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• Über die Verwendung von Maple für die Simulation von Mechanismen

  21-39

  Engin Can

  Views:

  21

  Maple is used to do numerical computation, plot graphs and do exact symbolic manipulations and word processing. This paper demonstrates how Maple can be used for the simulation of mechanisms. This offers the possibility for students to become familiar with this particular section of mathematical modelling. The mechanism under consideration is a so-called F-mechanisms, i.e., a planar parallel 3-RRR robot with three synchronously driven cranks. It turns out that at this example it is not possible to find the poses of the moving triangle exactly by graphical methods with traditional instruments only. Hence, numerical methods are essential for the analysis of motions which can be performed by an F-mechanism.

• Different approaches of interplay between experimentation and theoretical consideration in dynamic geometry exploration: An example from exploring Simson line

  63-81

  Yip-Cheung Chan

  Views:

  26

  Dynamic geometry environment (DGE) is a powerful tool for exploration and discovering geometric properties because it allows users to (virtually) manipulate geometric objects. There are two possible components in the process of exploration in DGE, viz. experimentation and theoretical consideration. In most cases, there is interplay between these two components. Different people may use DGE differently. Depending on the specific mathematical tasks and the background of individual users, some approaches of interplay are more experimental whereas some other approaches of interplay are more theoretical. In this paper, different approaches of exploring a geometric task using Sketchpad (a DGE) by three individual participants will be discussed. They represent three different approaches of interplay between experimentation and theoretical consid- eration. An understanding of these approaches may contribute to an understanding on the mechanism of exploration in DGE.

• Fuzzy Datalog with background knowledge

  257-281

  Ágnes Achs

  Views:

  8

  In this paper we give a possible model for handling uncertain information. The concept of fuzzy knowledge-base will be defined as a triplet of a background knowledge defined by the similarity of predicates and terms; a deduction mechanism: a fuzzy Datalog program, and a decoding set of the program, which help us to determine the uncertainty level of the results.

• Application of computer algebra systems in automatic assessment of math skills

  395-408

  Przemyslaw Kajetanowicz

  Jedrzej Wierzejewski

  Views:

  29

  Mathematics is one of those areas of education, where the student's progress is measured almost solely by testing his or her ability of problem solving. It has been two years now that the authors develop and use Web-based math courses where the assessment of student's progress is fully automatic. More than 150 types of problems in linear algebra and calculus have been implemented in the form of Java-driven tests. Those tests that involve symbolic computations are linked with Mathematica computational kernel through the Jlink mechanism. An individual test features random generation of an unlimited number of problems of a given type with difficulty level being controlled flat design time. Each test incorporates the evaluation of the student's solution. Various methods of grading can be set at design time, depending on the particular purpose that a test is used for (self-assessment or administrative exam). Each test is equipped with the correct solution presentation on demand. In those problems that involve a considerable amount of computational effort (e.g. Gauss elimination), additional special tools are offered in a test window so that the student can concentrate on the method of solution rather than on arithmetic computations. (Another obvious benefit is that the student is thus protected from the risk of frustrating computational errors). Individual tests can be combined into comprehensive exams whose parameters can be set up at design time (e.g., number of problems, difficulty level, grading system, time allowed for solution). The results of an exam can be automatically stored in a database with all authentication and security requirements satisfied.

• Geometry expressions: an interactive constraint based symbolic geometry system

  303-310

  Philip Todd

  Views:

  18

  Dynamic geometry systems such as Geometers' SketchPad or Cabri are productive environments for the exploration of geometric relationships. They are, however, strictly numeric, and this limits their applicability where the interplay between geometry and algebra are being studied. We present Geometry Expressions – a dynamic symbolic geometry environment. While retaining the ease of use of a typical dynamic geometry environment, Geometry Expressions diverges by using constraints rather than constructions as the primary geometry specification mechanism and by working symbolically rather than numerically. Constraints, such as distances and angles, are specified symbolically. Symbolic measurements for quantities such as distances, angles, areas, locus equations, are automatically computed by the system. We outline how these features combine to create a rich dynamic environment for exploring the interplay between geometry and algebra, between induction and proof.