10-327/Classnotes for Thursday October 21

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See some blackboard shots at BBS/10_327-101021-143325.jpg.

Dror's notes above / Student's notes below

Here are some lecture notes..

Lecture 11 page 1

Lecture 11 page 2

Lecture 11 page 3

Lecture 11 page 4

Lecture 11 page 5

Lecture 11 page 6

Lecture 11 page 7

Riddle Along

Can you color \mathbb{R}^2 with 4 colors such that no points with distance one are the same color? Sorry, I meant 3, not 4!

10-327/Solution to coloring R2

  • Are you asking us to solve the Hadwiger-Nelson problem?
    • Only to give the relatively easy bound... Drorbn 08:58, 6 November 2010 (EDT)
      • Perhaps I am misreading the question, but according to the Wikipedia article and some quick conformational googling, it seems to be an open question as to whether or not it is possible with four colours. Three and Seven seem to be the easy bounds. Though, I suppose it is possible that four has recently been ruled out and the results require a bit more searching to find. Indecently, this was the Wikipedia's Mathmatics portal picture of the month which is how I stumbled across it. - Johnfleming
        • Ooops, I had a typo! Sorry. Anyway, now the problem becomes a bit pointless, as right above there's a link to its solution... Drorbn 18:32, 6 November 2010 (EDT)