Tuesday, July 15, 2008

Red, Green, Blue, Yellow

Leora accused me of being too left-brain. I'm not, really! Look at this pretty picture!

Well, I think my brain is ambidextrous. This picture is an example of a Four Color map:
The four color theorem (also known as the four color map theorem) states that given any plane separated into regions, such as a political map of the states of a country, the regions may be colored using no more than four colors in such a way that no two adjacent regions receive the same color. Two regions are called adjacent only if they share a border segment, not just a point. Each region must be contiguous: that is, it may not have exclaves like some real countries such as Angola, Azerbaijan, Italy, the United States, or Russia.

It is often the case that using only three colors is inadequate. This applies already to a map with one region surrounded by three other regions (although with an even number of surrounding countries three colors are enough) and it is not at all difficult to prove that five colors are sufficient to color a map.

The four color theorem was the first major theorem to be proven using a computer, and the proof is not accepted by all mathematicians because it would be unfeasible for a human to verify by hand (see computer-assisted proof). Ultimately, in order to believe the proof, one also has to have the belief (which can be justified or not) that the proof assistant software works as intended and that there were no other errors - such as in the functioning of the hardware - that corrupted the output. The proof is also considered inelegant.(wikipedia)

(The computer assisted proof was implemented by two guys at my alma mater, UIUC, in 1976)


Blogger Leora said...

Is that what I said? Will have to read more about color theory later. Or maybe not. I leave that to other members of my family, who study this sort of stuff for a living.

July 15, 2008 9:30 AM  

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