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Thursday, February 11, 2010

MT365 - More video programmes

MT365 - Video 2.
Video 2 is about tilings at the Alhambra. One of the options I considered for 2010 was studying m336 next to m208. I decided not to because of the geometry part of M336: it's about tiling patterns which I find a rather difficult subject. Designs 1 of MT365 is about the same subject. But where in M336 one must be able to prove that the only rotational patterns possible are of orders 2,3,4 and 6 that fact is accepted as is without proof in MT365. Designs 1 could very well be the step I need to start confident on M336 I have in my plan for 2012.

MT365 - Video 5.
This video is about the proof of the four colour theorem. No more than four colors are needed to color any map. Thomas Kempe, a 19th century mathematician ( played by an actor of course ) explains his proof in detail based on unavoidable sets and reducibility. I knew it couldn't be the real proof because I knew the real proof wasn't found until 1976 but I didn't see why Kempe's proof was flawed. Neither did the mathematicians he explained it to at the time. After ten years or so it became apparent that his proof wasn't entirely correct. In 1976 the theorem was proved but by a computer. The proof consisted of hundreds of computer-generated pages. - I wonder if there are still people around who hope for a compacter proof. The 1976 proof was largely based on Kempe's proof by the way. What if there is an entirely different approach possible to tackle this problem?

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