Talk:Diameter of a set

Proposed merge of Diameter (computational geometry) into Diameter of a set

This is a stub article, mainly a list. It's a practical aspect of the general concept. The first sentence in their leads is nearly a duplication, implying the definition of "diameter" is nearly the same concept. The only conceptual difference might be the assumption of Euclidean metric and isolated points, but this special case is not explicit enough in the child article. Splitting the whole Diameter of a set in Euclidean spaces (including its computational aspect) would be more justifiable. fgnievinski (talk) 13:28, 8 January 2025 (UTC)[reply]

This is a WP:Summary style article, separating out a subtopic of a subtopic of diameter of a set (in Euclidean spaces, subtopic algorithms for computing diameter) that could easily overwhelm and unbalance the whole article. It is incorrect to call it "a practical aspect of the general concept"; for one thing, much of its study is theoretical rather than practical, and for another, it has generally been studied only for finite point sets and polygons in Euclidean spaces, while the general subject has significant aspects that concern curved sets and non-Euclidean metrics. I just took significant effort to split off multiple topics that were all conflated together in the article on the diameter of circles and I think keeping them separate is worthwhile; you may not care about my effort but you are stomping all over my cleanup efforts in this general area and making it difficult for me to do that. Diameter (computational geometry) was stubby not because it is inherently stubby but because it is new and I haven't had time to expand it much. Additionally, Diameter (computational geometry) is easily a separately notable topic (it already has 8 in-depth sources directly about it and could easily have more) so there is no good reason for merging it and summarizing it rather than expanding it. It is also a very distinct flavor of topic in that Diameter (computational geometry) focuses on computer science while diameter of a set focuses on mathematics. For all these reasons, I oppose the merge. —David Eppstein (talk) 18:31, 8 January 2025 (UTC)[reply]

Oppose I don't think this article would be better if it included all of Diameter (computational geometry). However, as a non-mathematician I find this article unsatisfying. I am left wondering what other "diameters" might exist. The "of a set" part implies that this is a subtopic of "Diameter" but, no, it is a generalization of one particular "diameter", that is "diameter of a circle or sphere". Diameter vaguely promises other generalizations. I would rather read a section of Diameter named "Diameter of a set" with the summaries that are listed here and maybe other "Diameters of ...". That way the entire context of the diameter concept would be available in one article. That is, merging these summaries into Diameter would be clearer to me. Johnjbarton (talk) 19:38, 8 January 2025 (UTC)[reply]

The "of a set" is intended as a form of WP:Natural disambiguation because the un-disambiguated name "diameter" is taken by the diameter of a circle (often meaning a line segment rather than a number). The two topics used to be merged but that was unsatisfactory, in part because they have very different audiences (elementary school kids learn about diameters of circles but not about metric spaces). The diameter of a circle is more commonly generalized in a different way to the diameters of an ellipse, which in that context means any central section, inconsistent with the definition here. —David Eppstein (talk) 19:47, 8 January 2025 (UTC)[reply]

I don't think elementary school kids read Diameter. But if they do they will find that the content is not at all as you describe. The first subsection is "Generalizations". Any reader not interested in generalizations can stop reading. But those who are interested don't have the nice outline of the topic that you provide here. How is this article related to Metric space#Diameter of a metric space? We can't tell. To make my comment another way: here in this article we have an outline of a subtopic but there is outline of the next level up. Johnjbarton (talk) 20:02, 8 January 2025 (UTC)[reply]

I would prefer to think of the "diameter" article as being primarily about circles and ellipses rather than as an outline of a more general topic. I don't think there is a more general topic for it to be an outline of, and there is more about circles that it could be expanded with: for instance, given a circle, constructing its diameter with compass and straightedge. As for "How is this article related to Metric space#Diameter of a metric space?": that subsection tag no longer exists. The metric space article had only two lines about diameter, and the diameter of a metric space redirect is better targeted here, an article that is entirely about that topic. —David Eppstein (talk) 20:11, 8 January 2025 (UTC)[reply]

Oppose per above, also echoing it might be worth expanding the summary of Diameter of a set at Diameter a bit, as well as Diameter (computational geometry) in Diameter of a set, eventually. Noting computational geometry on non-Euclidean spaces exists, so not really helpful to break off/merge into a Euclidean-specific article. Tule-hog (talk) 20:25, 8 January 2025 (UTC)[reply]

I'm not aware of research on diameter algorithms in geometric but non-Euclidean spaces, and this may be one of those problems for which the hyperbolic or spherical versions are not really different from the Euclidean version, but if you know of publications in this area please let me know. —David Eppstein (talk) 04:36, 9 January 2025 (UTC)[reply]

Preparata and Shamos's Computational Geometry (see Section 4.2.3, p.176) points to Hartigan's Clustering Algorithms for "a large number of different such measures and procedures for clustering using them". I didn't see any big-O analysis circa Diameter (computational geometry) from a quick skim though. Tule-hog (talk) 06:07, 9 January 2025 (UTC)[reply]

Spherical geometry gets funky on this kind of question for anything that doesn't fit within some hemisphere. –jacobolus (t) 06:23, 9 January 2025 (UTC)[reply]

True. But then the problem flips from being about farthest pairs to being about bichromatic closest pairs (of points and their reflections), still easy enough. If we find a published source for that we could mention it but I suspect that there might not be one. —David Eppstein (talk) 06:33, 9 January 2025 (UTC)[reply]

Oppose the merge: They seem to me to be concepts that are different enough to warrant separate articles. MathKeduor7 (talk) 05:16, 9 January 2025 (UTC)[reply]

Totally bounded is bounded

I have attempted to include the link to Metric space § Bounded and totally bounded spaces because of the following passage there:

The space $M$ is called precompact or totally bounded if for every $r > 0$ there is a finite cover of $M$ by open balls of radius $r$ . Every totally bounded space is bounded. To see this, start with a finite cover by $r$ -balls for some arbitrary $r$ . Since the subset of $M$ consisting of the centers of these balls is finite, it has finite diameter, say $D$ . By the triangle inequality, the diameter of the whole space is at most $D + 2 r$ . The converse does not hold: an example of a metric space that is bounded but not totally bounded is $\mathbb {R} ^{2}$ (or any other infinite set) with the discrete metric.

In my opinion, this passage is not 'prominently linked' in this article, considering the size of metric space; further it is a useful and concise demonstration of the application of the definition of diameter while manipulating metric spaces. (Ping to David Eppstein) Tule-hog (talk) 00:18, 9 January 2025 (UTC)[reply]