The Corner

Concavity Index

Incidentally, there is actually a mathematical theory of convexity. Prof.

C.A. Rogers, one of my teachers at University College, London, was an

authority on it. It doesn’t seem to be well represented on the web — I

can’t find a neat summary. If you want to try for yourself, good additional

Google arguments are “steiner symmetrization” and “isoperimetric


I have often wondered whether this branch of math might have some

application in politics. We read a lot about the convoluted electoral

districts produced by computer-selecting precincts to make every

congressional seat a safe one. Perhaps that kind of thing could be stopped

if some convexity requirement was placed on the shape of congressional



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