Abstract
In this paper, we will make explicit the relationship existing between geometric objects and figures in planar Euclidean geometry. Geometric objects are defined in terms of idealizations of the corresponding figures of practical geometry. We name the relationship between them as a relation of idealization. It corresponds to a resemblance-like relationship between objects and figures. This relation is what enables figures to have a role in pure and applied geometry. That is, we can use a figure in pure geometry as a representation of geometric objects because of this relation. Moving beyond pure geometry, we will defend that there are two other ‘layers’ of representation at play in applied geometry.
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