ICMS 2016 Session: Interactive operation to scientific artwork and mathematical reasoning

ICMS 2016:  Home, Sessions

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 short abstract will appear on the permanent conference web page (see below) as soon as accepted.
      ・An extended abstract will appear on the permanent conference web page (see below) as soon as accepted.
        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.

          presentation file (PDF)

  2. Theoretical Physics, Applied Mathematics and Visualizations

      Haiduke 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 KeTCindy

      Satoshi 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.

          presentation file (PDF) 

  5. The actual use of KeTCindy in education

      Masataka 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.

          presentation file (PDF) 

  6. Function Enhancement of Math Input Environment with Flick Operation for Mobile Devices

      Yasuyuki 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 document

      Hisashi 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 models

      Naoki 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 System

      Shigeki 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.

          presentation files (website)