It would be nice if this were a post to something with more context than just a link to an image on imgur (frankly, I'd support not allowing this type of post), though it is quite interesting....
It would be nice if this were a post to something with more context than just a link to an image on imgur (frankly, I'd support not allowing this type of post), though it is quite interesting. Nevertheless, I felt compelled to look into it a bit, in part out of my own embarrassment about my inadequate knowledge of mathematical tilings.
Wikipedia has a reasonable article on pentagonal tilings. One should note the following:
There are more than 15 pentagonal tiling patterns. 15 is the number of types of convex pentagons that can tile a plane monohedrally. This is an important distinction, because the types of pentagons can tile the plane in different ways, both periodic and non-periodic, even though the image only shows periodic tilings.
The 15 types of convex pentagons are the convex pentagons that can tile a plane. There are non-convex monohedral pentagonal tile types that can tile the plane (some aperiodically tiling it), for example, in Chapter 10 of Grünbaum and Shephard's Tilings and Patterns (Wikipedia somewhat incorrectly attributes this to someone else).
Why pentagons? As Jaap Scherphuis points out on their tilings page, every triangle or quadrilateral can form a monohedral tiling. Pentagons are the first polygons where there is actually a limitation. Additionally, if considering regular polygons, pentagons are perhaps a bit oddly different than their neighbours: regular triangles, squares, and hexagons can all tile the plane monohedrally, and these are the only regular polygons that can: thus, while higher polygons are alike in their inability, pentagons are a bit unusual.
Yeah this was my thought as well. Without context this post has very little value. Whereas if it was an article/blog/whathaveyou with context similar to what you just wrote along with the image it...
Yeah this was my thought as well. Without context this post has very little value. Whereas if it was an article/blog/whathaveyou with context similar to what you just wrote along with the image it would have true value.
I think this was @RespectMyAuthoriteh's attempt to show us that pure images have value though... and they are not entirely wrong, IMO. It's going to be a tricky line to draw if we want to ban fluff sitewide because of cases like this where there is potential for them to have value and spark conversation (which does have value even if the picture itself doesn't).
I think the question here should not be whether a post has value, but whether a post has more value than an alternative post. In this case, as far as I can tell, the images are probably just...
I think the question here should not be whether a post has value, but whether a post has more value than an alternative post. In this case, as far as I can tell, the images are probably just copied without any attribution from Jaap Scherphuis' website (or at least, I am quite confident they were generated with their software). Unlike the inaccurate and outdated title of this post, that page actually gives quite a bit of information on pentagonal (and other) tilings. Posting it would have required no more effort, or likely even less effort, than taking the images from it and posting them without context; even just having the image from elsewhere, finding the page was quite simple in searching for pentagonal tilings and looking on Wikipedia.
It is only, I would speculate, the culture of Reddit encouraging image posts that would discourage posting a link to actual websites.
It would be nice if this were a post to something with more context than just a link to an image on imgur (frankly, I'd support not allowing this type of post), though it is quite interesting. Nevertheless, I felt compelled to look into it a bit, in part out of my own embarrassment about my inadequate knowledge of mathematical tilings.
Wikipedia has a reasonable article on pentagonal tilings. One should note the following:
Wikipedia points out that Michael Rao put up a proof of 15 tile types being complete late last year, using a computerized exhaustive search. Thus, short of a significant error in that preprint, it's likely that the 15 are, in fact, the only possible tile types.
Why pentagons? As Jaap Scherphuis points out on their tilings page, every triangle or quadrilateral can form a monohedral tiling. Pentagons are the first polygons where there is actually a limitation. Additionally, if considering regular polygons, pentagons are perhaps a bit oddly different than their neighbours: regular triangles, squares, and hexagons can all tile the plane monohedrally, and these are the only regular polygons that can: thus, while higher polygons are alike in their inability, pentagons are a bit unusual.
Yeah this was my thought as well. Without context this post has very little value. Whereas if it was an article/blog/whathaveyou with context similar to what you just wrote along with the image it would have true value.
I think this was @RespectMyAuthoriteh's attempt to show us that pure images have value though... and they are not entirely wrong, IMO. It's going to be a tricky line to draw if we want to ban fluff sitewide because of cases like this where there is potential for them to have value and spark conversation (which does have value even if the picture itself doesn't).
I think the question here should not be whether a post has value, but whether a post has more value than an alternative post. In this case, as far as I can tell, the images are probably just copied without any attribution from Jaap Scherphuis' website (or at least, I am quite confident they were generated with their software). Unlike the inaccurate and outdated title of this post, that page actually gives quite a bit of information on pentagonal (and other) tilings. Posting it would have required no more effort, or likely even less effort, than taking the images from it and posting them without context; even just having the image from elsewhere, finding the page was quite simple in searching for pentagonal tilings and looking on Wikipedia.
It is only, I would speculate, the culture of Reddit encouraging image posts that would discourage posting a link to actual websites.
This reminds me of M.C. Escher's Tessellation work.