Visually Dynamic Presentation of Proofs in Plane Geometry

Abstract

With dynamic mediums such as computer displays, we propose a new kind of visually dynamic presentation of proofs in plane geometry. In a single diagram for the proof, when the proof text goes on step by step with mouse clicks, the related geometry elements in the diagram are added, animated, or deleted dynamically with various visually dynamic effects. It solves not only the problem of identifying geometry elements in the proof text with those in the diagram, but also makes the proof more vividly visualized and intuitive. Our ongoing developing system "Java Geometry Expert" (JGEX) uses two methods to create such visually dynamic presentations: the manual input method and the automatic method. In this first part of the series of our work, we propose the main features of our visually dynamic presentation of proofs and present the manual input method to create such presentations. The manual input method mainly uses mouse clicks to create the dynamic geometry diagram and the proof text.