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Topology Question

Posted by on | February 5, 2018 | Comments Off

Is there some sort of metric for the complexity of a boundary like this one for PA Distric 7, among those invalidated in PA (in a decision the Supreme Court today refused to review)?

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I keep wondering whether there is an objective standard we can set, rather just the sort of “I know it when I see it” one that everyone seems to use.

One way I can imagine testing is to do it Monte Carlo style by drawing a series of lines from one random point in the shape to another random point in the shape and calculating which percentage of the lines cross the boundary at least once.  That metric for a circle or a rectangle would be zero, but would be very high for this shape.

 

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