• KIPS Transactions on Software and Data Engineering
• /
• v.8 no.10
• /
• pp.421-426
• /
• 2019

In this paper, we propose a method to visualize the geometric features of the contact region between proteins in a protein complex. When proteins or ligands are represented as curved surfaces with irregularities, the property that the two surfaces contact each other without intersections is called shape compatibility. Protein-Protein or Protein-Ligand docking researches have shown that shape complementarity, chemical properties, and entropy play an important role in finding contact regions. Usually, after finding a region with high shape complementarity, we can predict the contact region by using residual polarity and hydrophobicity of amino acids belonging to this region. In the research for predicting the contact region, it is necessary to investigate the geometrical features of the contact region in known protein complexes. For this purpose, it is essential to visualize the geometric features of the molecular surface. In this paper, we propose a method to find the contact region, and visualize the geometric features of it as normal vectors and mean curvatures of the protein complex.

• Journal for History of Mathematics
• /
• v.18 no.2
• /
• pp.1-8
• /
• 2005

In this paper, we describe H. Hopf's life and works from the historical point of view. We have a very brief mention of history and results prior to Hopf. He raised the question of the topological implications of the sign of curvature. We discuss his contributions in the field of Riemannian geometry.

• Journal of Educational Research in Mathematics
• /
• v.19 no.1
• /
• pp.143-161
• /
• 2009

This study was designed to gain insights into students' visualization process in geometric problem solving. The visualization model for analysing visual process for geometric problem solving was developed on the base of Duval's study. The subjects of this research are two Grade 9 students and six Grade 10 students. They were given 2D-geometric problems. Their written solutions were analyzed problem is research depicted characteristics of process of visualization of individually. The findings on the students' geometric problem solving process are as follows: In geometric problem solving, visualization provided a significant insight by improving the students' figural apprehension. In particular, the discoursive apprehension and the operative apprehension contributed to recognize relation between the constituent of figures and grasp structure of figure.

• Tunnel and Underground Space
• /
• v.10 no.3
• /
• pp.257-270
• /
• 2000

사물의 거동, 현상에 대한 해석을 실시함에 있어 해석적 해법에 대비한 수치적 해법의 장점은 재질의 성질이 불균질하고 이방성이며 구조물의 형태가 기하학적으로 복잡할 뿐만 아니라 경계조건이 복잡하여 수학적인 표현이 어려울 때 그 해석을 가능케 해 주는 것이라고 볼 수 있다. 이러한 수치 해석법의 대표적인 것으로 유한요소법과 경계 요소법을 들 수 있다.(중략)

• School Mathematics
• /
• v.15 no.2
• /
• pp.481-501
• /
• 2013

The purpose of this study is to review the role of dragging in dynamic geometry environments. Dragging is a kind of dynamic representations that dynamically change geometric figures and enable to search invariances of figures and relationships among them. In this study dragging in dynamic geometry environments is divided by three perspectives: dynamic representations, instrumented actions, and affordance. Following this review, six conclusions are suggested for future research and for teaching and learning geometry in school geometry as well: students' epistemological change of basic geometry concepts by dragging, the possibilities to converting paper-and-pencil geometry into experimental mathematics, the role of dragging between conjecturing and proving, geometry learning process according to the instrumental genesis perspective, patterns of communication or discourse generated by dragging, and the role of measuring function as an affordance of DGS.

• Journal of KSNVE
• /
• v.3 no.3
• /
• pp.192-198
• /
• 1993

옥외에서 발생하는 소음은 음원과 수음점 사이의 시선을 차단하는 장애물을 설치하는 방법이외에는 달리 방도가 없는 경우가 많다. 빛과 마찬가지로 소리도 시선이 차단되면 소리의 그늘이 지는데 빛의 경우보다는 상당히 강한 음장이 이 그늘에 존재한다. 그늘 영역에서의 음장은 소리의 회절현상에 기인하는 것으로서 회절음장은 곧 방음벽의 차음효과를 좌우한다. 방음벽의 차음효과는 잉여감쇠(excessive attenuation)로 표시되는데 잉여감쇠에 영향을 주는 인자는 방음벽의 기하학적 조건, 음향학적 성질, 설치지면, 주변지형, 풍속 및 온도분포와 같은 기상조건, 음원의 특성 등 다양하지만 가장 기본적인 인자는 기하학적인 조건이다. 본고는 방음벽의 원리에 국한하여 살펴보기 위해 기술된 것이므로 주로 판 또는 쐐기 형태의 물체에 의한 회절현상을 취급하였다.

• Journal of Educational Research in Mathematics
• /
• v.22 no.2
• /
• pp.261-275
• /
• 2012

There are some geometry achievement standards presented indistinctly in middle school mathematics curriculum revised in 2011. In this study, indistinctness of some geometric topics presented indistinctly such as symbol $\overline{AB}{\perp}\overline{CD}$ simple construction, properties of congruent plane figures, solid of revolution, determination condition of the triangle, justification, center of similarity, position of similarity, middle point connection theorem in triangle, Pythagorean theorem, properties of inscribed angle are discussed. The following three agenda is suggested as conclusions for the development of next middle school mathematics curriculum. First is a resolving unclarity of curriculum. Second is an issuing an authoritative commentary for mathematics curriculum. Third is a developing curriculum based on the accumulation of sufficient researches.

• The Mathematical Education
• /
• v.15 no.1
• /
• pp.5-7
• /
• 1976

Euclid 기하학이 성립하는 공간은 우리들과 가장 밀접한 공간이다. Descartes의 해석기하학은 Euclid의 3차원공간에서 성립한다. 이 경우 점이라 해도 그것은 3개의 실수의 순서쌍(x, y, z)에 의해 표현되는 것으로 생각해도 좋다. 일반의 n차원 Euclid 공간 R$^n$에 대해서도 같은 생각으로 정의할 수 있다. 이 경우 n=1은 수치선, n=2는 평면, n=3은 소위 3차원의 공간으로서 직관적으로 상상할 수 있으나 n(equation omitted)4인 경우는 상상하기 어렵다. 여기서는 거리의 성질과 추상공간을 논하고 Euclid 공간의 거리에서 출발하여 그 성질중 삼각부등식을 계산을 통하여 증명하므로서 공간의 확장화가 이루워짐을 보였다.

• Journal of Educational Research in Mathematics
• /
• v.19 no.4
• /
• pp.479-491
• /
• 2009

This paper researches the possibility of introducing Descartes' theorem to mathematically gifted students. Not only is Descartes' theorem logically equivalent to Euler's theorem but is hierarchically connected with Gauss-Bonnet theorem which is the core concept on differential geometry. It is possible to teach mathematically gifted students Descartes' theorem by generalizing mathematical property in solid geometry through analogical reasoning, that is, so in a polyhedrons the sum of the deficient angles is $720^\circ$ as in an polygon the sum of the exterior angles is $360^\circ$. This study introduces an alternative method of instruction that we enable mathematically gifted students to reinvent Descartes' theorem through analogical reasoning instead of deductive reasoning.

• School Mathematics
• /
• v.13 no.3
• /
• pp.447-468
• /
• 2011

For the instruction of units dealing with the conic section, the most important factor that we need to consider is the connections. In other words, the algebraic approach and the geometric approach should be instructed in parallel at the same time. In particular, for the students of low proficiency who are not good at algebraic operation, the geometric approach that employs visual representation, expressing the conic section's characteristic in a dynamic manner, is an important and effective method. For this, during this research, to suggest the importance of dynamic visual representation based on GeoGebra in teaching Quadratic Curve, we taught an experimental class that suggests the instruction method which maximizes the visual representation and analyzed changes in the representation of students by analyzing the part related to the unit of a parabola from units dealing with a conic section in the "Geometry and Vector" textbook and activity book.