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Although there has been considerable scholarly interest in the nature of ancient cities, it has been difficult to identify and explore quantitative patterns in their design and amenities. Here, the authors offer a model for the relationship between the population size and infrastructural area of settlements, before testing it against measures of urban form in the Roman Empire. They advocate a more consistent approach to the investigation of settlements that is capable of not only incorporating sites with divergent physical forms and historical trajectories into the same model, but also able to expose their similarities and differences. Keywords: Roman Empire, urbanism, settlement-scaling theory, built environment, Introduction The dimensions of the forum should be based on the population; its area should neither be too crampedfor efficiency nor so large that for lack of population it looks [...]

Humanity has just crossed a major landmark in its history with the majority of people now living in cities. Cities have long been known to be society's predominant engine of innovation and wealth creation, yet they are also its main source of crime, pollution, and disease. The inexorable trend toward urbanization worldwide presents an urgent challenge for developing a predictive, quantitative theory of urban organization and sustainable development. Here we present empirical evidence indicating that the processes relating urbanization to economic development and knowledge creation are very general, being shared by all cities belonging to the same urban system and sustained across different nations and times. Many diverse properties of cities from patent production and personal income to electrical cable length are shown to be power law functions of population size with scaling exponents, [beta], that fall into distinct universality classes. Quantities reflecting wealth creation and innovation have [beta] [approximately equal to] 1.2 >1 (increasing returns), whereas those accounting for infrastructure display [beta] [approximately equal to] 0.8 < 1 (economies of scale). We predict that the pace of social life in the city increases with population size, in quantitative agreement with data, and we discuss how cities are similar to, and differ from, biological organisms, for which [beta] population | sustainability | urban studies | increasing returns | economics of scale