Geometry Expressions – a dynamic symbolic geometry environment

Abstract

Dynamic Geometry Systems such as Geometers' SketchPad or Cabri are productive environments for the exploration of geometric relationships. However, they are strictly numeric, and this limits their applicability where the interplay between geometry and algebra are being studied. We present Geometry Expressions - a dynamic symbolic geometry environment. While retaining the ease of use of a typical dynamic geometry environment, Geometry Expressions diverges by working symbolically rather than numerically. Constraints, such as distances and angles, are specified symbolically. Symbolic measurements for quantities, such as distances, angles, areas, locus equations, are automatically computed by the system. We outline how these features combine to create a rich dynamic environment for exploring the interplay between geometry and algebra, between induction and proof. Finally, the results of high school students' mathematical research using Geometry Expressions in conjunction with Computer Algebra System are summarised.