Talk:Euclidean distance

message: Is that formula for approximating the distance using only integers wrong? Surely if dx and dy are the same (eg, at a 45-degree angle) then dx + dy - 2×min(dx,dy) will always be 0, and the approximation will always be 100% error?
:Yea, it was wrong and has been changed. StuRat 16:40, 21 September 2005 (UTC)
replies: text: Sure, go ahead and add it. StuRat 20:07, 21 October 2005 (UTC)
thread_title: Comments

message: If you want to know whether objects A and B are at distance c or less, you can compare ((Ax - Bx)^2 + (Ay - By)^2 + (Az - Bz)^2) with c^2, and similarly for other numbers of dimensions.  This avoids the square root entirely.  If c is a constant, then c^2 can be precomputed as well. -- Myria 06:18, 21 July 2006 (UTC)
replies: text: True, but this is already implied by the section that talks about how distances can be compared while skipping the square root operation. StuRat 05:37, 29 July 2006 (UTC)
thread_title:  Comparing against a distance 

message: I corrected the formula for the distance in circular coordinates. --EarthJoker 12:25, 23 July 2007 (UTC)
thread_title:  Two-dimensional distance 

message: Why is the approximation section here? Euclidean metrics are very simple concepts, and I don't think you'd find anything about approximation in 99% of the textbooks that cover the topic. It seems like the audience for that material is different from the audience for the rest of the article. At the very least, there should be a reference here, or some explanation as to why it works.
Also, I moved the approximation sections to the end of the page because it seems important to at least see the 3D version before this is discussed. Triathematician (talk) 01:16, 20 December 2007 (UTC)
replies: text: As you can see in the first section of this talk page, the approximation section looks like unsourced original research, so I guess that it can be safely removed altogether. Afaic, go ahead. DVdm (talk) 13:55, 20 December 2007 (UTC)
thread_title:  Approximations 

message: Does this have anything to do with Euclid? If so, should it be mentioned or at least 'See also'ed? Bitwiseb (talk) 17:46, 4 April 2008 (UTC)
thread_title:  Euclid 

message: What's so unique about the Euclidean metric? What properties does the euclidian metric have that other metric spaces don't have, such as the other Minkowski metrics? What is a rotation in a metric space? Do other metric spaces not have the property that the composition of two rotations is always a rotation? Blackbombchu (talk) 02:03, 29 August 2015 (UTC)
thread_title:  Incomplete article 

message: The following edits were recently reverted.
1. Removal of reference to squared distance being called "quadrance" in rational trigonometry as WP:UNDUE.  This seemed clear enough; if the article were trying to catalogue appearances and avatars of squared distance, things like quadratic forms, Hilbert space and Bregman divergence would have far higher priority but are not even mentioned.  Rational trigonometry is a one-man show by its inventor, has not caught on whatsoever (as noted in its Wikipedia page), and is already being hyped at a number of other WP locations. No need to promote it where it is at best marginally related to the topic.
2. Reworking of the statements on non-Euclidean geometry.  The problematic passage states:
::"Although accurate measurements of long distances on the earth's surface, which are not Euclidean, had again been studied in many cultures since ancient times (see history of geodesy), the idea that Euclidean distance might not be the only way of measuring distances between points in mathematical spaces came even later, with the 19th-century formulation of non-Euclidean geometry".
This is wrong as a description of non-Euclidean geometry.  It is anachronistic; the notion of "mathematical space" came later, and distance functions on such spaces. It is also misleading: it was a familiar everyday fact that travel distance differs from Euclidean distance (hence the phrase "as the crow flies"), and well known to cognoscenti that maps of the Earth distort distance and that spherical geometry/trigonometry differ from the Euclidean version.   
My attempt to state this more correctly is the last paragraph of  https://en.wikipedia.org/w/index.php?title=Euclidean_distance&oldid=996504346#History .  This has been reverted as "tendentious" by , but I do not understand what he thinks is wrong with it or how it is inferior to the preceding. 73.89.25.252 (talk) 07:13, 27 December 2020 (UTC)
replies: text: It is ridiculously WP:TECHNICAL, for an article that at least in part needs to be readable by schoolchildren. It removes relevant and sourced information. And things like quadratic forms and Bregman divergence are not even close to being Euclidean distances. We have separate articles already where they belong much better. Hilbert spaces are already present (in a very non-technical way) in the mention of infinite dimensions in the "generalizations" section, with links for those looking for real information. In contrast, the material on squared Euclidean distance that you removed could plausibly be split off into a second article, but I am not convinced there is enough notability for it to stand alone as a separate article (certainly not under the "quadrance" title of the part you removed, as that is mostly just Wildberger reinventing the wheel) and in the meantime this article is the place for it. As for your removal of geodesy: it would be seriously misleading to say in this article that Euclidean distance was the only distance used even by non-mathematicians prior to the 19th century. And finally, reverting a set of bad edits once does not even come close to edit warring. —David Eppstein (talk) 07:17, 27 December 2020 (UTC)
thread_title:  Edit warring on rational trigonometry and description of non-Euclidean geometry 

message: (Moved from above. 73.89.25.252 (talk) 20:22, 30 December 2020 (UTC)
replies: text: I figured that if we're going to have an article on rational trigonometry at all, it would be better to mention it briefly in a context that we make very clear that squared Euclidean distance is far from a new idea, rather than avoiding the subject and allowing readers to keep the impression that "quadrance" is something new and different. But I suppose we could try again to delete the rational trigonometry article — if it were gone, I would support also removing mention of it from here. —David Eppstein (talk) 06:48, 28 December 2020 (UTC)
replies: text: I don't relish the thought of the inevitable "keep, because it's long and has footnotes" comments that rational trigonometry would get in an AfD, but the last one was in 2013, so maybe it's time again. XOR'easter (talk) 19:25, 28 December 2020 (UTC)
replies: text:  There are entire fields of mathematics that are in large part hype surrounding a prosaic foundation of ordinary theorems about previously unhyped areas.  E.g., chaos theory, catastrophe theory, complex systems, the set theory multiverse... and check out some of the math articles in Quanta these days!  Wildberger is comparatively humble in that he is only claiming a new approach to an old subject, and is putting out conventionally written articles on the Arxiv whose only crime is to introduce new terminology ("chromogeometry", anyone?).  He does not seem to be developing an institutionalized personality cult either, of the sort that has been a problem in some of those fields.  So it's pretty harmless and I don't see it as unreasonable to have an article on R.T as a mathematical subject rather than the book.  But the other way around is also acceptable. 73.89.25.252 (talk) 19:28, 30 December 2020 (UTC)

text:  If quadrance/rat.trig are unimportant to explaining or contextualizing Euclidean distance then regardless of the state of other articles, they should be removed from this one. Quadrance currently redirects to a place where it is, or can be, clearly explained that it is a new name for an old quantity. 73.89.25.252 (talk) 19:28, 30 December 2020 (UTC)

text: I tried rewriting the rational trig article to be about the book. If that sticks, I don't think we need to continue mentioning it here. —David Eppstein (talk) 18:22, 30 December 2020 (UTC)
thread_title:  Keep or remove "quadrance"/rational trigonometry (split from previous section) 

message: An editor has identified a potential problem with the redirect :Euclidean metric and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 May 4#Euclidean metric until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  fgnievinski (talk) 17:05, 4 May 2022 (UTC)
thread_title:  "Euclidean metric" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Article Metric (mathematics) says:
...a metric or distance function is a function that gives a distance between each pair of point elements of a set.
Article Metric space says:
In fact, a "metric" is the generalization of the Euclidean metric arising from the four long-known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line segment connecting them.
I still don't get why folks seem upset with applying MOS:BOLDREDIRECT to "Euclidean metric"? Squared Euclidean distance already calls it a "function" -- what else does the WP-Math cabal need? fgnievinski (talk) 22:35, 4 May 2022 (UTC)
replies: text: Do you really not understand the significant difference between "distance" (a number, between two points), "distance function" (a thing that takes pairs of points and spits out numbers), and "Euclidean metric" (a space of points together with a distance function on it)? Or the significant gap in audience maturity required to go from one of these concepts to the next? Despite having this repeatedly pointed out to you, none of your comments, including this one, exhibit any understanding of these issues. —David Eppstein (talk) 22:44, 4 May 2022 (UTC)
replies: text: "Euclidean distance" is also routinely interpreted as the "Euclidean distance function" between any two arbitrary points. Sometimes mathematicians have a very very narrow interpretation. The term Euclidean metric is used by physicists, programmers, etc. in a less strict manner. fgnievinski (talk) 22:56, 4 May 2022 (UTC)
replies: text:  is perfectly enough. Anyone who knows what a "metric" is (a small subset of this article's intended audience!) can reasonably infer what the "Euclidean metric" is. In all likelihood, such a person will have already been introduced to the Euclidean metric on R^n as their first example. WP math articles already have a reputation for turning elementary concepts into turgid prose, and imo we should do as much as possible to fight that. Readers first! Ovinus (talk) 00:33, 5 May 2022 (UTC)
replies: text: It is true that people who have some idea what a multivariate function is can reasonably infer that there is a function mapping pairs of points to their distance, and it is also true that that function is sometimes called, for short, "Euclidean distance". But, Fgnievinski, you are still wilfully continuing to miss the point. I want this article to be readable by people who are not experts in real analysis. I want it to be readable by people who have not yet really learned what a function is. I think it should be possible to understand the distance between points without understanding the nature of functions. I think this possibility is clearly demonstrated by the ancient nature of Euclidean distance and the much less ancient nature of real analysis: the ancient Greek mathematicians do not appear to have had an adequate notion of functions as a general class of mathematical objects, but still were well acquainted with lengths of line segments. —David Eppstein (talk) 00:52, 5 May 2022 (UTC)
thread_title:  "Euclidean metric"