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["WILLIAM JONES" <billj AT harborside.com>]

This weekend I'm painting 24 blackbottles black and silver.  I inquired of 
myself how big the central hub needs to be, to accommodate 12 bottles in a 
circle.  First I observed that two adjacent bottle centers together with the 
center of the hub form an isosceles triangle.  If R is the unknown radius of 
the central hub, and r is the radius of a 2-liter bottle, then we can apply 
the Law of Cosines to this triangle with legs R + r, central angle 30 
degrees, and an opposite side of length 2r.  By solving for R I obtained
R = 2 Sqrt(2 + Sqrt(3)) - 1 ~ 2.8637 times the radius of a 2-liter bottle
I think I'll look for a pair of old black plastic pots, and attach the 
bottles with clear tape around the fat end, and just a lashing around the 
bottlenecks.