• Journal of applied mathematics & informatics
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• v.23 no.1_2
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• pp.321-327
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• 2007

We say that a triangle ${\Delta}$ tiles the polygon ${\rho}\;if\;{\rho}$ can be decomposed into finitely many non-overlapping triangles similar to ${\Delta}$. Let ${\rho}$ be a parallelogram with angles ${\delta}\;and\;{\pi}-{\delta}\;(0<{\delta}{\leq}{\pi}/2)$ and let ${\Delta}$ be a triangle with angles ${\alpha};{\beta},\;{\gamma}\;({\alpha}{\leq}{\beta}{\leq}{\gamma})$. We prove that if ${\Delta}$ tiles ${\rho}$ then either ${\delta}{\in}\;({\alpha},\;{\beta},\;{\gamma},\;{\pi}-{\gamma},\;{\pi}-2{\gamma})\;or\;dimL_{\rho}=dimL_{{\Delta}}$. We also prove that for every parallelogram P, and for every integer n $(where\;n{\geq}2,\;n{\neq}3)$ there is a triangle ${\Delta}$ so that n similar copies of ${\Delta}\;tile\;{\rho}$.

• Archives of Craniofacial Surgery
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• v.22 no.3
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• pp.161-163
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• 2021

The soft tissue triangle is an easily recognizable subunit of the nose. Therefore, deformities in this region resulting from trauma or complications after cosmetic surgery can have serious cosmetic impacts. Various reconstruction choices exist for deformities such as depression of the soft triangle but choosing the most appropriate treatment in each case remains a challenge. In the case described herein, a patient underwent augmentation rhinoplasty with a silastic implant and experienced implant exposure in the soft triangle area. After implant removal, the patient complained of depression in this area. The authors effectively solved this problem through a de-epithelialized composite tissue graft. In this report, we present this case and review similar cases of reconstruction of the soft triangle.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.275-286
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• 2015

It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. In this article, we consider whether this property and similar ones characterizes parabolas. As a result, we present three conditions which are necessary and sufficient for a strictly convex curve in the plane to be an open part of a parabola.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.343-350
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• 2005

In this paper we prove two results about tilings of orthogonal polygons. (1) P be an orthogonal polygon with rational vertex coordinates and let R(u) be a rectangle with side lengths u and 1. An orthogonal polygon P can be tiled with similar copies of R(u) if and only if u i algebraic and the real part of each of its conjugates is positive; (2) Laczkovich proved that if a triangle $\Delta$ tiles a rectangle then either $\Delta$ is a right triangle or the angles of $\Delta$ are rational multiples of $\pi$. We generalize the result of Laczkovich to orthogonal polygons.

• East Asian mathematical journal
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• v.31 no.4
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• pp.459-481
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• 2015

In this study, we investigated whether the theorem is established even if we replace a 'square' element in the Euclidean proof of the Pythagorean theorem with different figures. At this time, we used different figures as equilateral, isosceles triangle, (mutant) a right triangle, a rectangle, a parallelogram, and any similar figures. Pythagorean theorem implies a relationship between the three sides of a right triangle. However, the procedure of Euclidean proof is discussed in relation between the areas of the square, which each edge is the length of each side of a right triangle. In this study, according to the attached figures, we found that the Pythagorean theorem appears in the following three cases, that is, the relationship between the sides, the relationship between the areas, and one case that do not appear in the previous two cases directly. In addition, we recognized the efficiency of Euclidean proof attached the square. This proving activity requires a mathematical process, and a generalization of this process is a good material that can experience the diversity and rigor at the same time.

• The Journal of the Korea Contents Association
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• v.14 no.3
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• pp.113-124
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• 2014

Ah! My Goddess has impressive narrative structure including a "narrative as a discourse," a "narrative as a story" and a "narrative by narrator": in a narrative as a discourse, North and South Korean soldiers make friendship; in a narrative by a narrator, main characters (including Sun-ho, Seok-gu, Ju-hwa, Chang-seop and Dong-hyeon) appear in the outer story and narrate the inner story of characters (including Dong-hyeon, Goddess and Seok-gu) within the frame of a play within a play; and in a narrative as a story, reality and fantasy intersect by the appearance of the "Goddess." This narrative structure contributes largely to 1) the character formation of space, 2) the strategic minimization of the stage, 3) the multiplicity of main characters, 4) the repetition of similar life story, and 5) the flexible change of a point of view. And the musical number serves as dramatic functions such as 1) pursuing the multiplicity of characters, 2) maximizing the effect of the expression of tragic feelings, 3) drawing audience's interest by irony and fantasy, 4) evoking the nostalgia for delicate feelings and pure wishes, and 5) ordinary female characters' playing the role of healing and salvation, thereby contributing to the reconstruction of reality and the style of fantasy.

• Journal of the Korean Academy of Esthetic Dentistry
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• v.7 no.1
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• pp.28-31
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• 1998

It is difficult to make an artificial central incisor similar to natural tooth. All ceramic porcelain of this patient is not esthetic, and there is gingival recession due to ill-fitted margin. She has class II division 1 occlusion, so upper central incisors is labioversed. Upper light central incisor is well-characterized but the yellowish brown color of dentin is appeared on the incisal third portion of the central incisor. At 1st trial, the shape and characterization of restoration is good but shade is little dark. At 2nd trial, the shape is better but patient complained on black triangle of mid interdental space, so mesiocervical portion of restoration is overcontoured to compromise the black triangle. Completed metal ceramic crown is in harmony with the adjacent central incisor in aspect of shape, shade, and characterization.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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• pp.39-48
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• 2005

A convex region covers a family of curves if it contains a congruent copy of each curve in the family, and a 'worm problem' for that family is to find the convex region of smallest area. In this paper, we find the smallest triangular cover of any prescribed shape for the family S of all triangles of diameter 1.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2103-2114
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• 2013

Archimedes knew that the area between a parabola and any chord AB on the parabola is four thirds of the area of triangle ${\Delta}ABP$ where P is the point on the parabola at which the tangent is parallel to AB. We consider whether this property (and similar ones) characterizes parabolas. We present five conditions which are necessary and sufficient for a strictly convex curve in the plane to be a parabola.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1597-1617
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• 2017

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely many non-similar integer Sharygin triangles.