• Journal for History of Mathematics
• /
• v.15 no.1
• /
• pp.115-134
• /
• 2002

The increasing use of computers in mathematics and in mathematics education is strongly reflected in the teaching on Euclid geometry, in particular in the use of dynamic graphics software. This development has raised questions about the role of analytic proof in school geometry. One can sometimes find a proof which is rather more explanatory than the one commonly used. Because we, math educators are concerned with tile explanatory power of the proofs, as opposed to mere verification, we should devise ways to use dynamic software in the use of explanatory proofs.

• Journal of the Korean School Mathematics Society
• /
• v.13 no.2
• /
• pp.225-241
• /
• 2010

Even though geometry is an important part basic to mathematics, studies on the program designs and teaching strategies of geometry are insufficient. The aims of this study are to propose the model of program design for autonomous learners taking their characteristics of the mathematically gifted into consideration. The core of teaching materials are analytic geometry and projective geometry. And the new teaching strategy will introduce three steps ; a draft strategies step(problem presentation, problem solving), a supportive strategies step(abstraction of a mathematical concept, mathematical induction, and extension), a transference strategies step to teaching strategy suitable for mathematically gifted. As a result, this study will suggest the effective methods of geometry teaching for the mathematically gifted.

• Journal for History of Mathematics
• /
• v.21 no.2
• /
• pp.39-54
• /
• 2008

This paper investigate Descartes' , which is significant in the history of mathematics, from standpoint of problem-solving. Descartes has clarified the general principle of problem-solving. What is more important, he has found his own new method to solve confronting problem. It is said that those great achievements have exercised profound influence over following generation. Accordingly this article analyze Descartes' work focusing his method.

• East Asian mathematical journal
• /
• v.37 no.4
• /
• pp.499-521
• /
• 2021

This research is devoted to investigate Omar Khayyām's geometric solution for the cubic equation using conic sections in the Medieval Islam as a useful alternative connecting logic geometry with analytic geometry at a secondary school. We also introduce Omar Khayyām's 25 cases classification of the cubic equation with all positive coefficients. Moreover we study 6 cases with 4 terms of 25 cubic equations and in particular we reinterpret geometric methods of solving in 2015 secondary Mathematics curriculum and visualize them by means of dynamic geometry software.

• Proceedings of the Korean Nuclear Society Conference
• /
• 1996.05a
• /
• pp.131-136
• /
• 1996

An analytic nodal expansion method has been derived for the multigroup neutron diffusion equation in 2-D cylindrical(R-Z) coordinate. In this method we used the second order Legendre polynomials for source, and transverse leakage, and then the diffusion eqaution was solved analytically. This formalism has been applied to 2-D LWR model. $textsc{k}$$_{eff}$, power distribution, and computing time have been compared with those of ADEP code(finite difference method). The benchmark showed that the analytic nodal expansion method in R-Z coordinate has good accuracy and quite faster than the finite difference method. This is another merit of using R-Z coordinate in that the transverse integration over surfaces is better than the linear integration over length. This makes the discontinuity factor useless.s.

• Journal of Institute of Control, Robotics and Systems
• /
• v.5 no.8
• /
• pp.955-960
• /
• 1999

This paper describes the effect of impact configurations on a single robot manipulator. The effect of different configurations of kinematically redundant arms on impact forces at their end effectors during contact with the environment is investigated. Instead of the well-known impact ellipsoid, I propose an analytic method on the geometric configuration of the impact directly from the mathematical definition. By calculating the length along the specified motion direction and volume of the geometry, we can determine the characteristics of robot configurations in terms of both the impact along the specified direction and the ability of the robot withstanding the impact. Simulations of various impact configurations are discussed at the end of this paper.

• East Asian mathematical journal
• /
• v.28 no.4
• /
• pp.453-474
• /
• 2012

The conic sections is an important topic in the current high school geometry. It has been recognized by many researchers that high school students often have difficulty or misconception in the learning of the conic sections because they are taught the conic sections only with algebraic perspective or analytic geometry perspective. In this research, we suggest a way of teaching the conic sections using a dynamic geometry software based on some mathematics teaching and learning theories such as Freudenthal's and Dienes'. Students have various experience of constructing and manipulating the conic sections for themselves and the experience of deriving the equations of the quadratic curves under the teacher's careful guidance. We identified this approach was a feasible way to improve the teaching and learning methods of the conic sections.

• 한국지구물리탐사학회:학술대회논문집
• /
• 2003.11a
• /
• pp.238-243
• /
• 2003

As there are many advantages on underground caverns, such as safety and operation, they can also be used for gas storage purpose. When liquefied gas is stored underground, the cryogenic temperature of the gas will affect the stability of the storage cavern. In order to store the liquefied gas successfully, it is essential to estimate the exact temperature distribution of the rock mass around the cavern. In this study, an analytic solution and a conceptual model that can estimate three-dimensional temperature distribution around the storage cavern are suggested. When calculating the heat transfer within a solid, it is likely to consider the solid as the intersection of two or more infinite or semi-infinite geometries. Therefore heat transfer solution for the solid is expressed by the product of the dimensionless temperatures of the geometries, which are used to form the combined solid. Based on the multi-dimensional transient heat transfer theory, the analytic solution is successfully derived by assuming the cavern shape to be of simplified geometry. Also, a conceptual model is developed by using the analytic solution of this study. By performing numerical experiments of this multi-dimensional model, the temperature distribution of the analytic solution is compared with that of numerical analysis and theoretical solutions.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.18 no.4
• /
• pp.308-320
• /
• 2006

An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.

• Biomedical Engineering Letters
• /
• v.8 no.4
• /
• pp.383-392
• /
• 2018

For prompt gamma ray imaging for biomedical applications and environmental radiation monitoring, we propose herein a multiple-scattering Compton camera (MSCC). MSCC consists of three or more semiconductor layers with good energy resolution, and has potential for simultaneous detection and differentiation of multiple radio-isotopes based on the measured energies, as well as three-dimensional (3D) imaging of the radio-isotope distribution. In this study, we developed an analytic simulator and a 3D image generator for a MSCC, including the physical models of the radiation source emission and detection processes that can be utilized for geometry and performance prediction prior to the construction of a real system. The analytic simulator for a MSCC records coincidence detections of successive interactions in multiple detector layers. In the successive interaction processes, the emission direction of the incident gamma ray, the scattering angle, and the changed traveling path after the Compton scattering interaction in each detector, were determined by a conical surface uniform random number generator (RNG), and by a Klein-Nishina RNG. The 3D image generator has two functions: the recovery of the initial source energy spectrum and the 3D spatial distribution of the source. We evaluated the analytic simulator and image generator with two different energetic point radiation sources (Cs-137 and Co-60) and with an MSCC comprising three detector layers. The recovered initial energies of the incident radiations were well differentiated from the generated MSCC events. Correspondingly, we could obtain a multi-tracer image that combined the two differentiated images. The developed analytic simulator in this study emulated the randomness of the detection process of a multiple-scattering Compton camera, including the inherent degradation factors of the detectors, such as the limited spatial and energy resolutions. The Doppler-broadening effect owing to the momentum distribution of electrons in Compton scattering was not considered in the detection process because most interested isotopes for biomedical and environmental applications have high energies that are less sensitive to Doppler broadening. The analytic simulator and image generator for MSCC can be utilized to determine the optimal geometrical parameters, such as the distances between detectors and detector size, thus affecting the imaging performance of the Compton camera prior to the development of a real system.