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

  1. Feb 5, 2012 #1
    My question have been post elsewhere, but since no one answer, please help me

    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?
     
  2. jcsd
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