To put it another way, I thought that any connected surface morphs to a triangle (object of minimum sides) and assume that a collection of such objects (such as a map) is morphable to a collection of (arbitrary) triangles, therefore the maximum colours required is 4. Hence 5 for volumes based on morphing to irregular tetrahedra. On 30 Apr 2013, at 03:55, David Makin wrote:
On 30 Apr 2013, at 02:06, Bill Gosper wrote:
Dave Makin>I assume these "countries" didn't include any "holey" ones i.e. rings etc. ? Connectedness is obviously required. I don't see simple-connectedness mattering.
DM> Also given the equivalent assumptions is the answer for 3D just 5 colours ? Infinity, obviously. Scott Kim once showed me that the answer for *convex* 3D countries is "arbitrarily large".
Oh, that's interesting, I'll have to consider it more carefully....
Thanks.
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The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.