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.