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Time: Friday, 26/Sep/2014: 11:00am - 1:00pm Session Chair: Masataka Kaneko |
Location: VSP 1.04 Von-Seckendorff-Platz 1 Room 1.04 |
Using Dynamic Geometry as a Robotics Interface
1PH Ludwigsburg, Germany; 2University of Halle-Wittenberg, Germany
Lego Mindstorms is an easy to use construction kit for robotics that perfectly fits to educational purposes. There are several programming environments available that have different advantages and disadvantages. Graphical programming environments like Lego NXT-G are easy to use but often limited in the possibilitys of implemented projects. On the other hand, librarys for common programming languages like BricxCC or LeJOS provide a wide range of functions for flexible progamms, but deeper programming skills are required before one gets started.
The interactive geometry software Cinderella comes with an easy to learn but powerfull functional scripting interface CindyScript to control geometric constructions and perform mathematical calculations. But using an internal timer integrated in Cinderella's scripting environment even sophisticated interactive animations ans simulations can be implemented with only a little programming effort.
We use a Cinderella plugin that wraps LeJOS commands to CindyScript functions to controll the Mindstorms NXT motors and sensors. Connecting the framework with geometric construction elements, one gets a new kind of interactive robot remote control. Vivid visualization of sensor results are possible.
In this talk we present some applications developed during a course for teacher students in computer science. The examples arise from the boarderline of mathematics, physics and computer sience and cover aspects of mathematical areas like functional thinking or analytical geometry.
The interactive geometry software Cinderella comes with an easy to learn but powerfull functional scripting interface CindyScript to control geometric constructions and perform mathematical calculations. But using an internal timer integrated in Cinderella's scripting environment even sophisticated interactive animations ans simulations can be implemented with only a little programming effort.
We use a Cinderella plugin that wraps LeJOS commands to CindyScript functions to controll the Mindstorms NXT motors and sensors. Connecting the framework with geometric construction elements, one gets a new kind of interactive robot remote control. Vivid visualization of sensor results are possible.
In this talk we present some applications developed during a course for teacher students in computer science. The examples arise from the boarderline of mathematics, physics and computer sience and cover aspects of mathematical areas like functional thinking or analytical geometry.
Sketchometry - Dynamic Mathematics on Mobile Devices
University of Bayreuth, Germany
The internet goes mobile and mobile devices like tablet computers and smartphones are entering the classrooms. How do these developments influence learning? What opportunities are opened for mathematics education?
These questions are the introduction of the talk about sketchometry, a new kind of dynamic mathematics software, especially designed for mobile devices. Lines, circles or triangles are simply sketched with the finger on the screen. The software transforms them into geometric objects. The fingers become compass or ruler. In contrast to PCs, software on mobile devices is ready-to-use right after power-up. Creating constructions with sketchometry in mathematics lessons becomes as easy as the usage of pocket calculators. The mobile devices can be used point by point by the students. It is not necessary to go to a computer lab for the whole lesson.
For a gainful integration of these advantages in mathematics education, it is necessary to rethink didactical and methodical concepts. Traditional media, as text books or printed worksheets, can be used together with sketchometry on the mobile device. The usage of computers does no longer happen isolated but integrated.
These questions are the introduction of the talk about sketchometry, a new kind of dynamic mathematics software, especially designed for mobile devices. Lines, circles or triangles are simply sketched with the finger on the screen. The software transforms them into geometric objects. The fingers become compass or ruler. In contrast to PCs, software on mobile devices is ready-to-use right after power-up. Creating constructions with sketchometry in mathematics lessons becomes as easy as the usage of pocket calculators. The mobile devices can be used point by point by the students. It is not necessary to go to a computer lab for the whole lesson.
For a gainful integration of these advantages in mathematics education, it is necessary to rethink didactical and methodical concepts. Traditional media, as text books or printed worksheets, can be used together with sketchometry on the mobile device. The usage of computers does no longer happen isolated but integrated.
 Miller-CADGME2014-157_b.pdf
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Cross-browser graphic user interface for interactive geometry
University of East Sarajevo, Bosnia and Herzegovina
This presentation will introduce a new cross-browser dynamic geometry system with graphic user interface, based on JSXGraph. JSXGraph is library for interactive geometry completely implemented in JavaScript and it does not rely on any other library. Developed cross-browser interactive geometry system depends only on JavaScript and it does not require any additional plugins. It has a very small footprint and works on all devices, including multi-touch devices running iOS, Android, firefoxOS and Windows 8. This system is an excellent solution for the development platform-independent interactive web elements for geometry constructions.
 Drakulic-CADGME2014-159_b.zip
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Geometric Algebra – A foundation for the combination of Dynamic Geometry Systems with Computer Algebra Systems?
TU Darmstadt, Germany
Geometric Algebra is a very general mathematical system including many other systems such as linear algebra, complex numbers, Plücker coordinates, projective geometry or quaternions.
The specific compass ruler algebra, for instance, is very well suited to compute similar to working with compass and ruler. Geometric objects such as circles and lines as well as geometric operations with them can be handled very easily inside of the algebra. A circle, for instance, can be described based on the outer product of three points of the circle.
The compass ruler algebra is a 4D algebra describing the 2D plane with two additional basis vectors representing the origin and infinity. You are able to directly compute with infinity, for instance, when expressing the center point of a circle as the inversion of infinity in the circle.
Gaalop is an easy to handle tool in order to compute and visualize with compass ruler algebra. While in the background a computer algebra system is responsible for the symbolic computations, its visualizing component offers basic DGS functionality. Based on this combination of geometry and algebra Gaalop is also very well suited for proving of geometric relations.
The specific compass ruler algebra, for instance, is very well suited to compute similar to working with compass and ruler. Geometric objects such as circles and lines as well as geometric operations with them can be handled very easily inside of the algebra. A circle, for instance, can be described based on the outer product of three points of the circle.
The compass ruler algebra is a 4D algebra describing the 2D plane with two additional basis vectors representing the origin and infinity. You are able to directly compute with infinity, for instance, when expressing the center point of a circle as the inversion of infinity in the circle.
Gaalop is an easy to handle tool in order to compute and visualize with compass ruler algebra. While in the background a computer algebra system is responsible for the symbolic computations, its visualizing component offers basic DGS functionality. Based on this combination of geometry and algebra Gaalop is also very well suited for proving of geometric relations.
| Hildenbrand-CADGME2014-136_b.pdf
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