http://xorshammer.com/2008/08/16/two-different-solutions/ Some things in mathematical logic that I find interesting Wed, 18 Jan 2012 18:13:09 +0000 hourly 1 http://wordpress.com/ http://xorshammer.com/2008/08/16/two-different-solutions/#comment-151 Thu, 19 Feb 2009 23:06:19 +0000 http://xorshammer.wordpress.com/?p=44#comment-151 Indeed…and what is even more surprising, if I got it right, is that it’s even possible to have all circles to be the same size with the second construction. And here the geometric solution seems impossible.

]]> http://xorshammer.com/2008/08/16/two-different-solutions/#comment-16 Sun, 17 Aug 2008 15:28:08 +0000 http://xorshammer.wordpress.com/?p=44#comment-16 Great observation, I hadn’t thought of that. It did occur to me that the set-theoretic solution gives the extra information that any family of disjoint circles can be extended to a partition when . The problem of getting a geometric solution even for or finite seems like it’s probably very hard.

]]> http://xorshammer.com/2008/08/16/two-different-solutions/#comment-15 Sun, 17 Aug 2008 15:07:50 +0000 http://xorshammer.wordpress.com/?p=44#comment-15 This is a fun observation! The set-theoretic solution gives a hint to the obvious follow-up question: Why 3? I don’t see how to get that information from the (very clever) geometric solution. It seems odd that the non-constructive solution gives more information than the constructive one. Perhaps the geometric solution is too clever?

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