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Re: Tiling the plane with checkerboard patterns
Posted:
Jul 14, 2010 5:01 PM
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On Wed, Jul 14, 2010 at 12:14:48PM +0000, Mary Krimmel wrote:
> From: Mary Krimmel <mary@krimmel.net>
> Date: Wed, 14 Jul 2010 12:14:48 +0000 (UTC)
> To: approve@support1.mathforum.org
> To: geometry-puzzles@support1.mathforum.org
> Subject: Re: Tiling the plane with checkerboard patterns
>
> Thank you all for an easy-to-understand puzzle. Mark's point that a
> plane tiling has no orientation seems to me to make his identifying
> rotations of the wallpaper a reasonable simplification of the original
> problem, as does Avni's separating even n from odd.
Hello Mary, I think it's Mark's formula that talks about even
and odd n. Avni's does not distinguish.
I am curious myself about rotational symmetries. I intend
to look into them when I find some free time.
> What about starting directly with the number of possible patterns?
> Maybe that's what you're doing, but not what I understood.
Well, yes, I computed a(1) through a(5) by examining all
possible patterns. This does not work for a(6) because
the number of patterns becomes too large for a computer
to handle.
> What if we started with an m by n rectangle where m and n
> are not necessarily equal?
My computer program is written to handle m by n rectangles
but I would rather resolve the n by n case before getting
into the general case.
Rouben
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