Use several different lengths of "ruler" to measure the circumference and from that obtain an average fractal dimension. However if such districts are anything like in the UK then irregularity is more down to local geography and population density/location so I don't see how it could be used to detect politically motivated adjustment of boundaries - unless cross-referenced with even more local data relating to which locatuons voted for what. On 20 Jun 2014, at 23:27, Allan Wechsler wrote:
Area of convex hull divided by area of region?
On Fri, Jun 20, 2014 at 6:21 PM, Wouter Meeussen <wouter.meeussen@telenet.be
wrote:
a nice one for Steven Finch? He did work on the 'HullMeanWidth' for convex polytopes in 3D. This has a similar flavour:
circumference (alias 'outer boundary length') / circumference of equal-area circle ?
Wouter.
-----Original Message----- From: Neil Sloane Sent: Friday, June 20, 2014 11:38 PM To: fun Subject: [math-fun] measuring the irregularity (or salamander-ness) of aplanar region
Is there a good measure of how irregular a region of the plane is?
something that gives 0, say, for a circular disk, and 1 (or infinity) for a fractal gasket?
the motivation is to find a measure of how irregular (or gerrymandered) a congressional district is.
Neil
-- Dear Friends, I have now retired from AT&T. New coordinates:
Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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