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Re: honeycombs
Posted:
Jan 23, 2013 8:50 PM


In comp.dsp RichD <r_delaney2001@yahoo.com> wrote: > On Jan 21, Martin Brown <newspam...@nezumi.demon.co.uk> wrote:
(snip) >> 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.
(snip)
> 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.
As far as I know, hexagonal packing is the optimal packing for an (infinite) array of circles. (For smaller arrays, there edge effects are important.)
Also, either HCP or FCC are optimal for a 3D array of spheres, or in general any combination of the two.
If you arrange a hexagonal layer of spheres, and then want to add a new layer on top, there are two possible optimal packed positions for that layer.
The resulting reqular arrays can be described by the sequences:
1  2  1  2  1  2 ... (HCP) or
1  2  3  1  2  3 ... (FCC).
I don't know if this helps or not.
 glen



