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

@David Eppstein: 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)

GA Review

This review is transcluded from Talk:Cairo pentagonal tiling/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: Some Dude From North Carolina (talk · contribs) 01:21, 18 July 2021 (UTC)

GA review – see WP:WIAGA for criteria

1. Is it well written?

   A. The prose is clear and concise, and the spelling and grammar are correct:

   "for layered hydrate crystals, for certain compounds of bismuth and iron, and for penta-graphene" - a little overuse on "for"

   • @Some Dude From North Carolina: Is that all? Repetitions of "for" removed. —David Eppstein (talk) 18:24, 19 July 2021 (UTC)

   It is all I could find. Great work! Passing the article.

   B. It complies with the manual of style guidelines for lead sections, layout, words to watch, fiction, and list incorporation:

2. Is it verifiable with no original research?

   A. It contains a list of all references (sources of information), presented in accordance with the layout style guideline:

   B. All in-line citations are from reliable sources, including those for direct quotations, statistics, published opinion, counter-intuitive or controversial statements that are challenged or likely to be challenged, and contentious material relating to living persons—science-based articles should follow the scientific citation guidelines:

   C. It contains no original research:

   D. It contains no copyright violations nor plagiarism:

3. Is it broad in its coverage?

   A. It addresses the main aspects of the topic:

   B. It stays focused on the topic without going into unnecessary detail (see summary style):

4. Is it neutral?

   It represents viewpoints fairly and without editorial bias, giving due weight to each:

5. Is it stable?

   It does not change significantly from day to day because of an ongoing edit war or content dispute:

6. Is it illustrated, if possible, by images?

   A. Images are tagged with their copyright status, and valid fair use rationales are provided for non-free content:

   B. Images are relevant to the topic, and have suitable captions:

7. Overall:

   Pass or Fail:

Did you know nomination

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Desertarun (talk) 09:45, 28 July 2021 (UTC)

(

• Comment or view
• Article history

)

• ... that the Cairo pentagonal tiling was a favorite pattern of M. C. Escher? Source: Kaleidocycles (book reference cited in the article), p. 22, "One of Eschers favorite geometric patterns was the tiling by congruent pentagons." Context makes clear that it is this pentagon tiling that is intended.

• Reviewed: Jo Beall

Improved to Good Article status by David Eppstein (talk). Self-nominated at 07:36, 20 July 2021 (UTC).

• so the article is a (very) Good Article, is a really interesting read, is nicely illustrated too for us non-experts. The hook is hooky, not too long, assume good faith with this highly trusted editor on the offline source. Finally, QPQ checks out too, so this is good to go. The Rambling Man (Keep wearing the mask...) 20:02, 22 July 2021 (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)