Pen-based Input of Geometric Constructions∗

Pen-based input is the classical approach to drawing. Without computers, using a pen was the natural approach to do drawings, and the simplicity of this “device” always called for similar electronic solutions. Today, a broad range of electronic input devices is available that try to pair the simplicity of input with the power of computing. They come in all sizes: from small touch-screens with stylus in personal digital assistants, via desktop-size input tablets or interactive displays, to electronic whiteboards with rearor front-projection. These devices all share a direct interaction paradigm. The challenge in using these devices for geometric constructions is to automatically annotate the drawn objects with their relations to the other objects. A basic example is the drawing of a right-angled triangle: How can we automatically recognize the user’s intention to have a right angle? Can we do that at all? Do we really want to do that? If not – what is the easiest pen-compatible way to have the user add this information? We will demonstrate several approaches to these problems, implemented in a development version of Cinderella. Another interesting issue is the presentation of hand-drawn figures: Is it possible to preserve the look of a sketch while still guaranteeing mathematically correct figures? Using the additional information gathered by automatic theorem proving we show some solutions. ∗Supported by the DFG research center Matheon, "Mathematics for key technologies" (FZT 86) in Berlin.