Building Dynamic Mathematical Models with Geometry Expert, preprint

This is an extended abstract for the paper [?] written in Chinese. Geometry Expert (GEX) is a software for dynamic geometric drawing and automated geometry theorem proving and discovering [?]. With GEX, we can draw geometric diagrams dynamically, that is, we can change these diagrams in a continuous way and at the same time keeping the geometric relations in the figure intact. This feature of GEX provides a powerful and convenient platform for teaching mathematical concept in an intuitive way. With GEX, we have proved hundreds of difficult geometry theorems and generated elegant proofs [?]. Furthermore, we can use GEX to build a database which contains all the properties of a given diagram that can be deduced using a set of geometric axioms. With this feature, teachers can easily make exercises and test problems; students can enhance their ability of solving problems by fully explore the properties of a given diagram. By dynamic models, we mean models built by computer softwares that can be changed dynamically. In this series of papers, we shall show how to build dynamic models for various mathematical concepts using GEX. We will consider the following four classes of models. 1. Geometric transformations on diagrams that can be drawn with ruler and compass. B