In ancient Greek cities the social structure tries to adapt to its urban form. From this perspective, this article is a review of Aristotelian thought, especially the one developed in the Politics, in order to analyze the link between the ideal Greek social order and its associated space. For Aristotle (348-322 BC), the ideal form of the city is a contained, limited and finite space, built in order to avoid human overpopulation, and thus, to ensure its self-sufficiency, beauty, virtuosity and governance. This article presents the definition of Aristotle for Greek polis, followed by, a brief evolution of the concept of infinity through history is offered, starting from the Aristotelian approach to our days. It is important to state that the reflections here presented make up an initial advance of a historical research on the process of urban growth and the ways to limit its physical expansion. [ABSTRACT FROM AUTHOR]