I don't know how to read sewing patterns, but here's what I think you're describing: Take a square, and put arrows pointing left on the top and bottom sides, and an arrow pointing up on the left and an arrow pointing down on the right If we join the top and bottom so that the arrows match up, we have a cylinder. If we join the left and right edges so that the arrows match up, we have a Mobius strip. If we join both of these pairs of arrows in this way (impossible in three dimensions without self-intersection), we have a Klein bottle. Andy On Sun, May 3, 2020 at 12:46 PM Steve Witham <sw@tiac.net> wrote:
What does one call a tube looped around as if to make a torus, but connected clockwise-to-counterclockwise, as in this sewing pattern?
z y>--C-->z y +---------+ x|w>--A-->x|w v|^ v|^ ||| ||| B|D B|D ||| ||| v|^ v|^ y|z<--C--<y|z +---------+ w x<--A--<w x
Unless I'm fooling myself, this makes a way to wrap the sides of the board around for a game like Life or Langton's Ant, in such a way that the space is locally flat everywhere--without any local kinks or anomalies that would snarl the game rules. I have tried to think of such a thing so many times in the past and failed...
Is this consistent? What's it called?
--Steve
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Andy.Latto@pobox.com