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.
- landscape metrics
ASJC Scopus subject areas
- Geography, Planning and Development
- Earth-Surface Processes