Talk:Quincunx

Untitled

This page makes no reference to the use of the quincunx in recusant Britain.

If it is believed that a repeated quincunx is not in fact a quincunx, the we should remove the line "A quincunx is a standard pattern for planting an orchard..." —Preceding unsigned comment added by 24.99.119.37 (talk) 11:35, 1 April 2008 (UTC)

Portuguese Shield

If a quincunx has to be a square or rectangle, then the Portuguese shield pictured on this page is not actually a quincunx, as it does not have right angles. Alphius 22:47, 17 May 2011 (UTC)

The five blue shields are arranged more in a cross shape, but the five small white roundels inside each one form quincunxes. —David Eppstein (talk) 02:32, 18 May 2011 (UTC)

Unicode

If U+2059 FIVE DOT PUNCTUATION is unicode for a quincunx, then what is U+26bb QUINCUNX? Note that the unicode character looks very different. — Preceding unsigned comment added by 68.205.8.166 (talk • contribs)

That's the astrological quincunx, the subject of a different article, not the dot pattern that is the subject of this article. (On Wikipedia, articles are about specific subjects, not about the words that name them, so the existence of other things with the same name is largely irrelevant to this article; see WP:NOTDICT.) —David Eppstein (talk) 00:07, 8 July 2018 (UTC)

Revert with no explanation

Rectangle quincunx in an optimal orchard

@David Eppstein: You reverted this edit without giving any explanation. Could you please explain why you reverted it? Thanks! Syced (talk) 08:19, 1 November 2020 (UTC)

It is unnecessarily confusing. Quincunx is described in the text of the article as a pattern for planting an orchard, but in that text it means a pattern of five trees, not a piece of a larger lattice pattern. Your image depicts and is described as depicting an orchard, but one with more than five trees, in which we can pick out five that are in a rectangular quincunx pattern. Why those five? What does it have to do with the orchard described in the text of the article? It is as relevant as if I picked an aerial view of a car parking lot or suburban housing development, circled one car or house and its four nearest neighbors, and said they were a quincunx. Maybe, but how does that inform us of anything important and encyclopedic for this topic? Beyond that, the word "optimal" in your caption is problematic. Optimal under what optimization criterion? Why is its optimality relevant to quincunxes? Basically, it has the flavor of trying to re-squeeze in your earlier off-topic text addition about optimal orchards being a triangular lattice, in a different way. —David Eppstein (talk) 17:34, 1 November 2020 (UTC)

@David Eppstein: You wrote "if I [...] circled one car or house and its four nearest neighbors, and said they were a quincunx": no, nobody calls that a quincunx, and you know it. On the other hand, when people plant trees in the pattern seen on the right, they do call it quincunx pattern, and that's why this article must explain it in details. Actually, how about we stop fighting each other, and just create a new section at the bottom of this article to detail the meaning of "quincunx" in the context of orchards? Cheers! Syced (talk) 01:45, 2 November 2020 (UTC)

In which pattern? The square grid but viewed diagonally? The triangular grid? This article is purely about the five-point pattern, not about other things like orchards with more than five trees; more generally Wikipedia articles are about concepts, not words. See WP:NOTDICT. —David Eppstein (talk) 01:46, 2 November 2020 (UTC)

@David Eppstein: Thanks for asking. The answer is: both. The first uses a square quincunx, while the second uses a rectangle (1*√3) quincunx. I totally agree with you that a Wikipedia article should be about a concept, not about a word; but sections explaining how the concept is casually used are common, see for instance how the Fractal article has sections "Natural phenomena with fractal features" and "In creative works", these sections are not what you would consider "pure", yet they are useful and anyone would add them if they were not present. You wrote "This article is purely about the five-point pattern, not about other things like orchards": You might have missed the 5 sentence of the first section: "The first citation for the geometric meaning, as a pattern used for planting trees". Cheers! Syced (talk) 03:55, 2 November 2020 (UTC)

I understand that to mean: a pattern for planting FIVE trees. —David Eppstein (talk) 05:54, 2 November 2020 (UTC)

@David Eppstein: Fair enough. I just ran a Google Images search and observe that 80% of the images show more than 5 trees. I will let you think about it, and I will take a break from this topic for a few weeks at least (probably forever). I trust that you and other contributors will keep making this article better and better. Thanks for caring, and thanks for your numerous other math-related contributions! :-) Syced (talk) 13:10, 2 November 2020 (UTC)

3O Response: The question seems to be about whether quincunx in the context of orchard planting is a pattern of exactly 5 trees or more than five trees. It doesn't matter what editors think is more appropriate. It matters what sources say is appropriate. I can't consult the source referenced in the article about orchard planting. However, I did find this reference. It's pretty clear the pattern here is about more than 5 trees. Regardless of the reference, I think it's clear to most readers that pattern means to "repeat in a predictable manner", i.e., the quincunx pattern of 5 trees repeats in an orchard. I don't know of any orchards that only have 5 trees. An illustration is helpful to explain what a repeating quincunx pattern in an orchard might look like. As a matter of fact, in the link I provided, it's notable in the illustration that the repeating patter actually degrades into a simple grid when viewed at 45 degrees, as pointed out in the accompanying text. Having said that, I do think a better image would be more helpful. The image in dispute here seems somewhat abstract and shows no spacing between the trees. The illustration in the link I provided is more representative of an orchard, because there is spacing among the trees. I suggesting using a different illustration, and yes, the illustration should include more than 5 trees. Coastside (talk) 01:58, 7 November 2020 (UTC) Coastside (talk) 01:58, 7 November 2020 (UTC)

The article is not about the word "quincunx" and its meaning in orchards. It is about patterns of five spots, often called a "quincunx". Topics that are about that pattern of five spots but do not call it a quincunx (such as the five-dot tattoo) are on-topic. Topics that are about the word quincunx but are not about the pattern of five spots are off-topic (see the astrological aspect). See WP:NOTDICT, again. So your proposed illustration of a many-more-than-five tree orchard are off-topic. Also, since the part about orchards is about a historical meaning, I suspect that the number of trees reflects the typical size of medieval orchards, not of modern commercial orchards. —David Eppstein (talk) 02:26, 7 November 2020 (UTC)

3O Response: The orchard reference is one example in a list of examples of the quincunx pattern in the article. Several of these including repeating patterns. The image of Cosmatesque inlay stonework in the article clearly shows two such patterns repeating in the rug. The illustration in the article about Galton's Bean machine is almost identical to the orchard pattern and shows repeating quincunx patterns forming a grid. The quincuncial plan as illustrated in the church of Santa Maria dei Carmini in Venice in the groin vault article shows a repeating pattern of quincunxes. Your objection to an illustration of the common application of the quincunx pattern in planting orchards seems rather arbitrary. Coastside (talk) 02:52, 7 November 2020 (UTC)

3O Response: I thought some more about your point that the article is not about the word "quincunx" but about the pattern. I think you mean to say that for the orchard example, it's just a historical word, such as when an orchard only had five trees and is not about the pattern per se. I think you're missing the point for orchards. The reason it's argued that this pattern is "optimal" is because if you line the trees up in a grid, they compete for water and light, or as suggested here the "canopies of adjacent trees will overlap". If you offset each row, then they are spaced optimally because each pair of trees alternates with a single tree placed evenly offset, and then another pair of trees. This is the quincunx pattern. However, as pointed out here this is somewhat silly. If you rotate the pattern, you just get another grid. So the idea that a repeating quincunx pattern is optimal is a fallacy based on lack of perspective. This isn't just about the orchard pattern, though. If you look at the Bean machine example, there is a reason it's called a quincunx. It's not just a name - it's the pattern. That's because the binary distribution of the falling balls is due to the fact that each row is offset from the previous row so that the ball has a 50/50 chance of falling to the left or right at each level. The alternation of two pegs, then one centered peg, then two pegs, is the quincunx pattern repeating. Again, if you rotate the bean machine 45 degrees, it's also just a grid, so it's somewhat silly to call it a quincunx. But the pattern is inherent in the thinking about the arrangement for orchard planting and for the bean machine. It's more than a name, it's a pattern. Hope that helps... Coastside (talk) 04:26, 7 November 2020 (UTC)

There is nothing in the article about optimality of patterns of more than five things, nor should there be; that's a different topic (maybe circle packing). The article does use the word "optimal" but for a specific mathematical problem where the number of points is exactly five and the goal is merely to get as many rows of three as you can. As for "it's more than a name, it's a pattern": Yes. A pattern of five things. Other patterns can be in other articles. Incidentally, part of the reason I am opposed to including the pattern of more than five trees: because for orchards, or other things in the physical world, it is exactly the same pattern as a square grid. The only difference is what direction you look at it when you stand in it, not the positions of the trees themselves. For pixels on a screen, there is a difference, because there is a preferred orientation for the screen (you don't usually tilt them diagonally), but for trees in a field not so much. I think maybe a better solution would be to remove the line "A quincunx is a standard pattern for planting an orchard" and leave the mention of orchards only in the historical origins section, because it is not a standard pattern for planting modern orchards (they generally have more than five trees) and the source we have for that line is not very specific. —David Eppstein (talk) 06:18, 7 November 2020 (UTC)

3O Response: You should refrain from changing an article when a discussion is ongoing without consensus, especially when editors requested a third party opinion. You are inconsistent in your view of what qualifies as an example for this article. No one is arguing that a quincunx is a pattern consisting of five points. Nevertheless, the section on examples says "Quincunx patterns occur in many contexts:", and then lists examples of contexts in which the quincunx pattern appears. The examples of an orchard and of the bean machine are contexts in which the quincunx pattern appears. This isn't to say that the larger set of points is in itself a quincunx pattern.

Furthermore, you are being entirely inconsistent in your filter. You say it's reasonable to include the pixel pattern on a screen as an example of a quincunx pattern because there is a preferred orientation. This is your own personal view of what makes sense to include. No source established that definition - you just think that's logical. It shouldn't be up to editors what is considered an example of a quincunx pattern. It's up to the sources. More specifically, you deleted the reference to bean machine, because you argue it is a pattern of more than exactly five things. The bean machine was called a "quincunx board" because of the internal alternating pattern, as I explained. It's not simply an editor's opinion that this qualifies as an example. As with the pixel example, which you decided was acceptable, you can't rotate the pattern in the bean machine either. The orientation must be vertical for the machine to work properly. Gravity implies orientation, and the balls must fall alternately between the pegs in that specific orientation. You're just applying your own arbitrary filter on what qualifies as an example of a quincunx pattern. By your logic, Galton's machine was called a quincunx machine for some unknown historical reason, and now it shouldn't serve as an example of a quincunx pattern because the machine has more than five pegs. That's not a reasonable argument. It's just an application of an arbitrary filter you made up and ignores sources that indicate otherwise.

The orchard as an example of a quincunx pattern is also valid in the sources. I've already provided several that use the term in a contemporary usage. It's not reasonable for you to preclude these examples just because you don't like the usage of the term. Here's yet another example: [1] Look at the illustration in the article here: [2] The illustration makes clear that the quincunx is repeated as a pattern in the orchard, and the idea that the pattern "allows more per hectare than a straight grid" clearly shows this is a context in which the quincunx is repeated in a pattern. This is clearly not an orchard of five trees. It's an orchard of sets of five trees. You and I might agree that if you look askance at the diagram, it's still just a tilted grid. But that's our opinion. That's doesn't change the fact that in popular usage, orchard planting is a valid context in which the quincunx pattern appears. It's valid because that's how the term is used in the sources. Coastside (talk) 08:09, 7 November 2020 (UTC)

I don't see why I should stop editing this article just because you preface your comments by 3O and tell me I shouldn't do things.

Again, this article is about five-point patterns only. We have a disambiguation page for other uses of quincuncx. We also have a page for the repeating pattern of more than five points, in which one point and its four nearest neighbors form a quincunx five-point pattern: it is square lattice. Material about that repeating pattern belongs there, not here. Material about five points in a cross belongs here regardless of whether it is called "saltire", "five-spot", or the "five-point tattoo" instead of "quincunx" (as it is in various of the items, which the sources do not use the word "quincunx" for). Your final sentence, "It's valid because that's how the term is used in the sources", indicates that you still do not understand WP:NOTDICT. Wikipedia articles are about concepts, not terms.

It occurs to me that maybe you do think of this as being about a concept but have the wrong concept in mind. A quincunx (five points in a cross) is still a quincunx if you rotate it by 15°, or 30°, or 45°, or your favorite other angle. A square lattice (repeating pattern in which a point and its four nearest neighbors form a cross) is still a square lattice if you rotate it by 15°, or 30°, or 45°, or your favorite other angle. If there is something in the text of this article that leads you to believe that it is about points lined up diagonally (when the intended meaning is that they form a cross shape regardless of orientation) or if there is something in square lattice that leads you to believe that the lattice must be horizontal and vertical (when in fact any rotation gives another square lattice) maybe we could get something more constructive out of this discussion by pointing out that misleading wording so it can be fixed. —David Eppstein (talk) 09:58, 7 November 2020 (UTC)

3O Response: I find it very strange how we are talking past each other like this. The point is that these are examples where quincunxes appear in various contexts. Such examples are relevant to this article. A bean machine is called a "quincunx machine" because others recognize that the peg pattern includes and is in fact explicitly based on quincunxes, not because the whole grid is a quincunx. The only new point I'll make is that your reference to and use of the quincunx (disambiguation) page is also problematic. You are the editor who added an entry for "an orchard planted in a quincunx pattern" to the disambiguation page, apparently because you didn't want it included in this article about quincunxes. Including this entry in the dab page is simply incorrect. An "orchard planted in a quincunx pattern" is not a quincunx. It's an example of something that employs a quincunx pattern. Nothing in the article on orchards says that an orchard planted in a quincunx pattern is known as a quincunx. For you to have added it to the dab page is more of a reflection of your desire to exclude it as an example of quincunxes in the quincunx article than anything else. Including bean machine as an entry is appropriate because it is sometimes referred to as a "quincunx". For more information on what entries are appropriate to include in dab pages, see WP:DABENTRY. Coastside (talk) 18:28, 7 November 2020 (UTC)

Including bean machine as an entry is appropriate because it is sometimes referred to as a "quincunx". No no no. Again, I refer you to WP:NOTDICT which you are consistently failing to address. Imagine that this article were titled "Five-point cross" and had more or less the same content, about five-point crosses, but that it never mentioned the word "quincunx". Imagine that this article was translated into a language whose vocabulary did not include any word derived from "quincunx". Would your argument based on what things are sometimes referred to have any merit in those hypothetical cases? As for the bean machine pattern being "based on" five-point crosses: also no, no more than it is based on rhombuses or triangles or any other pattern you can see in its grid of points. —David Eppstein (talk) 19:17, 7 November 2020 (UTC)

When I said "Including bean machine as an entry is appropriate" I was referring to including it on the quincunx (disambiguation) page, which is appropriate for the reason I said. I was contrasting that with your inclusion of orchard on the disambiguation page, which is incorrect. I was making a very simple point: orchards are not called quincunxes and shouldn't be included on the dab page, whereas bean machines are called quincunxes, which is why it makes sense to include them on the dab page. Is that not clear? Regarding WP:NOTDICT, I well understand the meaning of the policy. I fail to see how that governs whether things that include quincunx patterns can be included in an article on quincuxes in a section that clearly says "Quincunx patterns occur in many contexts:" and then lists such contexts where quincunx patterns appear. WP:NOTDICT provides policy guidance on what is relevant to include in Wikipedia, and specifically what should be included as a topic in Wikipedia. Referring to WP:NOTDICT does not justify excluding examples in an article on the grounds that such examples are "dictionary definitions". All I'm saying is that examples of quincunx patterns in various contexts is relevant to an article on quincunxes. Obviously you have a different opinion about that. I would invite others to contribute to this debate at this point, should they care to. Perhaps a request for comment might be appropriate as it appears my attempt to provide a helpful third party opinion is not helping to resolve this dispute.Coastside (talk) 20:05, 7 November 2020 (UTC)

Why are you even talking about what to include on the disambiguation page? I didn't think that was under dispute. Stuff belongs on the disambiguation page if it is called "quincunx". The bean machine is called a quincunx, so it belongs there. That has nothing to do with the content of this article and nothing to do with the pattern of the bean machine. As for an RFC, I don't even know what you are trying to dispute any more in order to frame an RFC. Is the pattern of five points in a cross frequent and noteworthy enough to warrant a separate article, and is there enough content to make an article about that topic? Yes, obviously. Are five-point crosses called quincunx often enough to satisfy WP:COMMONNAME and make it reasonable to title this article, about five-point crosses, "quincunx"? Yes, obviously. Are there other meanings of "quincunx" that belong on a disambiguation page? Yes, obviously. Does the pattern of trees in a modern orchard have only five trees, making it relevant for an article about five-point patterns? No, obviously not. Does the pattern of pegs in a bean machine have only five pegs, making it relevant for an article about five-point patterns? No, obviously not. Do we have a separate article on those point patterns, where orchards and bean machines might reasonably be mentioned? Yes. So what about the current state of the article makes you keep carrying on at such great length and calling for RFCs? The only point that might be in contention is "is the fact that you can pick out five-point crosses in orchards and bean machines distinct enough from the fact that you can pick them out of any other kind of grid, distinct enough from the fact that you can pick out squares and octagons and triangles and trapezoids and hexagons and all other manner of patterns in orchards and bean machines and grids, and significant enough to mention on an article about five-point crosses?" I think the answer is clearly no and I am baffled that there is even any disagreement on this point. —David Eppstein (talk) 20:53, 7 November 2020 (UTC)

Five points in a cross

Quincunxes vs square lattices of trees

This article is intended to be about a geometric pattern of five points in a cross. I strongly believe that this pattern is notable, and that the content of the article (somewhat haphazardly organized as it is) should focus on that pattern and not on its name. There is a name for that pattern, "quincunx", that we happen to be using for the article title, in place of clunkier equivalent formations like five-point cross pattern. User:Johnbod continues to edit-war to expand off-topic material about other meanings of the title word (plantings of trees that are not necessarily in fives and not necessarily cross-shaped), making this article less focused and confusing its topic with that of Quincunx (disambiguation) (which really is about the word not the pattern). It's as if some editor insisted on adding to our article on geometric squares, long paragraphs of material about Squares in London focusing on the trapezoidal shape of Leicester Square. Is there another article where this material would better belong, that Johnbod could be sent to spam his 18th-century books on tree-planting? Would it improve matters to move this article to Quincunx (five-point pattern) and let Quincunx point to the disambiguation page on articles using a similar title? Alternatively, is there some way to emphasize even more strongly than we currently do that this article is only about geometric patterns of five points in a cross, and not about meanings of words? —David Eppstein (talk) 18:16, 29 April 2022 (UTC)

You are the only person insisting on that narrow definition of the subject, which you have defended with extraordinary tenacity against a number of other editors above. Taking the geometrical material off to Quincunx (five-point pattern) may be the best solution, if you intend continuing to edit-war. Most of the other material does not have articles covering it, so a disambiguation page is not the best solution. "Is there another article where this material would better belong", you ask. No, there isn't. It should stay here. Johnbod (talk) 01:13, 30 April 2022 (UTC)

What do you want to make the other article about? 45°-rotated square grids of trees? How is that a notable topic, distinct from other grids of trees only in their orientation with respect to the edge of the plantation? I am defending the fact that this article should have a topic, and not just be about things related only by having the same name. As WP:NOTDICT demands. If the topic is not "five points arranged in a cross", then what is it? If you take out all of the material that is only about five-point-cross-arrangements and not about tree-planting to make the article you think it should be, what is left? —David Eppstein (talk) 01:28, 30 April 2022 (UTC)

You keep complaining the article is dealing with the word, so all the closely-related meanings should be covered. They are not "related only by having the same name". I must say, I'm completely confused by the line or lines in the sand you have drawn between what does and doesn't belong in the article as you see it, but please don't explain. Johnbod (talk) 01:34, 30 April 2022 (UTC)

There are two meanings of geometric patterns that use the same word: (1) a square grid that has been rotated by 45°, (2) five points in a cross. They are separate topic. They should not have a single article because of the singularity of their names, any more than any other two topics that have similar names should be glommed into a single article. NOTDICT. Encyclopedia articles are about topics, not about lists of different topics that happen to have the same name. I am also completely baffled. I don't understand what you think this article is about. Try describing it in words that do not use "quincunx". I can do that for my intended meaning: five points in a cross. What is yours? —David Eppstein (talk) 01:38, 30 April 2022 (UTC)

Relatedly, I temporarily removed the bullet point saying that this was a common planting pattern for 16th-18th century European gardens, because none of the sources talk about the planting pattern being the same as the geometric pattern that is the topic here: five trees in a square, with one at the center, and no more than five trees. I think it is likely that this five-tree pattern was a common planting pattern, and I would like to re-add this bullet point, but we need a source that explicitly talks about five-tree groupings and none of the ones we had does. Gardens of Court and Country, which was used to source the "more specialized meaning, referring specifically to groups of trees with their branches stripped from the trunk", explicitly contradicts this meaning, saying that its use of the word mostly referred to a square grid but should properly have referred to a 60-degree triangular grid. Also note that if you take an orchard of trees planted in a larger square grid, and add more trees at the centers of the squares, the result is still a square grid (rotated 45 degrees from the starting grid), so for the purposes of describing mathematical patterns it is not any different than the square grid itself, and not the five-point pattern that this article is about (at least, not any more than any other square grid, which also contains many copies of the same pattern). This leads to much confusion in trying to find early sources on five-tree patterns, because many sources write as if the diagonally-oriented square grid and the orthogonally-oriented square grid are different patterns, and talk about the diagonally-oriented pattern being grouped in fives, when they are not different and when you could just as easily find smaller square groups of four in the same pattern or larger groups of five in the orthogonally-oriented square grid. —David Eppstein (talk) 21:57, 29 April 2022 (UTC)

Similar words

Are there other words that name specific arrangements of dots which could be mentioned? The Tetractys, Therefore sign, and Ellipsis symbols come to mind. I did a bit of googling and I'm a little surprised I couldn't find a name for the 3x2 dot pattern found on most six-sided dice. 2600:1700:7BE4:BD0:844F:D7A7:256E:8F85 (talk) 21:35, 21 December 2024 (UTC)

If so, they should be listed in Category:Dot patterns. I don't see anything else obvious there. —David Eppstein (talk) 21:56, 21 December 2024 (UTC)

The name for throwing two sixes in dice is "boxcars", so I guess a single die showing 6 could be a "boxcar". Also, see the general article figurate number... AnonMoos (talk) 03:58, 23 December 2024 (UTC)