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EUCLID: A System for the Exploratory Discovery of Geometrical Properties of Triangles

We describe the system Euclid for automatically finding various geometrical properties of a triangle starting from a set of relations and operators defined over categories like scalars, points, lines (or line-segments), angles and triangles. Euclid is comprised of a knowledge base consisting of the definitions of categories, relations and operators, a search algorithm and a set of constraints and pruning strategies to guide the search. We describe each component and also the theoretical properties of the search algorithm. Euclid’s efficacy is demonstrated by the interesting potential theorems it is able to discover about triangles.