Miguel de Guzman* (Spain), mdeguzman@bitmailer.net
Discovery Experiences in Synthetic Geometry with DERIVE

The capabilities of DERIVE for combining its graphical with its analytical
tools in dealing with the exploration of certain traditional and less
traditional problems of synthetic geometry have not been used as much as they
deserve, in the author's opinion. DERIVE as a geometrical tool presents certain
advantages over more familiar programs dealing with geometrical constructions,
although of course it is not designed to be such an interactive instrument in
the teaching of geometry like CABRI or GEOMETER SKETCHPAD. In this presentation
several experiences are described on how DERIVE has helped the author to
conjecture, and sometimes to prove, some new facts connected with such objects
as the Wallace-Simson line, Jakob Steiner's deltoid, Morley's triangle,... The
way one can proceed is to define certain DERIVE functions that allow one to
graphically experiment in concrete cases and then one can use DERIVE's
analytical capabilities in order to prove the conjectures one makes by
exploring the figures one has obtained. This path has led for example to an
interesting extension of the Wallace-Simson theorem which is going to be
published in the American Mathematical Monthly (June-July, 1999).