Mathematical Screen Metaphors

Abstract

Mathematical thinking and teaching has been liberated by the graphics computer screen. Mandelbrot’s fractal geometry revivified theoretical work by Julia and Fatou, and the screen images of structure in’ chaos’ have entranced people, particularly artists, mathematicians, and entrepreneurs eager to find an effective image for marketing purposes. Spreadsheets enable people to lay out their calculations and see the results all at once (depending on screen size). LaBorde’s Cabri-géomètre and Jackiw’s Geometer’s Sketchpad, which enable users to make Euclidean constructions on general rather than specific geometrical objects, have offered a new lease of life to Euclidean geometry and we can expect to see the same construction mechanism employed for other forms of geometry and in other domains. Modelling tools like STELLA provide a graphic language in which to express complex inter-relationships based on the single image of controlled flow through pipes. Symbolic manipulators like Maple and Mathematica have the potential for providing many more people with access to symbolic generality than ever before. ISETL enables the language of sets and relations to be as used by mathematicians to be deployed and tested out on a wide range of particular (finite) examples. LOGO and Boxer present exploratory and expressive environments which depend upon and exploit the graphics screen.