Talk:Cairo pentagonal tiling

Equilateral cairo pentagon
you can create an equilateral pentagon that tessalates like the cairo tiling with the following angles:


 * 131.4096221092708593384805021869257207417840511487285383700575° ( 90 + 2*arcsin( 1/(2*sqrt(2)) ) )


 * 90°


 * 114.29518894536457033075974890653713962910797442563573081497124° ( 45 + arccos( 1/(2*sqrt(2)) ) )


 * 114.295...


 * 90°

I'm pretty sure they are transcendental numbers. Introscopia (talk) 02:03, 23 July 2013 (UTC)


 * Introscopia is probably aware that 90 is not a transcendental number.
 * Units, such as degrees or radians, should be specified. — Preceding unsigned comment added by 31.54.202.247 (talk) 07:08, 30 June 2018 (UTC)

Ordinary
Under "Geometry", ordinary mathematical symbols could be used, instead of computer code. — Preceding unsigned comment added by 31.54.202.247 (talk) 06:43, 30 June 2018 (UTC)

Formatting
Somehow the tomb image was too much. (diff) --Watchduck (quack) 12:50, 11 December 2020 (UTC)
 * Weird. It doesn't do that for me. But I've rearranged it in such a way that the multiple image should never be able to flow into the references. —David Eppstein (talk) 17:51, 11 December 2020 (UTC)

Variations
I hadn't looked at geometric solutions before, so I made a chart to show a cycle of solutions with 2 nonadjacent right angles, and 4 equal edge lengths. The 5th horizontal edge varies between zero length and twice as long. I also show the convex equilateral solution in the center. I showed at angle multiples of 30. Convex in first quadrant, concave second quadrant, self-contact in third quadrant and flipped geometry fourth quadrants (turn angle sum is zero). I also found there are two equilateral solutions, the second one in the flipped form. All of them can tile the plane, but will get crazy when edges cross and flip. Tom Ruen (talk) 23:00, 11 December 2020 (UTC)
 * Without sources, this is all original research. Also, the article is heavily illustrated already, to the point where the image placement has been causing rendering problems (see previous thread). —David Eppstein (talk) 23:17, 11 December 2020 (UTC)
 * It is much better than before but, too many floating images doesn't mean too many images. There's no reason it can't have a table of images showing varied forms, if they can be referenced, as you say. Tom Ruen (talk) 23:52, 11 December 2020 (UTC)
 * I want to avoid your tendency to cram articles full of big tables of barely-relevant images that cover material that is neither discussed in thee text of the article nor covered by reliable sources and that, by repeating the same tables in many different articles, make them all indistinguishable from each other. —David Eppstein (talk) 01:21, 12 December 2020 (UTC)
 * You're fighting a fake fight. I merely rearranged flow of YOUR selected images, only adding one more context and a header row again for context you neglect! Tom Ruen (talk) 01:24, 12 December 2020 (UTC)
 * See new discussion thread on WT:WPM. —David Eppstein (talk) 01:39, 12 December 2020 (UTC)

MCE
I do not find a print Shells and Starfish (1941) in the book M.C.Escher: His Life and Complete Graphic Work. —Tamfang (talk) 22:38, 4 August 2021 (UTC)
 * Turns out to be a drawing, not a print. Sometimes numbered as "symmetry drawing number 42", "Euclidean notebook drawing number 42", or something similar. I changed "print" to "drawing" here. —David Eppstein (talk) 00:17, 5 August 2021 (UTC)
 * I thought that might be the case. Thanks. —Tamfang (talk) 17:05, 5 August 2021 (UTC)

Incorrect side length
The image with caption "Geometry of pentagons for the dual snub square tiling" has the non unit side labeled as 1-sqrt(3). This is slightly incorrect as that would be negative, the correct number is sqrt(3)-1. Slight mistake but otherwise good article. 206.126.214.171 (talk) 02:00, 10 February 2022 (UTC)
 * Paging User:Extemporalist, whose image this is. I also left a note for Extemporalist on commons. —David Eppstein (talk) 05:42, 10 February 2022 (UTC)