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 .