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Topic: honeycombs
Replies: 9   Last Post: Jan 24, 2013 5:40 PM

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glen herrmannsfeldt

Posts: 323
Registered: 12/7/04
Re: honeycombs
Posted: Jan 23, 2013 8:50 PM
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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



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