• 대한수학회보
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• 제52권3호
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• pp.925-933
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• 2015

It is well-known that the area of parabolic region between a parabola and any chord $P_1P_2$ on the parabola is four thirds of the area of triangle ${\Delta}P_1P_2P$. Here we denote by P the point on the parabola where the tangent is parallel to the chord $P_1P_2$. In the previous works, the first and third authors of the present paper proved that this property is a characteristic one of parabolas. In this paper, with respect to triangles ${\Delta}P_1P_2PQ$ where Q is the intersection point of two tangents to X at $P_1$ and $P_2$ we establish some characterization theorems for parabolas.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.583-595
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• 2016

Archimedes showed that for a point P on a parabola X and a chord AB of X parallel to the tangent of X at P, the area S of the region bounded by the parabola X and chord AB is four thirds of the area T of triangle ${\Delta}ABP$. It is well known that the area U formed by three tangents to a parabola is half of the area T of the triangle formed by joining their points of contact. Recently, the first and third authors of the present paper and others proved that among strictly locally convex curves in the plane ${\mathbb{R}}^2$, these two properties are characteristic ones of parabolas. In this article, in order to generalize the above mentioned property $S={\frac{4}{3}}T$ for parabolas we study strictly locally convex curves in the plane ${\mathbb{R}}^2$ satisfying $S={\lambda}T+{\nu}U$, where ${\lambda}$ and ${\nu}$ are some functions on the curves. As a result, we present two conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open arc of a parabola.

• 한국전자파학회논문지
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• 제14권8호
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• pp.787-795
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• 2003

본 논문에서는 무궁화 3호 위성방송을 수신하기 위한 3종류의 배열 안테나가 제작되었다. 먼저 무궁화 3호 위성을 수신하기 위한 설계규격을 결정하였다. 두 번째로 위성 수신을 위한 다양한 종류의 안테나 중 radial waveguide의 특성을 이용한 안테나의 특성과 장점을 알아보았다. 세 번째로 3 종류의 안테나의 설계 방법을 연구하고, 각각의 특성을 고찰한 다음 설계규격을 만족하는 안테나를 제작, 측정하였다. 마지막으로 기존 parabola 안테나와 마이크로스트립 배열 안테나와 비교하여 제한된 크기에서 최대의 이득과 효율을 나타내는 안테나에 대해 결론을 내렸다.

• 한국소음진동공학회논문집
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• 제12권1호
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• pp.82-88
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• 2002

This paper deals with the free vibrations of horizontally curved beams with transition curve. Based on the dynamic equilibrium equations of a curved beam element subjected to the stress resultants and inertia forces, the governing differential equations are derived for the out-of-plane vibration of curved beam wish variable curvature. This equations are applied to the beam having transition curve in which the third parabolic curve is chosen in this study. The differential equations are solved by the numerical procedures for calculating the natural frequencies. As the numerical results, the various parametric studies effecting on natural frequencies are investigated and its results are presented in tables and figures. Also the laboratory scaled experiments were conducted for verifying the theories developed herein.

• East Asian mathematical journal
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• 제30권4호
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• pp.451-474
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• 2014

The purpose of this study is to analyze error patterns third-year middle school students make on quadratic function graph problems and to examine about the possible correct them by providing supplementary tutoring. To exam the error patterns that occur during problem solving processes, to 82 students, We provided 25 quadratic function graph problems in the preliminary-test. The 5 types of errors was conceptual errors, false intuition errors, incorrect use of conditions in problems, technical errors, and errors from slips or carelessness. Statistical analysis of the preliminary-test and post-test shows that achievement level was higher in the post-test, after supplementary tutoring, and the t-test proves this to be meaningful data. According to the per subject analyses, the achievement level in the interest of symmetry, parallel translation, and general graph, respectively, were all higher in the post-test than the preliminary-test and this is meaningful data as well. However, no meaningful relation could be found between the preliminary-test and the post-test on other subjects such as graph remodeling and relations positions of the parabola. For the correction of errors, try the appropriate feedback and various teaching and learning methods.

• 한국멀티미디어학회논문지
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• 제20권12호
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• pp.1992-1999
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• 2017

This study proposes a decorative typeface which is produced through the concept of trigonometric functions in an open-source programming language known as Processing. First, the theoretical background of Processing and trigonometric functions as well as previous research in this area are analyzed. Second, basic modules of 'V', 'I', 'O', and 'M' were created for use as the final alphabet typeface with the concept of a trigonometric function. Third, a decorative parabolic curve that encircles the base module was created. Finally, the modules created on Processing were edited in Adobe Illustrator to create a typeface set with characters from A to Z. Various artworks using Programming can produce an infinite number of different versions by modifying only some of the variables and codes, and this method can include multimedia features such as text, images, videos, interactive art and various forms of content and media. Therefore, with regard to expression, the possibilities are endless. In this study, I attempt to expand the field of visual culture using programming and computational methodologies. In contrast to the digital typeface production method, which relies on existing graphic tools, this study is meaningful because it expands the range of use of decorative typefaces.

• 천문학회지
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• 제55권1호
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• pp.1-9
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• 2022

We present the photometric properties of V608 Cas from detailed studies of light curves and eclipse timings. The light curve synthesis indicates that the eclipsing pair is an overcontact binary with parameters of ∆T = 155 K, q = 0.328, and f = 26%. We detected the third light ℓ₃, which corresponds to about 8% and 5% of the total systemic light in V and R bands, respectively. Including our 6 timing measurements, a total of 38 times of minimum light were used for a period study. It was found that the orbital period of V608 Cas has varied in some combination of an upward parabola and two periodic variations. The continuous period increase with a rate of +3.99 × 10^-7 d yr^-1 can be interpreted as a mass transfer from the secondary component to the primary star at a rate of 1.51 × 10^-7 M_⊙ yr^-1. The periods and semi-amplitudes of the two periodic variations are about P₃ = 16.0 yr and P₄ = 26.3 yr, and K₃ = 0.0341 d and K₄ = 0.0305 d, respectively. The most likely explanation of both cycles is a pair of light-traveling time effects operated by the possible presence of third and fourth components with estimated masses of M₃ = 2.20 M_⊙ and M₄ = 1.27 M_⊙ in eccentric orbits of e₃ = 0.66 and e₄ = 0.52. Because the contribution of ℓ₃ is very low compared to the estimated masses of two circumbinary objects, they can be inferred as very faint compact objects.

• Journal of Astronomy and Space Sciences
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• 제28권3호
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• pp.163-172
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• 2011

An intensive analysis of 185 timings of WZ Cep, including our new three timings, was made to understand the dynamical picture of this active W UMa-type binary. It was found that the orbital period of the system has complexly varied in two cyclical components superposed on a secularly downward parabola over about 80y. The downward parabola, corresponding to a secular period decrease of $-9.{^d}97{\times}10^{-8}y^{-1}$, is most probably produced by the action of both angular momentum loss (AML) due to magnetic braking and mass-transfer from the massive primary component to the secondary. The period decrease rate of $-6.^{d}72{\times}10^{-8}y^{-1}$ due to AML contributes about 67% to the observed period decrease. The mass flow of about $5.16{\times}10^{-8}M_{\odot}y^{-1}$ from the primary to the secondary results the remaining 33% period decrease. Two cyclical components have an $11.^{y}8$ period with amplitude of $0.^{d}0054$ and a $41.^{y}3$ period with amplitude of $0.^{d}0178$. It is very interesting that there seems to be exactly in a commensurable 7:2 relation between their mean motions. As the possible causes, two rival interpretations (i.e., light-time effects (LTE) by additional bodies and the Applegate model) were considered. In the LTE interpretation, the minimum masses of $0.30M_{\odot}$ for the shorter period and $0.49M_{\odot}$ for the longer one were calculated. Their contributions to the total light were at most within 2%, if they were assumed to be main-sequence stars. If the LTE explanation is true for the WZ Cep system, the 7:2 relation found between their mean motions would be interpreted as a stable 7:2 orbit resonance produced by a long-term gravitational interaction between two tertiary bodies. In the Applegate model interpretation, the deduced model parameters indicate that the mechanism could work only in the primary star for both of the two period modulations, but could not in the secondary. However, we couldn't find any meaningful relation between the light variation and the period variability from the historical light curve data. At present, we prefer the interpretation of the mechanical perturbation from the third and fourth stars as the possible cause of two cycling period changes.

• Journal of Astronomy and Space Sciences
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• 제22권2호
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• pp.113-124
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• 2005

두개의 식쌍성 V343 Aql 와 CX Aqr 의 가능한 모든 극심시각을 수집하여 두별의 공전 주기변화를 연구하였다 . 그 결과 두 별의 공전주기는 모두 포물선 모양의 영년 변화 위에 주기적인 항이 겹쳐 변화한다. V343 Aql 은 $-261{\times}10^{-7}$ d/y의 영년 주기감소를, 반면 CX Aqr 은 $+2.55{\times}10^{-8}$d/y의 영년 주기증가를 보인다. 두 별의 영년 주기변화의 가능한 원인들에 대하여 논의하였다. 공전주기의 주기적인 변화의 원인을 제3천체에 의한 광시간 효과로 해석하였다. 광시간 궤도의 주기, 반 진폭과 이심율은 V343 Aql인 경우, 각각 30.3 년, 0.0092 일, 그리고 0.85이며, 반면 CX Aqr인 경우, 각각 33.0년, 0.0037일, 그리고 0.64으로 계산되었다. V343 Aql 와 CX Aqr계에 제안된 제3천체의 성질들이 논의된다.

• Journal of Astronomy and Space Sciences
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• 제23권2호
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• pp.105-116
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• 2006

근접촉쌍성 EG Cep의 8개의 새로운 극심 시각을 제시하였다. 우리의 관측치를 포함한 EG Cep의 관측된 모든 극심시각을 수집하여 이 별의 공전 주기변화를 연구하였다. 그 결과 EG Cep의 공전주기는 위로 향한 포물선 모양의 영년 변화 위에 주기적인 항이 겹쳐 변화한다는 것을 발견하였다. 관측된 영년 주기 증가량은 약 $3.22{\times}10^{-8}d/y$이며, 보존적인 질량이동을 가정하면, 이는 매년 약 $3.18{\times}10^{-8}M_{\odot}$의 항성 가스가 질량이 작은 반성으로부터 주성으로 이동하고 있음을 의미한다. 공전주기의 주기적인 변화의 원인을 제3천체에 의한 광시간 효과로 해석하였다. 광시간 궤도의 주기, 반진폭과 이심율은, 각각 38.4년, 0.0034일, 그리고 0.29이다. EG Cep계에 제안한 제3천체의 질량 범위는 $i_3{\geq}30^{\circ}$일 때 $0.10M_{\odot}{\leq}M_3{\leq}0.21M_{\odot}$으로 상당히 작다.