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Topic: Tiling the plane with checkerboard patterns
Replies: 21   Last Post: Jul 14, 2010 10:33 PM

 Messages: [ Previous | Next ]
 Rouben Rostamian Posts: 193 Registered: 12/6/04
Re: Tiling the plane with checkerboard patterns
Posted: Jul 14, 2010 5:01 PM

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

Date Subject Author
7/6/10 Rouben Rostamian
7/7/10 Avni Pllana
7/8/10 mark
7/9/10 Rouben Rostamian
7/9/10 Avni Pllana
7/9/10 Rouben Rostamian
7/10/10 Avni Pllana
7/10/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/11/10 Rouben Rostamian
7/11/10 mark
7/12/10 Rouben Rostamian
7/13/10 mark
7/14/10 Rouben Rostamian
7/14/10 mark
7/11/10 Rouben Rostamian
7/14/10 Avni Pllana
7/14/10 Rouben Rostamian
7/13/10 Mary Krimmel
7/14/10 Rouben Rostamian
7/14/10 mark