes of the study were to investigate how children define a triangle, their reasoning types in identifying examples and non-examples of a triangle, and the relationship between their reasoning types and geometrical levels. Twenty-nine students consisted of 3th to 6th grades were involved in the study. Using the van Hiele levels of geometrical thought, children's reasoning types for identifying a figure as a triangle or non-triangle were categorized into visual reasoning, reasoning based on the figure's attributes and formal reasoning. The figure's attributes were further divided into critical and non-critical attributes. Most children identified a figure as a triangle or non-triangle based on critical attributes of the figure(e.g. closed figure, three, vertices, straight sides etc.) Some children identified a figure based on non-critical attributes of the figure(e.g. the length of the sides, the measurement of the angles, or the orientation of the figure). Particularly, some children who had lower levels of geometry identified a figure using visual reasoning, taking in the whole shape without considering that the shape is made up of separate components.

• Journal of the Korean School Mathematics Society
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• v.14 no.2
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• pp.227-239
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• 2011

The circumcenter of a triangle is introduced in logic geometry part of 8th grade mathematics. To handle certain characteristics of a figure through mathematical proof may involve considerable difficulty, and many students have greater difficulties especially in learning textbook's methods of proving propositions about circumcenter of a triangle. This study compares the methods how the circumcenter of a triangle is explored among the Elements of Euclid, a classic of logic geometry, current textbooks of USA and those of Korea. As a result of it, this study tries to abstract some significant implications on teaching the circumcenter of a triangle.

• Journal of the Korean Society of Costume
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• v.57 no.7
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• pp.45-52
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• 2007

This study is based on the observation of women's Jangui in 17th centuries. As we observed, Jangui in seventeenth century was shown the same style. They were not headdress but coat. The characteristics of shape are Mokpankit, double-seop, straight sleeve, triangle moo, sam-su(which is attached to the end of sleeves) and a little coat string etc. There is no specific mode difference with the change of times. However, the straight sleeve is shown straight line in the early Chosun dynasty. Jangui in seventeen century are all oblique line sleeve except Jangui of Jin-ju Ha's family. Jangui put on coat do not seem clear-cut difference with the change of times. From Jangui of Yang-chun Hu's family in 14th centuries till An-dong Kim's family, the special features of Jangui are the same style. In addition, The double-seop in 17th centuries was not completely symmetry. However, after 19th centuries, Jangui for headdress was shown perfectly symmetry.

• Journal of the Korean School Mathematics Society
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• v.10 no.3
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• pp.341-351
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• 2007

The primary purpose of this treatise is to suggest the solutions as follows for the errors concerning the triangle determination and congruence in every Korean mathematics textbook for 7th graders: showing that SsA, along with SSS, SAS, ASA, should also be included as the condition for triangle determination, congruence and similarity; proving that contrary to what has been believed, minimality applies only to congruence and similarity but not to determination; examining related Euclidean propositions; discussing the confusion about the characteristics of determination and congruence; and considering the negative effects of giving definite figures in construction education. The secondary purpose is to analyze the significance of triangle determinant that is not dealt with in either Euclid's Elements or the text books in the U.S. or Japan, and suggest a way to effectively deal with triangle determination and congruence in education.

• The Pure and Applied Mathematics
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• v.20 no.3
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• pp.207-221
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• 2013

In this work we study the tribonacci numbers. We find a tribonacci triangle which is an analog of Pascal triangle. We also investigate an efficient method to compute any $n$th tribonacci numbers by matrix method, and find periods of the sequence by taking modular tribonacci number.

• Education of Primary School Mathematics
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• v.20 no.2
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• pp.163-175
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• 2017

The purpose of the study is to identify the effect of length and right angle indication on the understanding of the concept of the figure when presenting the task of classifying the plane figures. we recorded thirty three 4th grade students' performance with eye-tracking technologies and analyzed the correct answer rate and gaze duration. The findings from the study were as follows. First, correctness rate increased and Gaze duration decreased by marking length in isosceles triangle and equilateral triangle. Second, correctness rate increased and Gaze duration decreased by marking right angle in acute angle triangle and obtuse triangle. Based on these results, it is necessary to focus on measuring the understanding of the concept of the figure rather than measuring the students' ability to measure by expressing the length and angle when presenting the task of classifying the plane figures.