Monday, 26 March 2012

Summary (space-filling)

Here is part 5 of the meeting summary:

 + No space-filling foam with every F <= 13?
 + Is there a "worst" foam, in a sense to be defined?


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

  2. 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.