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I was thinking of concavity as a state which had the most distance outside the state between two points inside the state, somehow proportional to size or area.
by jlgreco 13y ago
I was thinking of concavity as a state which had the most distance outside the state between two points inside the state, somehow proportional to size or area. Florida seems particularly concave to me (it's practically shaped like a banana), Massachusetts slightly less so.
- klodolph 13y agoI think this metric might weight Tennessee higher than one would intuitively desire. Perhaps: 1. Draw a line segment between two connected points in the state, such that only the endpoints of the line are contained in the state. 2a. Draw a line segment perpendicular to this one, such that one end touches the first line, the other end touches the border of the state, and only one endpoint is contained within the state. The length of the largest such line is the "concavity" of the state. 2b. Alternatively, measure the area contained between line #1 and the state border. The largest such area is the "concavity" of the state. 2c. Alternatively, measure the ratio of the area in #2b to the length of the corresponding line in #1.