Bees' honeycomb can be elongated and scaled to have arbitrarily large surface area for unit-volume cells, but the closure at the end is not in equilibrium. See the wonderful:

Fejes Tóth, L., What the bees know and what they do not know. Bull. Amer. Math. Soc. 70 1964 468–481.

Conjecture: a bubble with at most 2 (or at most a certain number of sides) shrinks monotonically.

ReplyDeleteBees' honeycomb can be elongated and scaled to have arbitrarily large surface area for unit-volume cells, but the closure at the end is not in equilibrium. See the wonderful:

ReplyDeleteFejes Tóth, L., What the bees know and what they do not know.

Bull. Amer. Math. Soc. 70 1964 468–481.