• Archives of design research
• /
• v.12 no.2
• /
• pp.89-95
• /
• 1999

Carlo H. Sequin, a computer scientist, became to know a sculpture of subtle space construction which was created by Brent Collins, a sculptor, and introduced it as 'Visual Mathematics' in a journal. Sequin who was able to deduce a basic logic of the construction, has developed a software which can be used for virtual modeling merely by substituting simple numerical values using a computer and supplied it to Collins. The present author who was exposed to their collaboration works through series of their papers published in the journal, Leonardo, introduces the Collins' sculptures and the author's modeling procedures of animation works both of which show many common things in visual characteristics and modeling expansion method. The author investigates the mathematical characteristics which is used as a basic motive of modeling and then supplied as a principal visual characteristics of a material. 'Modeling Development by Principle Expansion,' in which the expansion is developed on the base of space twist as for Collins whereas the space section as for the present author, is introduced in this study. With the same stream of the mutual reaction in 'arts, sciences and technology' which has been stressed with the development of sciences and technology, this modeling technology is suggested as a research theme which has a possiblity of various applications.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.25 no.4
• /
• pp.363-372
• /
• 2012

In this study, a new information-based hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections.

• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.339-352
• /
• 2014

In this paper we introduce mathematical modellings in teaching and learning differential equations which were adopted by 2009 revised curriculum. The textbook of 'Advanced Mathematics II' published in 2014 with one publisher includes the content of the second order differential equation y"+y=0 by the power series method. This paper discusses the issue of the power series and gives an alternative method to explain problems of differential equation. Also, we found that the textbook of 'Advanced Mathematics II' used the mechanical system not electrical system in solving differential equation problems. Thus this paper suggests a method using an electric circuit in teaching and learning the first order differential equation. Finally we suggest some terminologies in the teaching and learning of differential equations.

• Communications of Mathematical Education
• /
• v.28 no.3
• /
• pp.423-429
• /
• 2014

It is necessary to realize in advance the lessons and knowhow about how to live, which humankind have developed, through learning to decrease the number of trial and error in our first trip to life. The big problem that present mathematical education is faced with is just only to place much importance on doing microscopic research ignoring macroscopic perspective, which results in the ineffectiveness of mathematics for contributing to life. The purpose of present study is to examine the way of living, classify methods of gaining an insight into life using macroscopic perspective, and develop a life model which can suggest a way of gaining an insight into life from external perspective. Also, this study explores a way of building a creative mathematical model for effective insight about life.

• Journal for History of Mathematics
• /
• v.22 no.1
• /
• pp.53-74
• /
• 2009

Black-out Game(Lightout, Merlin Game, ${\sigma}$+Game) is an interesting game on the chessboard, when you click a button with black or white color, it changes color of itself and other buttons who shares edges. With this rule, we win the game when we have a chessboard with all same color after we click some of the buttons of it. Pretty much of research has been made on founding the winnable strategy for this type of game. In this paper, we first introduce a history of mathematical modeling on this game. Then we develop an algorithm to offer a winnable blackout game of any size. Our tools also show our new algorithm works. Finally, we show how we can use this game in mathematics education.

• Journal of the Korean School Mathematics Society
• /
• v.23 no.1
• /
• pp.45-65
• /
• 2020

This research is an analysis of communication that occurs during the quadratic function teaching and learning process of middle school students, which reflects mathematical modeling. For an in-depth analysis of the communication, Sfard(2008)'s discourse theory and language analysis framework were applied. A quadratic function mathematical modeling teaching and learning were conducted for the week second (1 hour) in June 2019 for students who studied the concept of a quadratic function and who passed a specified period (3 months). The results are as follows. First, The commo-gnitive conflict occurred because of differences in prior knowledge other than quadratic function among students. Second, in the course of communication, knowledge was expanded through problem-solving from different perspectives. These results can be interpreted as allowing students to clearly reveal problems in the communication process based on their understanding of the concept of quadratic functions and to facilitate cooperation among students. of the concept of quadratic functions and to facilitate cooperation among students.

• Journal of the Korean School Mathematics Society
• /
• v.3 no.2
• /
• pp.17-35
• /
• 2000

• Electronics and Telecommunications Trends
• /
• v.11 no.2 s.40
• /
• pp.45-59
• /
• 1996

종래의 현대제어이론은 플랜트의 수학적 모델링이 매우 중요한 역할을 한다. 그러나 비선형 시스템, 선형 시변 등과 같은 복잡한 프로세서는 수학적 모델링을 구성하기가 어렵고 또한 적절한 제어기를 설계하기가 쉽지 않다. 이에 비해, 퍼지제어는 선형시스템은 물론 비선형 시스템 대해 매우 유용한 것으로 알려지고 있다. 본 고는 퍼지논리에 대한 기본적인 개념과 퍼지제어기술에 대하여 서술하였다.

• Journal for History of Mathematics
• /
• v.20 no.4
• /
• pp.93-104
• /
• 2007

It is well known that a suspension bridge may display certain oscillations under external aerodynamic forces. Under the action of a strong wind, in particular, a narrow and very flexible suspension bridge can undergo dangerous oscillations. The collapse of the Tacoma Narrows suspension bridge caused by a wind blowing at a speed of 42 miles per hour, is one of the most striking examples. In this paper, we study models describing oscillations in suspension bridges and known results.

• Journal of Educational Research in Mathematics
• /
• v.15 no.1
• /
• pp.75-105
• /
• 2005

This study explored a mathematical modeling flow and the effect of interactions among students and between a student and Excel on modeling in a small group modeling environment with Excel. This is a case study of three 8th graders' modeling activity using Excel during their extra lessons. The conclusions drawn from this study are as follows: First, small group modeling using Excel was formed by formulating 4∼10 modeling cycles in each task. Students mainly formed tables and graphs and refined and simplified these models. Second, students mainly formed tables, algebraic formulas and graphs and refined tables considering each variable in detail by obtaining new data with inserting rows. In tables, students mainly explored many expected cases by changing the values of the parameters. In Graphs, students mainly identified a solution or confirmed the solution founded in a table. Meanwhile, students sometimes constructed graphs without a purpose and explored the problem situations by graphs mainly as related with searching a solution, identifying solutions that are found in the tables. Thus, the teacher's intervention is needed to help students use diverse representations properly in problem situations and explore floatingly and interactively using multi-representations that are connected numerically, symbolically and graphically. Sometimes students also perform unnecessary activities in producing data by dragging, searching a solution by 'trial and error' and exploring 'what if' modeling. It is considered that these unnecessary activities were caused by over-reliance on the Excel environment. Thus, the teacher's intervention is needed to complement the Excel environment and the paper-and-pencil environment properly.