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Compactness Measure Of A Shape




  • They are applicable to all geometric shapes.

  • They are independent of scale and orientation.

  • They are Dimensionless Number s.

  • They are not overly dependent on one or two extreme Points in the shape.

  • They agree with intuitive notions of what makes a shape compact.


A common compactness measure is the ratio of the area of the shape to the area of a Circle (the most compact shape) having the same perimeter. That ratio is expressed mathematically as M=4 \pi (area)/(perimeter)^2. For a circle, the ratio is one; for a square, it is \pi/4; for an infinitely long and narrow shape, it is zero.

A common use of compactness measures is in Redistricting . The goal is to maximize the compactness of Electoral Districts , subject to other constraints, and thereby to avoid Gerrymandering .


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