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Really don't know, Pat.  I've heard that 4 color thing, but in my graduate
work I pretty well kept to the meat & potatoes of real & complex analysis
and abstract algrebra.  Only one course in topology and that was pretty
straight math / set theory / logic.  My undergraduate classes were a tad
more varied (Boolean algrebra, number theory, differential equations, ring
theory, some upper division probability and statistics courses that used
calculus, etc) but never studied the 4 color thing as far as I can remember.

Robert 

	-----Original Message-----
	From:	[log in to unmask] [SMTP:[log in to unmask]]
	Sent:	Monday, March 12, 2001 3:36 PM
	To:	[log in to unmask]
	Subject:	Re: (VERY) OFF TOPIC - Map coloring

	In a message dated 3/12/01 5:16:17 PM Eastern Standard Time, 
	[log in to unmask] writes: 
	
	
	

		I meant "both rational and irrational numbers".  Had
problems with that 
		insert / delete mode on the keyboard. 
		
		Robert 
		
		   



	How did they arrive at 1200 for the number of possible arrangements?
I think 
	the number has to be much lower, at least for the way I was doing
it, which 
	is to assume that any map, no matter how large, can be broken down
into   
	modules of four shapes, each of which is colored in the 4 colors.
There could 
	be one, two, or three "leftover" shapes, but they can be treated as
an 
	incomplete module. The hard part is figuring how to construct  any
map from 
	the 24 sets of color arrangments possible for any individual module.
I think 
	one might have to go back and make an accommodation for whether an
individual 
	module has 1, 2, or3 internal vertices that don't touch the
perimeter of the 
	module. 
	
	But how did they compute the 1200? 
	
	pat