A dynamic-symbolic interface for geometric theorem discovery

This paper describes Discover, a program for learning and teaching geometry with the help of a computer. The program is a dynamic geometry environment that can communicate with Mathematica, using its symbolic capabilities to perform geometric discovery or rediscovery. Discover is specially suited to be used as a learning tool for geometry from the ages of 12 up to University. It permits the replacement of the traditional ruler and compass by electronic substitutes, as in standard dynamic geometry environments. Through its link with the computer algebra software, it enhances the process of conjecturing and proving. The results can be expressed in natural language or through the use of equations. The mathematical methods that Discover uses are sound, although not complete. Despite this last fact, almost all parts of the school curricula in plane geometry can be adequately treated with the program. # 2002 Elsevier Science Ltd. All rights reserved.