Masataka Kaneko

A New Application of CAS to

In many cases, mathematicians or mathematics teachers, as well as other scien-tists,needtopreparegoodillustrationsoreducationalmaterials.Ingeneral,CASgives us a set of highly accurate numerical data. Therefore, it is quite naturalto utilize CAS for the purpose of creating fine pictures. CASs support beautifuland impressive graphics and some of them can output the picture in graphicalformats (EPS, JPEG, GIF, BMP, etc). However, the authors have not been sat-isfied with printed matters obtained as a direct output from CASs, as well asfrom CADs (Computer Aided Design) or from data/function-plotting programs,like Gnuplot. The reason is that mathematical lettering in their pictures is notclear. We need to optimize their outputs so as to be available for mathematicaltextbooks or academic papers.On the other hand, L

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We have been developing KETpic as a macro package of a CAS for drawing fine LTEX-pictures, and we use it efficiently in mathematical education. Printed materials for mathematics classes are prepared under several constraints, such as “without animation”, “mass printings”, “monochrome”, and “without halftone shadings”. Because of these constraints, visualization in mathematical education tends to be unsatisfactory. Taking full advantages of LTEX and CAS, KETpic enables us to provide teaching materials with figures which are effective for mathematical education. The effects are summarized as follows: (1) The plottings of KETpic are accurate due to CAS, and enable students to deduce mathematical laws. (2) KETpic can provide adequate pictures for students’ various interest. For example, when some students who understand a matter try to modify it, KETpic can give them appropriate and experimental figures. (3) Even though CAS can draw 3D-figures beautifully and automatically, it is expensive for mass printings and the figures are sometimes not easy to understand. Oppositely, 3D-graphics by KETpic are monochrome, but are richly expressive. In this paper, we give various examples of LTEX-pictures which we drew by using KETpic. For instance, the picture which is used in order to explain the convergence theorem of Fourier series makes it easier for students to understand the idea that function series converge to another function. Also the picture of skeleton is endowed with clear perspective. KETpic gives us great potential for the teaching of combinatorial mathematics. Through these examples, we claim that KETpic should have great possibilities of rich mathematical expressions under the constraints above mentioned.

Plottings

This paper presents a new interactive, user-friendly graphical user interface (GUI) for generation and visualization of IFS. The program, called IFSGen4LaTeX, is particularly designed for proper Open image in new window editing in a WYSIWYG mode. During a working session, IFS are created interactively from scratch and visualized by using the IFSGen4LaTeX GUI; simultaneously, its engine generates source code that, once inserted in Open image in new window and compiled, displays the same fractal images in Open image in new window Ṫhis process leads to substantial savings in CPU time and memory storage, since the resulting source code is astonishingly small, but still of excellent visual quality because the number of iterations is decided by the user.

CAS-aided visualization in LATEX documents for mathematical education

Included among other mathematical software, dynamic geometry software has the great advantage of enabling teachers and learners to visualize and interactively control mathematical models. However they are not used in real classrooms as widely as expected. One reason is that it is not so easy for ordinary teachers and learners to install those software onto personal computers and to master the skills needed to operate them appropriately. As a result, teachers do not have enough knowledge about the theme and the manner in which those software will be used effectively. To overcome this difficulty, the extensions associated with some dynamic geometry software are being developed so that the teaching materials generated by them can be adapted to plugin-less web technology. In this paper, the author explains some case studies which illustrate the software’s influence on learners’ mathematical cognition. The method to identify the above mentioned influence will be applicable to wide range of researches concerning the interaction between learners’ reasoning processes and information technology.

IFSGen4 : Interactive Graphical User Interface for Generation and Visualization of Iterated Function Systems in

In mathematics research and education, harmonious use of high-quality mathematical expressions and mathematically precise artwork is desirable. To produce them, an environment in which several kinds of software (including editing tools, computing tools, and high-quality graphics generators) interact in a collaborative way, is needed. To accomplish this, we have developed Cindy, a plug-in for the popular dynamic geometry software Cinderella, to help mathematicians generate high-quality graphical images. Cindy also enables us to bind the high-performance graphics capability of Cinderella with the powerful computing capability of various computer algebra systems. In this paper, we will show some mathematical artwork to illustrate how the collaborative use of

Collaborative Use of KeTCindy and Free Computer Algebra Systems

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A CAS Macro Package as LaTeX Graphical Command Generator and Its Applications

LATEX, Cinderella, and computer algebra systems via Cindy can enhance the power and convenience of each other. Since all the related software are freely accessible, Cindy should be especially valuable for educational purposes.

Collaborative Use of Mathematical Content Generated by CindyJS on Tablets

Owing to its superb drawing utilities and symbolic computation capabilities, computer algebra system (CAS) has become one of the most preferred tools for drawing scientific artworks. However, according to the result of our questionnaire survey, many collegiate mathematics teachers in Japan feel difficulty in effectively using the graphics generated by CAS in printed materials. For instance, quite a number of mathematics teachers in universities are using TeX as their daily tool for editing high-quality mathematical documents, but the use of graphics generated by CAS in TeX documents seems not to be so easy task for usual TeX users. This difficulty seems to prevent many teachers from using CAS graphics. To fill this gap, some dynamic geometry softwares (DGS) and others have been equipped with the capability to export TeX-readable code of their graphical output. Also the authors have developed a macro package KETpic designed for CAS to supply high-quality graphics in TeX documents. In this paper, we will propose a scheme for demonstrating and improving the effect of CAS use in mathematics education. Through this scheme, it is shown that we can greatly improve the educational effect of our mathematics class materials by appropriately using the precise 2D-graphics generated by CAS and KETpic.