Ten compactness properties of circles: Measuring shape in geography

Shlomo Angel; Jason Parent; Daniel L. Civco

doi:10.1111/j.1541-0064.2009.00304.x

Ten compactness properties of circles: Measuring shape in geography

Shlomo Angel, Jason Parent, Daniel L. Civco

Urban Initiative

Research output: Contribution to specialist publication › Article

Abstract

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.

Original language	English (US)
Pages	441-461
Number of pages	21
Volume	54
No	4
Specialist publication	Canadian Geographer
DOIs	https://doi.org/10.1111/j.1541-0064.2009.00304.x
State	Published - Dec 2010

Keywords

circle
compactness
landscape metrics
morphology

ASJC Scopus subject areas

Geography, Planning and Development
Earth-Surface Processes

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10.1111/j.1541-0064.2009.00304.x

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AB - 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.

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Ten compactness properties of circles: Measuring shape in geography

Abstract

Keywords

ASJC Scopus subject areas

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