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Re: honeycombs
Posted:
Jan 23, 2013 5:22 PM
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On Jan 21, Martin Brown <|||newspam...@nezumi.demon.co.uk> wrote:
> > I saw a news item about a new technique to draw CO2 from
> > the atmosphere. It's a chemical process, using amines,
> > which binds with the molecule, coated on a large structure,
> > in the shape of a honeycomb.
>
> > According to the story, this maximizes surface area.
> > ok, mathematicians, which function gets optimized by a
> > honeycomb? What are the constraints and assumptions?
>
> 2D problem to *minimise* the surface area to occupy a given volume. Bees
> use it to make honeycomb with the least amount of wax.
>
> It is not difficult to show that the angle between sides must be 120
> degrees and that equal lengths minimise total length/area occupied.
>
> They have the structure just about as wrong as it is possible to be
> unless the stuff they are making it out of is extremely precious.
?
> The 3D problem to occupy volume with a foam of minimum surface area is
> far more interesting and gives rise to Plateau's laws of soap films. The
> Kelvin foam structure was optimal until fairly recently when
> Weare-Phelan discovered a 3% better solution using a pair of shapes. A
> whole new family has been found but as yet a proof of optimality eludes.
The claim is that honeycomb maximizes surface area
(of what?). This is new to me, so I'm looking for a
rigorous statement of the problem, and proof of the solution.
--
Rich
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