CONCLUSIONS

As it is well know, Cabri-Geométrè provides an interactive learning environment for elementary geometry; in particular it has been considered as an instrument for theorem proving in this context . We think that the interaction of such tool with our method could provide an intelligent, interactive environment for learning Euclidean geometry. The idea is to build a sort of Geometry Guide program that not only allows to experiment properties and to display figures, but that also has the ability of "knowing" in advance what is the correct direction that the user has to follow if some geometrical construction is set, in case he/she wants to find some stated property (or, even what could be some interesting properties hidden in a given construction). Accordingly, our examples are presented as open situations (Situation 1, Situation 2): we set up some construction and then we make an apparently impossible conjecture, but (please, computer...) tell me what other conditions I do need... Or, we might even wonder what a reasonable conjecture could be in some situation, without a priori stating any...We refer the reader to the collection of examples in the references for further details.


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