Ten compactness properties of circles: measuring shape in geography

This essay sheds new light on the meaning and measurement of compactness—one of the most intriguing and least‐understood properties of geographic shapes. We articulate a unified theoretical foundation for the study of shape compactness that rests on two simple observations: First, that the circle is the most compact of shapes. And second, that there are 10—and possibly more—distinct geometrical properties of the circle that make it the most compact of shapes. We introduce these 10 properties, illustrate them with real‐world examples and define indices associated with these properties that can be calculated using a geographic information system.     

Urban pattern and land cover variation in the greater Toronto area

Recent epistemological shifts in environmental geography have created a space to consider the interactions between ecological and urban systems more seriously. While openness to thinking about urban ecosystems has increased in recent years, there remain fundamental gaps in our knowledge. For example, recent research has examined the impact of urban–rural gradients on ecological conditions, but major voids exist regarding the relationship between urban development patterns and land cover heterogeneity, particularly for new forms of urbanization. This article attempts to address some of these gaps by examining the relationship between urban pattern and land cover in the greater Toronto area (GTA). In particular, measures of urban pattern that reflect aspects of development density, grain and function, as well as socio-economic characteristics, are systematically analyzed in relation to land cover heterogeneity. The regression analysis shows that multiple components of urban development pattern and socio-economic conditions are correlated with vegetated land covers, while urban density variables are not related. These results indicate more detailed representations of urban pattern should be incorporated into future human–environmental interaction studies in cities.