Re: [math-fun] Coordination sequence for 3.3.4.3.4 lattice
Funny, I was just thinking about that Archimdean tiling the day before, since it's dual to the "Cairo" tiling by (non-regular) pentagons. In fact of all the Archimedean tilings of the plane, I find that one to be the least appealing, aesthetically. And I was asking myself why I have that reaction. I think it's because of two contradictory first impression of those squares and triangles is that they're chaotic. And the second impression is that with so many triangles arranged edge-to-edge, it looks unduly tame. On the other hand, the dual tiling is perhaps the most beautiful Archimedean dual. http://en.wikipedia.org/wiki/Cairo_pentagonal_tiling . << There's a pretty Archimedian tiling with vertex figure 3.3.4.3.4 . . .
Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California
I concur that I miscounted term 4 as 22 rather than 21. And I think it's likely that the Freds have got the right recurrence pattern. Who'll make the OEIS entry? On 11/17/12, Dan Asimov <dasimov@earthlink.net> wrote:
Funny, I was just thinking about that Archimdean tiling the day before, since it's dual to the "Cairo" tiling by (non-regular) pentagons.
In fact of all the Archimedean tilings of the plane, I find that one to be the least appealing, aesthetically. And I was asking myself why I have that reaction.
I think it's because of two contradictory first impression of those squares and triangles is that they're chaotic. And the second impression is that with so many triangles arranged edge-to-edge, it looks unduly tame.
On the other hand, the dual tiling is perhaps the most beautiful Archimedean dual. http://en.wikipedia.org/wiki/Cairo_pentagonal_tiling .
<< There's a pretty Archimedian tiling with vertex figure 3.3.4.3.4 . . .
Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
OK, I submitted it. And now I'm feeling guilty that I haven't been doing any OEIS editing work. Maybe I will do some over the long weekend; it looks like there's quite a backlog. On Sun, Nov 18, 2012 at 10:31 AM, Allan Wechsler <acwacw@gmail.com> wrote:
I concur that I miscounted term 4 as 22 rather than 21. And I think it's likely that the Freds have got the right recurrence pattern. Who'll make the OEIS entry?
On 11/17/12, Dan Asimov <dasimov@earthlink.net> wrote:
Funny, I was just thinking about that Archimdean tiling the day before, since it's dual to the "Cairo" tiling by (non-regular) pentagons.
In fact of all the Archimedean tilings of the plane, I find that one to be the least appealing, aesthetically. And I was asking myself why I have that reaction.
I think it's because of two contradictory first impression of those squares and triangles is that they're chaotic. And the second impression is that with so many triangles arranged edge-to-edge, it looks unduly tame.
On the other hand, the dual tiling is perhaps the most beautiful Archimedean dual. http://en.wikipedia.org/wiki/Cairo_pentagonal_tiling .
<< There's a pretty Archimedian tiling with vertex figure 3.3.4.3.4 . . .
Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (2)
-
Allan Wechsler -
Dan Asimov