# Is there a solution to this case of the Boursk theorem?

1. Feb 5, 2012

### luie1168e

prove:

Every planar domain of diameter 1 can be partitioned into three sets of diameter at most {sqrt 3} /2 not 1

The proof that I think would not work (p.73 of The art of mathmatics* by Béla Bollobás

[2]: http://i.stack.imgur.com/ymRWr.png

i think the proof of part 1 that is below the graph is not making any sense because it is not telling what is $a_i(L)$ and how does it relate to the problem. Is there a explanation of this proof or a easier proof?