Visualisation and Animation in Mathematics and Physics

Visualisation and animation are of vital importance for the modern methods in mathematical education. They strongly support the understanding of concepts in mathematics and physics. We think that the application of a commercial graphics software package is neither a satisfactory approach for the illustration of the theoretical concepts, nor can it be used as their substitute. It should not be the aim of education to teach students to use some software package by instructing them which keys to press, and how to move the mouse, regardless of how convenient this may seem. The emphasis should be put on teaching the fundamental theoretical facts. In view of this, we developed an open software in PASCAL on programme level which provides the basic tools for computer graphics, in order to offer an alternative to existing graphics software packages. The main purpose of our software is to visualise the classical results in differential geometry on PC screens, plotters, printers or any other postscript device, but it also has extensions to physics, chemistry, crystallography and the engineering sciences. To the best of our knowledge, no other comparable, comprehensive software of this kind is available. The software is open which means that its source files are accessible to the users, thus enabling them to apply it in the solutions of their own problems. This makes it extendable and flexible, and applicable to both teaching and research in many fields. In contrast to this, almost all other available graphics packages are closed; in general, the area below the user interface is inaccessible and consequently the software cannot be extended beyond the scope of the solutions it offers. The software uses OOP, object oriented programming, and its programming language is PASCAL. The software is self-contained in the sense that no graphics package is needed other than PASCAL.