I think the video Jim is looking for would show three families of equally-spaced parallel lines, at 60-degree angles to each other, all moving at the same rate. The tilings shown would almost always consist of two families of equilateral triangles of two different sizes, and one family of hexagons whose edges alternate between the side lengths of the two triangular families. I have seen this animation -- I can't remember where -- and my recollection is that it is surprisingly boring. On Wed, Jul 31, 2019 at 1:16 PM Mike Stay <metaweta@gmail.com> wrote:
On Wed, Jul 31, 2019 at 10:08 AM George Hart <george@georgehart.com> wrote:
Mike,
That's odd. (It works for me from the SF web server.) Are you in a distant country at the moment where videos might be blocked?
No, I'm in Utah near Rich.
There is also a YouTube copy here:
Thanks!
And a Scientific American copy here:
https://www.scientificamerican.com/article/mathematical-impressions-the-surp...
George http://georgehart.com
On 7/31/2019 11:42 AM, Mike Stay wrote:
I get "Sorry. Because of its privacy settings, this video cannot be played here."
On Wed, Jul 31, 2019 at 9:29 AM George Hart <george@georgehart.com>
wrote:
Hi James,
There is an example of that about two minutes into this video, as
a
warmup to what happens when you slice the Menger Sponge:
https://www.simonsfoundation.org/2012/12/10/mathematical-impressions-the-sur...
George http://georgehart.com
On 7/31/2019 8:10 AM, James Propp wrote:
I just realized that, to illustrate Warren Smith's way of proving
the Wall
of Fire theorem at my August 7 talk, it'd be cool to have a video or GIF showing how the intersection between the 2-skeleton of a moving cubical network and a fixed plane evolves in time. For instance, say the plane is {(x,y,z): x+y+z=0} and the cubical network is the standard one in Z^3 moving at constant speed in the (1,1,1) direction, which one can write as {(x,y,z); x≡t (mod 1) or y≡t (mod 1) or z≡t (mod 1)}. We see a dynamic dissection of the plane in which equilateral triangles grow and turn into hexagons and then turn into shrinking triangles pointing the other way.
Can anyone dash off such a video? If I use it in my talk I will of course give credit.
Thanks,
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-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike https://reperiendi.wordpress.com
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