Of course, since you use three dimensional space. I believe the Four Color Theorem assumes a single plane. If you could create a map in two dimensions then I'd be impressed.
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Of course, since you use three dimensional space. I believe the Four Color Theorem assumes a single plane. If you could create a map in two dimensions then I'd be impressed.
That was my point. It is easy if you change the assumptions, and probably impossible if you don't. :)
alright, ill take a shot at it.
*note: black region counts as a region that needs to be coloured. I guess i could have used orange or something :rolleyes:
Change the inner black to blue and the outer black to yellow.
According to this page:
So if you want to 'solve' it maybe you should try using more than 25 regions.Quote:
http://www.math.gatech.edu/~thomas/FC/fourcolor.html
The next major contribution came from Birkhoff whose work allowed Franklin in 1922 to prove that the four color conjecture is true for maps with at most 25 regions.
hmm.. how about this?
color red gree and and the middle and outside red.
Back to kindergarten.
I bet he would seeing as it would make your prof instantly famous. No one has proved or disproved the theorem for a map of more than 25 regions. The proof published by Appel-Haken is not accepted and will not be accepted for a couple reasons.Quote:
Originally Posted by axon
1). Parts are done on computers and cannot be verified by hand.
2). No one has been able to check the rest of the proof in it's entirety.
Can anyone link to a site that says in the theorem the regions cannot touch at a point? I searched and didnt find anything about that.
If no one can I will continue to think I am the winner so I feel special.
http://mathworld.wolfram.com/Four-ColorTheorem.htmlQuote:
The four-color theorem states that any map in a plane can be colored using four-colors in such a way that regions sharing a common boundary (other than a single point) do not share the same color.
Awwww....
What about this one? (find the black one) :confused:
Change all of the dark green ones to light green and then you can colour the black part dark green.
what about this one?
Exchange either yellow and red vertically and color the square yellow or red.