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Wolfram Alpha also has some things about tiling: http://www.wolframalpha.com/input/?i=pentagon+tiling http://www.wolframalpha.com/input/?i=pentagon+type+5+tiling
This is cool, but I'm not sure why it's a hard problem to solve for a computer running through a ton of 5-sided polygons with some basic rules and attempting to tessellate them? Is there a reason that approach doesn't work, other than being rather un-romantic as far as discovering cool new things like this goes?
That approach does work. From the article: "We discovered the tile using using a computer to exhaustively search through a large but finite set of possibilities,” said Casey.
Kudos for not using the same clickbait title The Guardian did. Journalistic integrity is dead.
Even the example in the article can be viewed as a regularly tessellating nonagon. I don't see what's "irregular" about it? The article doesn't mention that word, but the HN title does.
I think it's kinda funny that most of the tessellations are just using pentagons to make other shapes that tessellate naturally. I suppose the same could be said of most tessellations though, but it's still interesting.
That's because there are only 17 wallpaper groups ( https://en.m.wikipedia.org/wiki/Wallpaper_group ). Any _repeating_ pattern must match one of them (non-repeating patterns by definition do not)
Earlier quoted context omitted.
I don't think that tiling a plane is exactly a "simple" problem.
I mean something simple enough to understand, and could be played by average programmer in a IPython Notebook. I didn't mean simple to solve, just lower barrier of entry.
http://www2.stetson.edu/~efriedma/squinsqu/
Can be easily generalized to other shapes and more dimensions too.
"Attack on the pentagon" ...aaaand the guardian has lowered themselves to buzzfeed's standards.
Perhaps the more impressive number is that they found 7 quintillion new irregular pentagons that can't tile the plane.
I've read your comment a few different ways. I'm concluding that you find it impressive that it took 7 quintillion tries to find a new pentagon that can tile the plane.
Edit: The article is talking about building structures but isn't a triangle the most rigid form? And triangles are already used in building.
Besides tiling your bathroom is there any use case for this? Or is this pure for fun and gaining knowledge? Edit: The article is talking about building structures but isn't a triangle the most rigid form? And triangles are already used in building.