User talk:Tomruen

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Pentagonal tiling[edit]

Aperiodic pentagonal tessellation

Hi Tom, apropos of the recent activity on pentagonal tiling, I thought you might be interested in the tiling at File:Exotic pentagonal tiling.png, if you haven't seen the pattern before. I don't particularly propose adding it to the article ... I just uploaded it for interest. Another Matt (talk) 01:51, 23 October 2015 (UTC)

It looks very nice. I copied your comment to the article talk page. I outlined a "base" edge in color, and then colored seemingly 22 radial subtilings. Tom Ruen (talk) 09:45, 24 October 2015 (UTC)

Regular heptadecagon construction[edit]

"Another construction of the regular heptadecagon" without function! Problem image size? --Petrus3743 (talk) 10:34, 24 October 2015 (UTC)G

I was hoping Wikipedia was being slow computing a rescaling of the animated gif. Tom Ruen (talk) 11:38, 24 October 2015 (UTC)

Tridecagon, Construction[edit]

it would be well for the reader if you could improve the arrangement of the two representations yet. These representations include images that can not understand directly the reader! Perhaps you succeed again an arrangement as described in article heptagon (text next to the image)? For now, thank you for your efforts! --Petrus3743 (talk) 12:56, 24 October 2015 (UTC)

Okay, I put the layout back as it was. Tom Ruen (talk) 13:12, 24 October 2015 (UTC)
Please also see the same thing in Enneadecagon, Construction. Thanks...--Petrus3743 (talk) 13:24, 24 October 2015 (UTC)

all those polygonal symmetries[edit]

Very nice pics! Any chance of getting them up for the range {40, 50, 60, 64, 70, 80, 90, 100}? (I think that'd be near the end of it. Apart from {34, 48, 51, 68, 85, 96} there aren't any more constructible polygons with standard names, although {36, 72} have clean whole- or half-degree angles but are not constructible.)

(A mammoth case would be {210}, 2×3×5×7, but I don't think there is a reliable source that names it like the polygons up to {100}, and I suspect that even you would be tired out by it.) Double sharp (talk) 15:10, 25 October 2015 (UTC)

I was thinking of a 360-gon for degrees and it would have 7 subgroups r720, i240, i144, i80, i48, i16, and each of those leads a 11 symmetry graph of index 2 subgroups (like octagon#symmetry graph). I'm leaning to just drawing the Conway names like I did for 60. I added 42 defend by the tiling connection. The 42 graphic took quite a while to try to label symmetry elements and vertex colors on all the polygon. Constructiblity is another point for notability for 32, 64, etc. Tom Ruen (talk) 15:16, 25 October 2015 (UTC)
True, 360 has a lot of factors, though 210 would give 2×3×5×7. I agree that drawing the Conway names would be clearer, but then it looks odd to have {42} but not the smaller {40}.
I added {48, 96} (earlier I added {64}) from Archimedes' pi approximation. Double sharp (talk) 15:35, 25 October 2015 (UTC)
I think that'd be the end of the constructible-polygon additions, because the values for sin(π/n) for n = 34, 51, 68, 85 (derived from the heptadecagon) are ugly, ugly things. If you want to show a case with lots of factors that is still constructible, I'd love {120} (hecatonicosagon? dodecacontagon? we can extrapolate this from Johnson's name for the 120-cell). Then maybe {600} can be considered named from the hexacosichoron. Double sharp (talk) 15:45, 25 October 2015 (UTC)
The additions look good. I'll see about adding more symmetry graphs, whether names-only or with pictures. Also interesting for smaller ones are examples of each symmetry in irregular polygons, like 6 symmetry, 8 symmetry, 12 symmetry. Tom Ruen (talk) 16:18, 25 October 2015 (UTC)
Cool! BTW, could you make a picture for {120} with the vertices marked (like File:Regular polygon 100.svg)? I think that'd be the end of it as the other constructible polygons don't really have standard names, or have ugly angles like {34, 51, 68, 85} (and these come about simply from the case of {17}). Also, did you miss {50} when going through the diagrams? Double sharp (talk) 02:39, 27 October 2015 (UTC)
OK, I found {50} and added its diagram and section. Double sharp (talk) 02:42, 27 October 2015 (UTC)
BTW, could we have the star 120-gons? There's only fifteen, so it makes sense to show them all (like we do for {64}). Double sharp (talk) 02:55, 27 October 2015 (UTC)
Yes check.svg Done Double sharp (talk) 12:44, 27 October 2015 (UTC)

I daresay Stella's not too happy with me right now[edit]

I tried making a {360/179} prism in Stella. The result was entertaining, but soon afterwards it threw a tantrum and stopped responding. >_< Double sharp (talk) 12:43, 27 October 2015 (UTC)

Comparison of the final stellations of polygons for which their number of sides is a superior highly composite number (ignoring {6}, as that just makes a hexagonal prism):

Double sharp (talk) 12:54, 27 October 2015 (UTC)

Looks like we need some more oversampling pixelation on the last one. Tom Ruen (talk) 08:02, 28 October 2015 (UTC)
Yes, but it freezes the program, so the most I could do was to take a screenshot. Double sharp (talk) 15:26, 28 October 2015 (UTC)

This made me remember that I forgot you said you were thinking of a 360-gon for degrees, so I added it. Now that should really be it. (Do we have a table somewhere of polygons with integer-degree interior angles?) Double sharp (talk) 12:56, 29 October 2015 (UTC)

Thank you for adding the symmetries diagram to {360}! Double sharp (talk) 13:26, 29 October 2015 (UTC)
I'm currently using Tyler to make the 47 360-grams and am currently halfway at {360/89}. It sure gives tedium a new meaning! Double sharp (talk) 13:34, 29 October 2015 (UTC)
I could make them in SVG, but don't have my script handy for the moment. Tom Ruen (talk) 13:50, 29 October 2015 (UTC)
It's OK: I'm at {360/119} now and would rather not have my pictures obsoleted before they are even finished! (^_^) They show beautiful moiré patterns and are even more symmetric than the chiliagon (1000 has 16 factors, while 360 has 24). Double sharp (talk) 13:51, 29 October 2015 (UTC)
{360/149} now. I have to see this through to the end at {360/179}! Double sharp (talk) 13:57, 29 October 2015 (UTC)

OK, I've done them all and put them into 360-gon. The size of the 360-gon in the middle should keep decreasing as we increase the denominator. Incidentally I can answer my own question – the only convex regular polygons whose interior angles are a whole number of degrees have n sides, where n is one of the factors of 360, i.e. a member of the set {(1), (2), 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180, 360}. Double sharp (talk) 14:31, 29 October 2015 (UTC)

Tyler's regular polygon colour scheme[edit]

It seems to repeat every 45 polygons, so {15} and {60} have the same colour. So I put them in a picture: Polygons comparison.png (I went up to {60}, as it may be a little difficult to see the smaller polygons, so it seemed useful to show their colours again with {48} to {60}.) Double sharp (talk) 11:02, 30 October 2015 (UTC)

A nice spiral of polygons. I added SVGs for 120, 360, unsure what else is needed. Tom Ruen (talk) 18:48, 30 October 2015 (UTC)
Thank you!
{65537}, {106} would be good to replace the actual circles we currently use, but are probably not doable. Thank you for the SVGs!
Actually I think what Tyler is doing is repeating the colour scheme every 9 polygons, but it gets darker each round, until five lots of 9, i.e. the 45, are complete and we return to the beginning at {48}, with the same colour as {3}. Double sharp (talk) 05:02, 31 October 2015 (UTC)

Flower of Life[edit]

Hey there. I see that you did a lot of work on Flower of Life (geometry) after I did the other day. A lot... it looks like hundreds of edits. Ya probably wanna use that 'preview' button! You probably made that a hundred times harder on yourself. And you did rearrange some of my contributions, which is good, because it needs to be demonstrated to be primarily a naturally occuring and long-recognized phenomenon. I see that you're not a deletionist zealot, so I appreciate that. I see that you've listed a lot of sources. Do you happen to know where Flower of Life appears in the book A New Kind of Science and can you show it online? I have searched every way I know, and can't find it there. Also, perhaps you can help to organize the sources you've given in order of WP:RS, ancillary nonfictional mention, artistic work, and fictional work. And then the bottom of the barrel is the weblog or most self-published sources, which can probably be deleted. As someone else noted, even mentions in fiction do establish the cultural notability of the ideas as an ornament or as Drunvalo's ideas. I think we can definitely do this, and the opposition is rational on the surface but is also WP:IDONTLIKEIT. The article totally sucked before, but I just don't understand deletionism, especially when they waste so much effort on it. You can see my comment here. Thank you. — Smuckola(talk) 08:04, 7 November 2015 (UTC)

Thank you on your work on this article. I concur: do use fewer edits, testing the changes in the Preview window first, if needed. Zezen (talk) 15:05, 7 November 2015 (UTC)
I see lots of edits is hard to follow. I do use preview, but my mind works better with small incremental changes and evaluation. I do confess I'm lazy about comments explaining what I'm changing and why, should do better there. I'm hopeful the article can be defended, even if more work is needed on sourcing more clearly. Tom Ruen (talk) 17:09, 7 November 2015 (UTC)
@Tomruen and Zezen: I see. Well then you might like to create a draft in a sandbox, and then publish and explain it. :) If you haven't already, I also hope that you can delete all of the weblogs and then organize the sources like I asked. Make sure that ALL new contributions to a contested article are reliably sourced; weblogs can only be added as situational sources if they contain ancillary minor information for an already reliably sourced body. The reason is because you are clearly much smarter about geometry than I am. I know almost nothing about this stuff. I am more of a general copy editor. If I knew a few solid core top level reliable sources, I could probably read them 10 times and synthesize some copy from it. And I am definitely very good at creating citations and formatting. Also see the deletionist brigade at Metatron's Cube. :( thank you very much for everything. — Smuckola(talk) 21:51, 7 November 2015 (UTC)
@Tomruen:You are a scholar and a gentleman, sir. Thank you for your work, because you're teaching me about an interesting subject in the process. Metatron beckons! — Smuckola(talk) 01:01, 10 November 2015 (UTC)
@Tomruen:BTW, regarding your vote about Metatron's Cube, we are voting on the notabiilty of a *subject* (which is a geometrical, ornamental, and historical figure), not on one name. Thank you for your research! — Smuckola(talk) 00:09, 16 November 2015 (UTC)
I'd be happier if we had ANY idea who actually named or defined anything here. I have ZERO reliable sources, reliable not in terms of wikipedia standards, but in terms of better than "someone made something up" and here it is. Tom Ruen (talk) 05:36, 16 November 2015 (UTC)
@Tomruen: I certainly do understand what you mean. But regarding the name, as with "Flower of Life", we do at least have many different printed sources who *utilize* the name "Metatron's Cube", which is significant or nontrivial as far as that goes. So that's something.  :/ — Smuckola(talk) 12:29, 16 November 2015 (UTC)

Thank you😊😊😊😊 — Preceding unsigned comment added by (talk) 00:59, 21 November 2015 (UTC)

Hermann–Mauguin notation table[edit]


I didn't remove the column. I changed it. In principle, the rows of this table correspond to families of Schoenflies notations: Cn, Cnv, Dh, ..., not to the similar HM symbols. Now the first column looks confusing, because most rows contain (or should contain) several HM symbols. For example, row \mathbf{\tfrac{n}{m}} should be \mathbf{\tfrac{n}{m}} or 2n, row \mathbf{\tfrac{n}{m}\tfrac{2}{m}\tfrac{2}{m}} should be \mathbf{\tfrac{n}{m}\tfrac{2}{m}\tfrac{2}{m}} or 2nrm or 2nm2. Last row should be \mathbf{\bar{n} \tfrac{2}{m}} or \mathbf{\bar{n}2m} or \mathbf{\bar{n}m2}.

I created this table in 2011 and I never liked the first column, and only yesterday I realized that actually each row corresponds to families of Schoenflies notations. The second reason, why it is better to use Schoenflies in the first column, because usually people know Schoenflies notation, but do not know HM, so this column will give them quick connection between two symbols.

Right now the first column looks ugly, doesn't have all information (and if we add missing HM notations in the first column, it will look worse), and actually it is redundant, because table already shows HM symbols for different n in each row.

Bor75 (talk) 15:36, 24 November 2015 (UTC)

I think the first column is useful. I prefer to see a summary of the pattern that will follow. I think the Schoenflies addition is good, but there's no reason not to keep both I think. Tom Ruen (talk) 16:36, 24 November 2015 (UTC)
I split the table entries 2 rows top/bottom to help clarify the two series. There's plenty of room for an extra column. Tom Ruen (talk) 16:43, 24 November 2015 (UTC)
I restored the Schoenflies notation column, but its still somewhat of a mess (inconsistent). You can probably clarify better than me. I used this article for comparison: List of spherical symmetry groups. Tom Ruen (talk) 18:39, 24 November 2015 (UTC)
Thank you! I will try to clarify tomorrow Bor75 (talk) 22:10, 24 November 2015 (UTC)