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