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Topic: Power of 2 divisible by 3
Replies: 19   Last Post: Feb 1, 2006 10:37 PM

 Messages: [ Previous | Next ]
 Brian Quincy Hutchings Posts: 3,031 Registered: 12/6/04
Re: Power of 2 divisible by 3
Posted: Feb 1, 2006 2:18 PM

yes, nice, but I'll just correct the typo:

2^k = 3(2^k) - 2^(k+1).

thus:
I was going to say that the "map, below," was 3-colorable, but
the formatting became clear upon clicking for replying. anyway,
that is also the "neccesity" part of the 4-color proof,
a.k.a. "the tetrahedron, q.e.d." on a sphere
(more or less; your further result is the same,
as coloring/labelling the surrounding space .-)

> Please explain how a map demanding 5 colors can demand 5 colors without
> having 5 countries bordering each other? Anything except the specious
> countries! Consider the simple map below
> ----------------------------------------
> | A |
> |----------------------------------------|
> | | | |
> | B | C | D |
> | |______| |
> |__________ |___________ |

> If the analogy were valid, you could add country E between B & D, just
> below C and get a 5-color map . And there are no 5 countries bordering
> each other.

> But the analogy is not valid. Adding E actually makes the map 3-C.

> ------------------------------------------
> | A |
> |----------------------------------------|
> | | | |
> | B | C | D |
> | |______| |
> |_______ |__E__|_________|

--Give Earth a Trickier Dick Cheeny -- out of office, after gigayears!
http://larouchepub.com/other/2003/3045dems_dive_soros.html
http://tarpley.net/bush8.htm
http://www.benfranklinbooks.com/
http://members.tripod.com/~american_almanac
http://www.wlym.com/pdf/iclc/howthenation.pdf
http://larouchepub.com/other/2003/3048iraq_58_const.html
http://www.rand.org/publications/randreview/issues/rr.12.00/
http://www.rwgrayprojects.com/synergetics/plates/figs/plate01.html