• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.925-933
• /
• 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
• /
• v.56 no.2
• /
• pp.583-595
• /
• 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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
• /
• v.14 no.8
• /
• pp.787-795
• /
• 2003

Three types of array antennas are developed for broadcasting band of Koreasat III. First, the specification of the array antenna is decided. Second, characteristics and advantages of three types of antennas using the radial waveguide characteristics is investigated and discussed. Third, design method fur those antenna is studied to meet antenna specifications, and then antennas are designed and tested. Finally, it is concluded that these types of antennas can be efficiently design compared to both parabola antennas and microstrip array within the limited size.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.1
• /
• pp.82-88
• /
• 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
• /
• v.30 no.4
• /
• pp.451-474
• /
• 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.

• Journal of Korea Multimedia Society
• /
• v.20 no.12
• /
• pp.1992-1999
• /
• 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.

• Journal of The Korean Astronomical Society
• /
• v.55 no.1
• /
• pp.1-9
• /
• 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
• /
• v.28 no.3
• /
• pp.163-172
• /
• 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
• /
• v.22 no.2
• /
• pp.113-124
• /
• 2005

All times of minimum light for two eclipsing binaries V343 Aql and CX Aqr were collected and analyzed to study their orbital period variations. It was found that the orbital periods for both stars have varied in a cyclical way superposed on a parabola. A secular period decrease of $-261{\times}10^{-7}$ d/y for V343 Aql was calculated while CX Aqr showed a secular period increase of $+2.55{\times}10^{-8}$8 d/y. Possible causes of secular period variations for two systems were discussed. The cyclical period variation was interpreted as light-time effect due to a third body. The resultant period, semiamplitude and eccentricity of the light time orbit were calculated to be 30.3y, 0.0092d and 0.85, respectively, for V343 Aql and 33.0y, 0.0037d and 0.64, respectively, for CX Aqr. The properties of the third bodies suggested in V343 Aql and CX Aqr systems were discussed.

• Journal of Astronomy and Space Sciences
• /
• v.23 no.2
• /
• pp.105-116
• /
• 2006

New eight times of minimum light of the near-contact binary EG Cep were presented. All times of minimum light for EG Cep, including ours, were collected and analyzed to study it's orbital period variation. It was found that the orbital period have varied in a cyclical way superposed on an upward parabola. A secular period increase of $3.22{\times}10^{-8}d/y$ was calculated. Under the assumption of a conservative mass transfer, it implied that the stellar gaseous material of about $3.18{\times}10^{-8}M_{\odot}$ /year is transferring from the less massive secondary component to the primary. The cyclical period variation was interpreted as light-time effect due to an unseen third body in the system. The resultant period, semi-amplitude and eccentricity of the light time orbit were calculated to be $38.^y4,\;0.^d0034$ and 0.29, respectively. The mass range of the tertiary proposed in the system is deduced to be quite small as $0.10M_{\odot}{\leq}M_3{\leq}0.21M_{\odot}$ for $i_3{\geq}30^{\circ}$.