• Journal of the Korean School Mathematics Society
• /
• 제17권3호
• /
• pp.359-384
• /
• 2014

The purpose of this study is inquire the reaction and adaptability of the mathematically gifted student, in the case of introduce learning materials based on GeoGebra in real class. The study program using GeoGebra consist of 'construction of fundamental figures', 'making animation with using slider tools' (graph of a function, trace of a figure, definite integral, fixed point, and draw a parametric curve), make up the group report after class. In detail, 1st to 15th classes are mainly problem-solving, and topic-exploring classes. To analyze the application effects of developed learning materials, divide students in four groups and lead them to make out their own creative products. In detail, guide students to make out their own report about mathematical themes that based on given learning materials. Concretely, build up the program to make up group report about their own topics in six weeks, after learning on various topics. Expert panel concluded that developed learning materials are successfully stimulate student's creativity in various way, after analyze of the student's activities. Moreover, those learning programs also contributed to the develop of the mathematical ability to thinking that necessary to writing a report. As well, four creative products are assessed as connote mathematically gifted student's creative thinking and meaningful elements in mathematical aspects.

• Development and Reproduction
• /
• 제20권4호
• /
• pp.289-296
• /
• 2016

This report describes the sex differentiation of the Korean rose bitterling, Rhodeus uyekii, from hatching to 170 days post-hatch (DPH) in relation to total length (TL), body weight (BW), and integral water temperature (IWT). The growth curve of TL from just hatching to 83 DPH was $5.144e^{0.045t}$ ($R^2=0.961$; t, time), and that of BW was $2.398e^{0.086t}$ ($R^2=0.725$). Primordial germ cells (PGCs) were observed at 17 DPH (7.9 mm TL, 3.74 mg BW, $374^{\circ}C$ IWT), and thereafter began to protrude into the peritoneal cavity. At 21 DPH ($9.2{\pm}0.14mm$ TL, $4.8{\pm}0.07mg$ BW, $462^{\circ}C$ IWT), some PGCs contained condensed chromatin and oocyte were observed in meiotic prophase. In contrast to the ovaries, which grew gradually after sexual differentiation, testes began multiplying at 25 DPH (10.1 mm TL, 5.42 mg BW, $550^{\circ}C$ IWT), when testicular differentiation was first identified, and multiplied continuously thereafter. At 33 DPH (11.2 mm TL, 10.5 mg BW, $726^{\circ}C$ IWT), the developing testes contained spermatogonia that exhibited mitotic activity. No spermatocyte or sperm cell was observed until 83 DPH (18.9 TL, 48.2 mg BW, $1,826^{\circ}C$ IWT). At 170 DPH (32.5 mm TL, 270.1 mg BW, $3,740^{\circ}C$ IWT), which was the end point of this study, the mature ovaries showed germinal vesicle breakdown, while the mature testes contained observable spermatocytes and sperm cells. These results allow us to identify the sex differentiation type of the Korean rose bitterling as differentiated gonochoristic.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• 제30권5호
• /
• pp.371-380
• /
• 2017

The risk-targeted seismic design concept was first included in ASCE/SEI 7-10 to address problems related to the uniform-hazard based seismic concept that has been constructed without explicitly considering probabilistic uncertainties in the collapse capacities of structures. However, this concept is not yet reflected to the current Korean building code(KBC) because of insufficient strong earthquake data occurred at the Korean peninsula and little information on the collapse capacities of structures. This study evaluates the risk-targeted seismic performance of steel ordinary concentrically braced frames(OCBFs). To do this, the collapse capacities of prototype steel OCBFs are assessed with various analysis parameters including building locations, building heights and soil conditions. The seismic hazard curves are developed using an empirical spectral shape prediction model that is capable of reflecting the characteristics of earthquake records. The collapse probabilities of the prototype steel OCBFs located at the Korean major cities are then evaluated using the risk integral concept. As a result, analysis parameters considerably influence the collapse probabilities of steel OCBFs. The collapse probabilities of taller steel OCBFs exceed the target seismic risk of 1 percent in 50 years, which the introduction of the height limitation of steel OCBFs into the future KBC should be considered.

• Journal for History of Mathematics
• /
• 제25권4호
• /
• pp.53-67
• /
• 2012

Today, it is necessary to calculate orbits with high accuracy in space flight. The key words of Poincar$\acute{e}$ in celestial mechanics are periodic solutions, invariant integrals, asymptotic solutions, characteristic exponents and the non existence of new single-valued integrals. Poincar$\acute{e}$ define an invariant integral of the system as the form which maintains a constant value at all time $t$, where the integration is taken over the arc of a curve and $Y_i$ are some functions of $x$, and extend 2 dimension and 3 dimension. Eigenvalues are classified as the form of trajectories, as corresponding to nodes, foci, saddle points and center. In periodic solutions, the stability of periodic solutions is dependent on the properties of their characteristic exponents. Poincar$\acute{e}$ called bifurcation that is the possibility of existence of chaotic orbit in planetary motion. Existence of near exceptional trajectories as Hadamard's accounts, says that there are probabilistic orbits. In this context we study the eigenvalue problem in early 20th century in three body problem by analyzing the works of Darwin, Bruns, Gyld$\acute{e}$n, Sundman, Hill, Lyapunov, Birkhoff, Painlev$\acute{e}$ and Hadamard.

• Journal of the Korean School Mathematics Society
• /
• 제24권2호
• /
• pp.173-190
• /
• 2021

This study analyzed the proof of the inverse square law, which is said to be the core of Newton's , in relation to the geometric limit. Newton, conscious of the debate over infinitely small, solved the dynamics problem with the traditional Euclid geometry. Newton reduced mechanics to a problem of geometry by expressing force, time, and the degree of inertia orbital deviation as a geometric line segment. Newton was able to take Euclid's geometry to a new level encompassing dynamics, especially by introducing geometric limits such as parabolic approximation, polygon approximation, and the limit of the ratio of the line segments. Based on this analysis, we proposed to use Newton's geometric limit as a tool to show the usefulness of mathematics, and to use it as a means to break the conventional notion that the area of the curve can only be obtained using the definite integral. In addition, to help the desirable use of geometric limits in school mathematics, we suggested the following efforts are required. It is necessary to emphasize the expansion of equivalence in the micro-world, use some questions that lead to use as heuristics, and help to recognize that the approach of ratio is useful for grasping the equivalence of line segments in the micro-world.