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  • From: "WILLIAM JONES" <billj AT harborside.com>
  • To: <homestead AT lists.ibiblio.org>
  • Cc:
  • Subject: [Homestead] Heat Engine: Math Is Everywhere
  • Date: Sat, 30 Jun 2012 23:17:06 GMT

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.


  • [Homestead] Heat Engine: Math Is Everywhere, WILLIAM JONES, 06/30/2012

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