Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

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

 Messages: [ Previous | Next ]
 Rich Delaney Posts: 392 Registered: 12/13/04
Re: honeycombs
Posted: Jan 23, 2013 5:22 PM

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

Date Subject Author
1/22/13 Rich Delaney
1/22/13 Martin Brown
1/22/13 Repeating Rifle
1/23/13 Rich Delaney
1/24/13 Repeating Rifle
1/23/13 Rich Delaney
1/23/13 glen herrmannsfeldt
1/24/13 Martin Brown
1/24/13 Martin Brown
1/24/13 Brian Q. Hutchings