Organizers: ・ Setsuo Takato (Toho university, Japan) ・ Mastaka Kaneko (Toho university, Japan) ・ Ulrich Kortenkamp (University of Potsdam, Germany)Aim and Scope Because of the spectacular innovations in interactive computer tools, we are shocked by the paradigm shift in mathematical reasoning in a way we have never experienced. Among the innovations, the development of tools for interactively generating and visualizing mathematical artwork, including dynamic geometry software and computer algebra systems, has had a great influence especially on education. These tools help educators to make simulations, to formulate conjectures, to verify mathematical facts, and to observe mathematical mechanisms. Despite the capabilities of such software, a more efficient linkage to other technology, including scientific and graphical editors, word processors, high-performance computing tools, and mathematical utilities for the web, is needed if the tools are to fully support mathematical reasoning in both research and education. The aim of this session is to bring together researchers, developers and users of mathematical web/mobile interfaces, mathematical computing and editing facilities, and scientific visualization tools, and help them focus on all the exciting developments in these fields. The session accepts papers that address related research and development and present new technologies. Papers exploring educational experiences by using these technologies in an original way are also welcome. Publications ・A will appear on the permanent conference web page (see below) as soon as accepted.short abstract ・An will appear on the permanent conference web page (see below) as soon as accepted. extended abstract It will also appear on the proceedings that will be distributed during the meeting. Submission Guidelines ・If you would like to give a talk at ICMS, you need to submit first a short abstract and then later an extended abstract. See the guideline for the details. Talks/Abstracts 1. What is and How to use KeTCindy --- Linkage between Dynamic Geometry Software and TeX graphics capabilities --- Setsuo Takato (Toho University, JAPAN) Abstract: Though TeX has become a quite popular tool in the area of mathematical science because it offers extensive facilities to typeset high-quality mathematical documents, using the graphics capabilities originally inherited to it for the generation of high-quality mathematical artwork has not been an easy task for usual TeX users. One of the most hopeful schemes to remove this defect should be that we utilize other symbolic/numerical computing software (like Mathematica, Maple, Matlab, Maxima, Scilab, etc.) or dynamic geometry software (like GeoGebra, Cinderella, etc.) to compute graphical data and format it into TeX graphical code. In this talk, we will introduce KeTCindy which is a Cinderella plug-in to generate high-quality TeX graphics. While graphical images of mathematical objects are generated and handled interactively on Cinderella screen, the corresponding graphical data are formatted into TeX graphical codes which leads to the generation of high-quality graphical images in TeX final outputs. The interactive operation on PC display can be directly reflected to the generated image on TeX final output through KeTCindy system, and the generated image can be finely tuned by KeTCindy commands embedded into the scripting language of Cinderella. Therefore, KeTCindy can be regarded as one of the most prominent schemes to establish the effective linkage between visualization tools and editing tools. Moreover, KeTCindy makes it possible to import the data calculated or simulated by using other computing software (like Maxima, Scilab, Risa/Asir and R) and combine them with the graphical data, so that extremely wide range of mathematical objects can be presented. We will show some eminent capabilities of Ketcindy and also the usage of it. 2. Theoretical Physics, Applied Mathematics and VisualizationsHaiduke Sarafian (Pennsylvania State University, USA) Abstract: The conceptual aspects of the majority of physical phenomena readily are comprihensible, yet their analyses conductive to justiiable output require mathematical justifications. Applied mathematics is the background of theoretical physics. No field in physics in particular and science in general is immune. Within the last couple of decades advances in computer science introduced a fresh pathway, computational physics, augmenting the field. The offspring of these innovations is the scientific software capable of performing operations that could not be accomplished traditionally. The impact of these spectacular innovative technologies is evidence in scientific literature. The focus of this article is to demonstrate the graphical usefulness of one such scientific software, Mathematica, analyzing the electrostatic features of discrete charge distributions. This is an example of a theoretical physics problem focusing on the overlap of physics, graphics and math. Ever since its birth a quarter century ago, Mathematics steadily has been growing in popularity and practicality. This article embodies the codes compatible with the latest version of the software including one, two and three dimensional sliders. Practitioner physicists, interested individuals and mathematicians may adjust the code to meet their needs. 3. A Framework for Exploring Inference Processes using Reasoning Software Fumiya Iwama (Konan University, JAPAN) Tadashi Takahashi (Konan University, JAPAN) Abstract: We can use the reasoning software for mathematical theory exploration. Computer assisted proofs, involving language constructs from set theory, are a key component of theorem proving. We propose that using GeoGebra together with Theorema for our purpose. GeoGebra version 5.0 supported theorem proving. It was several preliminary planning steps until it implemented theorem proving facility. The Theorema system is primarily intended as an educational tool for supporting theorem proving in set theory at the undergraduate level. The Theorema system allows mathematical knowledge to be organized as hierarchies of interdependent theories. By condensing this knowledge, we can investigate properties of newly defined mathematical entities. The syntax, including all symbols, is interpreted unambiguously by the GeoGebra and Theorema parser into their internal representation. Using GeoGebra together with Theorema requires insight into both the procedures and concepts involved in mathematical logic. It allows the user to organize mathematical knowledge as hierarchies of interdependent theories and expression language allows the proof of abstract concepts. The framework presented here gives new results that are close in syntax to common mathematical language but are precise enough for automated theorem proving. 4. The Programming Style for Drawings from KeTpic to KeTCindySatoshi Yamashita (National Institute of Technology, Kisarazu College, JAPAN) Abstract: To make class materials with figures by using TeX, in 2011 we have completed KeTpic as a plug-in for a numerical analysis software Scilab. We describe KeTpic programs with a commandline user interface Scinotes. KeTpic users make KeTpic programs based on their original programming styles. This leads other KeTpic users to a demerit which makes it hard to utilize their KeTpic programs. To solve this inconvenience, we developed the KeTpic programming style for drawings in 2013. KeTpic programs include three parts; a preamble part which describes setting commands, a part for making plot data and a part for extracting plot data into a figure TeX file. Since 2014 we have improved KeTCindy as a plug-in for an interactive geometry software Cinderella. Cinderella has two screens; an interactive geometric screen and a screen which describes Cinderella commands called CindyScript. When a KeTCindy command is run in CindyScript, corresponding KeTpic commands are extracted to the proper position of the above-mentioned three parts in a Scilab executable file. In our presentation, we explain about the KeTCindy system from the viewpoint of the programming style for drawings and introduce our website which describes the utilization of KeTCindy. 5. The actual use of KeTCindy in educationMasataka Kaneko (Toho University, JAPAN) Abstract: Today, various tools to dynamically visualize mathematical objects have been developed. For example, some graphical user interface is implemented to many computer algebra systems like Mathematica in which dynamical presentation of geometric shapes and function graphs can be generated by using “sliders”. Among such tools, dynamic geometry software like Cinderella are quite excellent in that we can control those objects more interactively. At the same time, static presentation of those objects in printed matters is also indispensable for mathematical activities since it is through paper and pencil-based activities that we can most easily synchronize computation and observation. Thus, especially for educational purpose, the selection and the usage of these methods at each stage of learning context is crucial. Since KeTCindy which we have developed recently serves direct linkage between interactive presentation of graphics on Cinderella and its exported image into TeX, it can be expected that using KeTCindy enables mathematics learners to unify their intuitive reasoning through observation of the interactive presentation on PC and their discursive inference with the use of TeX document including finely tuned graphics. In this presentation, the effect of such unifiability on the learners’ reasoning processes is illustrated through time series detection of learners’ activities during some case studies of actually using KeTCindy. 6. Function Enhancement of Math Input Environment with Flick Operation for Mobile DevicesYasuyuki Nakamura (Nagoya University, JAPAN) Takahiro Nakahara (Sangensha LLC., JAPAN) Abstract: Math online test system with which mathematical expressions as answers are automatically assessed has been gathering interests among science and math teachers. Online drill testing can be delivered not only using PCs, but also using mobile devices such as smartphones to enhance the opportunities for students to practice anytime and anywhere. However, the problem of math input complexity arises for questions requiring entry of mathematical expressions as answers. Developing online test environments for e-learning for mobile devices will be useful to increase drill practice opportunities. In order to provide a drill practice environment for calculus using an online math test system, we develop math input interface with flick operation assuming the use of STACK for online mathematics testing. That can be easily used on mobile devices. We developed the interface with JavaScript in order to minimize the dependencies on mobile device OSs. We have already developed a conversion filter from MathDox to Maxima, and we use MathDox for describing entered mathematical expressions. Qwerty keyboard or specially designed keyboard layout can be selected depending on mathematical expressions that ones want to enter. It was confirmed that the number of taps required to enter mathematical expressions on a mobile device is considerably reduced using the new math input interface. 7. How to generate figures at the preferred position of a TeX documentHisashi Usui (National Institute of Technology, Gunma College, JAPAN) Abstract: When we use TeX to edit a document, we sometimes need to place the figure of preferred shape into suitable position. In this presentation, we propose a method using KeTCindy for this purpose. KeTCindy is a plug-in to Cinderella which converts the procedure to generate geometric shapes into TeX readable code to generate the corresponding image on TeX final output. One of the merit of using KeTCindy is its interactive character. On the screen of Cinderella, we can control the shape of the figure as we want. When we place the resulting image at the exterior side of text part, simple conversion to TeX graphical image through KeTCindy is sufficient. However, when we need to place it onto the text part, some extra elaboration is needed to ensure that both text part and the generated figure are finely balanced. The key idea is making the screen of Cinderella semi-transparent by the software named feewhee. 8. Generating data for 3D modelsNaoki Hamaguchi (National Institute of Technology, Nagano College, JAPAN)Setsuo Takato (Toho University, JAPAN) Abstract: KeTpic is a macro package which generates the graphical code that can be used in TeX. In 2014, commands for generating data in obj format were implemented in KeTpic. The data can also be converted to stl format, with which 3D printers can make 3D models. Teachers at the collegiate level often need 3D figures in their math classes. KeTpic enables teachers to make teaching materials in various ways: handouts to be distributed, slides to be presented on the screen, figures to be manipulated by the students on their tablets, and physical models to be displayed or passed around. Physical models have the most information about the real objects. However, they sometimes hinder students from catching the point under discussion. Therefore, some of these materials should be combined to suit the contents. KeTCindy which is a Cinderella plug-in generates data of above-mentioned teaching materials. As a result, KeTCindy lets teachers make a variety of materials with 3D models without much additional effort. In this presentation, we show KeTCindy commands for making 3D models in various ways with actual teaching materials. 9. Cooperation of KeTCindy and Computer Algebra SystemShigeki Kobayashi (National Institute of Technology, Nagano College, JAPAN)Setsuo Takato (Toho University, JAPAN) Abstract: In Sangaku (wooden plaques containing geometrical puzzles), there are problems of drawing smaller circles within a bigger circle in contact with it or a circle in contact with a quadratic curve like an oval. These kinds of problems can be interesting teaching materials. A dynamic geometry software like Cinderella or GeoGebra, can be used to solve these problems. We can use a high-quality TeX graphics with KeTCindy (Cinderella plug-in) to draw these figures. We can also draw figures by solving simultaneous equations using Computer Algebra System like Maxima, Risa/Asir. Though we can deal with simultaneous equations in Maxima, it takes time, or it doesn't work when there are many variables. In such cases, it's possible to convert it to the system of equations easier to solve using a Grobner base in Risa/Asir, and deal with it successfully by giving the result to Maxima. We can deal with this on Cinderella through KeTCindy, and draw circles using the result. This method can also be applied to another problem. In our presentation such examples will be shown. Martin von Gagern (University of Potsdam, GERMANY)Ulrich Kortenkamp (University of Potsdam, GERMANY)Stefan Kranich (Technical University of Munich, GERMANY)Aaron Montag (Technical University of Munich, GERMANY)Jurgen Richter-Gebert (Technical University of Munich, GERMANY)Michael Strobel (Technical University of Munich, GERMANY) Abstract: Visualization and real-time interactive simulation play an important role both in mathematical research and in mathematical communication. The CindyJS Project aims at the development of a software platform and its mathematical foundation that allows a versatile and fast prototyping of mathematical experiments and visualizations which can be used for research and demonstration. The project attacks both the mathematical and the software related aspects of such a platform. In particular, the system should be usable as a flexible authoring system for providing mathematical content that can run in contemporary web browsers, taking advantage of modern hardware and software technologies. Within the CindyJS project a special emphasis (on the mathematical side) is laid on the creation of a system that provides a high mathematical consistency and expressiveness. Another focus (on the computer science side) is to provide an intuitive authoring system that can in particular be used for the creation of web based demonstrations and microlaboratories that run within a browser and on mobile devices. The system, among other aims, should provide easy access to an interactive geometry viewing environment (2D and 3D), to a versatile scripting language and to a reliable physics simulation engine. |