Open AccessIn the present paper we consider to determine the relative position between a point and a simple polygon in a plane. For this purpose we build a model of the polygon, which manipulation carries us, in a very natural way, to the solution of this problem and it allows us to arise a more ambitious problem based on the same model: the determination of the polygon area. This geometric example is useful to illustrate the creation process in Mathematics. It is especially interesting the way in which the formalization of a simple problem with a successful notation and a great dose of algebraic exploration results in a rediscovery of an interesting geometric result which is much more important than the original objective.
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