Tictactoe on Mobius strip has something counterintuitive. Please help!
 From: Bhushit Joshipura <joshipura@xxxxxxxxx>
 Date: Tue, 19 Aug 2008 02:28:33 0700 (PDT)
Hello,
I am not a mathematician.
I am trying to define tictactoe on Mobius strip. (http://
surfaces.sourceforge.net)
I came across a problem while defining the diagonals. I need help.
Here is how I defined a Mobius strip board: (hopefully the picture
looks good)
++
 
+>(0,2)(1,2)(2,2) >+
(0,1)(1,1)(2,1)  
+>(0,0)(1,0)(2,0) >+ 
 
++
.... and (0,1) and (2,1) "roll around" to each other.
Horizontal "three in a line" conditions would mean any three
consecutive coordinates from below:
(0,0)(1,0)(2,0)(0,2) notice it twisted  (1,2)(2,2)(0,0) twist
and back  and so on
and (0,1)(1,1)(2,1)
If I define "right and up" diagonal, one of them could be: (1,0)(2,1)
(0,2)
But if I define "up and right" diagonal, one of them could be: (1,0)
(2,1)(0,0)
That means the operations "up" and "right" are not symmetric to each
other(?) anymore. I coming across two diagonals originating with two
common points.
Which one of the above definition for diagonal is correct?
Confused,
Bhushit
.
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