Talk:Angle

message: Reddwarf2956 has been making some improvements to this article (which I support), but we seem to disagree on the definition of a turn.  I don't understand how it can be a period.  Am I missing something?  Dbfirs 07:29, 15 September 2013 (UTC)
replies: text: A circular movement is periodic, and the turn is its period. Nevertheless this concept seems too technical for this elementary article, and it is better to avoid to mention "period" here. However, I agree that this paragraph is not satisfactory, as giving a circular :-) definition. Therefore, I suggest "the turn is the angle for which the above circular arc is the complete circle". D.Lazard (talk) 09:53, 15 September 2013 (UTC)
replies: text: I agree that there might be some loose association of a turn with a period in some usage, but I still don't see how a turn can be a unit of time.  I agree with your suggested improvement.  Dbfirs 06:25, 18 September 2013 (UTC)
thread_title:  Turn is period? 

message: Comments at the article edit: "I don't see what the association is for polygons.  No mention at the linked article." See Angle#Polygon_related_angles.  Let's add to the current statements and move them to in a different section of angle. But, we still need some references to both interior angles and exterior angles of Transversal_(geometry) with the Transversal section in angle and with polygons. Maybe combine the transversal and polygons sections together and define the terms? 
John W. Nicholson (talk) 02:51, 23 September 2013 (UTC)
thread_title:  Transversal and polygons both have interior angles and exterior angles 

message: Who eviscerated this talk page?  Yesterday it had 36 sections and today it has 4?!!  Skylarkmichelle (talk) 22:43, 20 December 2013 (UTC)
replies: text: The discussions have been Archived but are still available for reading. At the header of this discussion page, click Show in the Archive bar. Then click on the numeral 1 that appears at the left. You can refer to issues that have been raised, but bring your discussion to this current Talk. It is common practice to Archive old discussions from lengthy talk pages.Rgdboer (talk) 03:14, 21 December 2013 (UTC)
thread_title:  talk page destruction! 

message: I had been contemplating merging the article Internal and external angle into the section Polygon related angles here since this section was better written and there did not appear to be much chance of expanding the current article. I would have done this myself, but a recent spate of activity suggests that I had better ask for some opinions on this merge. Bill Cherowitzo  (talk) 18:43, 4 October 2014 (UTC)
replies: text: Support, with sources added. Otherwise delete. - DVdm (talk) 19:21, 4 October 2014 (UTC)

text: weak Oppose - looking at this article leaves with a somewhat dissatisfied feeling as it mixes imho to many things which might be clearer to various readers if they are structured differently and distributed over several articles. That is in particular separate different levels of mathematical approaches from notational, engineering or unit related material. In addition the current mathematical part somewhat switches unstructured between rather abstract notions (without any motivation) and more elementary ones. We would need an angle treatment on highschool level (comprising angle between lines, 2d and 3d vectors, lines and planes, between planes), then the generalisation to curves and surves, more than 3 dimensions and non euclidean spaces. This could be handled in one large well structured article but imho for accessibilty/readabilty reasons 2-3 articles might be better. In any case those should be separated from the other (non-math) content in the current article. Since I favour the splitting and restructuring (as well as extending the splitted parts) of this article, I'm somewhat opposed to merging additional stuff into this article.--Kmhkmh (talk) 18:34, 7 April 2015 (UTC)

text: weak Oppose and conditional strong oppose: This topic is important in the history of mathematics. In addition, I can see this article being expanded in the future to describing how various cultures throughout history have measured angles (this is Ethnomathematics), which would help in countering Wikipedia:Systemic bias. I think that articles on English Wikipedia that deal with ancient topics in mathematics are consistently written with a greater focus on mathematics in the western world than elsewhere so if this article to expanded to include more mention of how throughout history other cultures have measured angles then I would say strong oppose. Mgkrupa (talk) 16:23, 3 September 2020 (UTC)
thread_title:  Proposed merge 

message: These terms are usually used to refer to pairs of angles rather than to sets of three or more.  A South African editor believes that the terms are applicable to larger sets of angles (and I asked the same question here several years ago).  The OED specifies "pair of angles", but is there a reference for more general usage?  (If there is, then I apologise for my reversion of the recent edit.)  Dbfirs 07:05, 14 July 2016 (UTC)
thread_title:  Supplementary & Complementary 

message: What about reflex angles?  — Preceding unsigned comment added by 75.139.254.117 (talk) 17:58, 24 November 2016 (UTC)
replies: text: Reflex angles are defined in the article, and explained with a figure. The phrase "reflex angle" appears 6 times. What do you want more? D.Lazard (talk) 18:05, 24 November 2016 (UTC)
thread_title:  It's all in the reflexes 

message: they overlap widely. fgnievinski (talk) 05:09, 7 May 2021 (UTC)
replies: text: Oppose: they are in appropriate Summary style. Klbrain (talk) 20:00, 22 May 2021 (UTC)

text: Support: Angular unit has a lot of material about angles and their measurement that does not belong there, and little detail about units that is not already at Angle#Units.  It does not merit a separate page in its current form.  —Quondum 20:15, 22 May 2021 (UTC)

text: Support per nom. In reply to , there is not enough unique and encyclopedic material in Angular unit to merit invoking WP:SUMMARY. — Cheers, Steelpillow (Talk) 17:40, 9 July 2021 (UTC)
replies: text: All fair points, which I'm happy to concede. No objections to a merge from me. Klbrain (talk) 22:57, 9 July 2021 (UTC)

text: Klbrain (talk) 15:40, 1 August 2021 (UTC)
thread_title:  Merger of [[Angular unit]] into [[Angle#Units]] 

message: The statement
::Angle is also used to designate the measure of an angle or of a rotation.
is meaningless as it stands.  A measure is only defined over a set, which is not given: an angle is simply defined here as "the figure formed by two rays [...] sharing a common endpoint".  To use a concept from measure theory, even if it were properly done, is totally inappropriate for an article such as this, especially in the lead where every word should be easily understood (and not easily misinterpreted) by a high-schooler.  The subject matter of this article is not too complicated to explain in everyday words.  I suspect that the average reader will misinterpret the word measure to mean measurement due to the similarity of the words.  Note also that angle is naturally interpretable as a signed quantity, especially in relation to a continuous rotation, which makes measure an especially poor fit.  Nowhere in the article is a measure used to define the angle as a quantity.
I suggest that any reference to measure theory should be omitted.  It is neither needed nor used in the article.  —Quondum 13:03, 24 May 2021 (UTC)
replies: text: It is only a wrong link, probably added by someone that searched in sections of Measure (disambiguation) without remarking that this is the primary meaning that applies here. I'll fix it. D.Lazard (talk) 17:07, 24 May 2021 (UTC)
replies: text: That was a definite improvement.  Wouldn't a more common and natural term be "size of an angle", as opposed to "measure of an angle"?  —Quondum 17:19, 24 May 2021 (UTC)
replies: text:  This is a question for a native English speaker. My opinion is that "size" is not convenient here. For example, an angle may have a negative measure, and a size is generally supposed to be positive. Also, "size" is generally qualitative, and "measure" is quantitative. For example, the area and the diameter are two different ways to measure the size of a plane figure. D.Lazard (talk) 17:55, 24 May 2021 (UTC)
replies: text:  Fair points.  I can't think of a word that works better while addressing what you mention, and it works adequately as is, so I'll leave it be at this stage.  —Quondum 18:16, 24 May 2021 (UTC)
thread_title:  "measure"? 

message: An editor has identified a potential problem with the redirect :Ángulo and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 14#Ángulo until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  ~~~~User:1234qwer1234qwer4 (talk) 06:11, 14 February 2022 (UTC)
thread_title:  "Ángulo" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: An editor has identified a potential problem with the redirect :Ângulo and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 14#Ângulo until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  ~~~~User:1234qwer1234qwer4 (talk) 06:11, 14 February 2022 (UTC)
thread_title:  "Ângulo" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: Joyous! | Talk 22:55, 19 February 2023 (UTC)
replies: text: Support Angle of rotation is just an unsourced stub, there is no benefit to having it separate. --Mathnerd314159 (talk) 18:07, 20 May 2022 (UTC)

text: Support – though it might make sense to delete it and consider leaving a redirect to Rotation instead of to Angle, since an angle might or might not parameterize a rotation.  —Quondum 13:10, 19 October 2022 (UTC)
replies: text: Support the alternative target, Rotation. It would be well placed there, perhaps before Rotation#Axis of 2 dimensional rotations which explicitly uses the angle of rotation without describing it in one dimension. Klbrain (talk) 10:08, 2 January 2023 (UTC)
replies: text:  This is a bad idea. If someone wiki-links to angle of rotation they are looking for a definition of an angle measure, not a definition of a rotation. –jacobolus (t) 19:45, 2 January 2023 (UTC)
replies: text: Good point; I had overlooked that common use. So, switching to support to the original target, Angle. Klbrain (talk) 08:43, 7 January 2023 (UTC)

text: —Quondum 01:41, 23 February 2023 (UTC)
replies: text: Thanks for the merger done sometime ago. I've recently sourced a definition for angular displacement from an authoritative source (ISO 80000-3) which states explicitly it may be a signed quantity. Therefore, I've retargeted the redirect Angle of rotation. fgnievinski (talk) 08:52, 22 July 2023 (UTC)
thread_title:  Proposed merge of [[Angle of rotation]] into [[Angle]] 

message: Like what is explanation of angles 185.76.177.40 (talk) 08:41, 6 May 2022 (UTC)
thread_title:  Math 

message: The redirect Angles has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  —Lights and freedom (talk ~ contribs) 00:50, 23 May 2023 (UTC)
thread_title:  "[[:Angles]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: The lead sentence specifies euclidean geometry, but angles are also a thing in spherical geometry and hyperbolic geometry as well.  Is there a common definition to all three that we can use in the lead sentence, and then briefly define the specifics for each geometry? It's a disservice to specify euclidean and then not discuss the other geometries as well, as doing so implies that only euclidean geometry has angles-- which is not true. Fieari (talk) 07:05, 23 May 2023 (UTC)
replies: text: I went ahead and was WP:BOLD and did it.  I welcome anyone to review my additions... I believe everything I said is accurate and lead-worthy, but I'd love a 2nd eye on it. Fieari (talk) 07:21, 25 May 2023 (UTC)
replies: text: Your addition would make sense in a specific section named for example "In other geomeries". It is definitively too WP:TECHNICAL for the lead: most people interested in triangles do not know anything on non-Euclidean geometries. So, I'll revert your edit. D.Lazard (talk) 10:14, 25 May 2023 (UTC)
thread_title:  Euclidean Geometry only? 

message: The following was removed: "Although the definition of the measurement of an angle does not support the concept of a negative angle," as unhelpful. Of course a definition can be contrived. Essentially one refers to area of a circular sector, using signed area according to the area being above or below the horizontal line of symmetry. This definition is for angles fixed in a standard position. Reference to area for definition is the historic basis of hyperbolic angle, so angle reference to area is one of the unifying theories in mathematics. Rgdboer (talk) 23:03, 9 November 2023 (UTC)
replies: text: This article needs to be clarified and expanded to more clearly describe and discuss the several different concepts of "angle" which are in common use. This is something I plan to do eventually; I've been occasionally gathering sources at User:Jacobolus/Angle but am not yet ready to write a solid survey. –jacobolus (t) 00:45, 10 November 2023 (UTC)

text: Of course, both circular and hyperbolic angle measure can be defined either via area or via arc length, with the latter using a Lorentzian (pseudo-Euclidean) concept of distance in the plane. –jacobolus (t) 02:25, 12 November 2023 (UTC)
thread_title:  Negative angle definition