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:{{merge done}} —[[User_talk:Quondum|Quondum]] 01:41, 23 February 2023 (UTC)
::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]]. [[User:Fgnievinski|fgnievinski]] ([[User talk:Fgnievinski|talk]]) 08:52, 22 July 2023 (UTC)
== Math ==
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{{reflist talk}}
== "[[:Angles]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] ==
[[File:Information.svg|30px]]
The redirect <span class="plainlinks">[//en.wikipedia.org/w/index.php?title=Angles&redirect=no Angles]</span> has been listed at [[Wikipedia:Redirects for discussion|redirects for discussion]] to determine whether its use and function meets the [[Wikipedia:Redirect|redirect guidelines]]. Readers of this page are welcome to comment on this redirect at '''{{slink|Wikipedia:Redirects for discussion/Log/2023 May 23#Angles}}''' until a consensus is reached. <!-- from Template:RFDNote --> —[[User:Lights and freedom|Lights and freedom]] ([[User talk:Lights and freedom|''talk'']] ~ [[Special:Contributions/Lights and freedom|'''contribs''']]) 00:50, 23 May 2023 (UTC)
== Euclidean Geometry only? ==
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. [[User:Fieari|Fieari]] ([[User talk:Fieari|talk]]) 07:05, 23 May 2023 (UTC)
: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. [[User:Fieari|Fieari]] ([[User talk:Fieari|talk]]) 07:21, 25 May 2023 (UTC)
::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. [[User:D.Lazard|D.Lazard]] ([[User talk:D.Lazard|talk]]) 10:14, 25 May 2023 (UTC)
== what about grad angle system? And forgot about circular angle? ==
I think we should add the following topics [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 12:05, 4 June 2023 (UTC)
:What do you mean by "circular angle"? Grads are discussed under {{slink|Angle#Units}}. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 20:35, 4 June 2023 (UTC)
::[[User:Jacobolus|@Jacobolus]] Sorry my fault I didn't noticed the grad angle system.I am talking about degree measure in which 1°= 60' and 1'= 60''. Here we are only talking about linear angles not about circular degree measure.Thanks for pointing out my mistake, I am a new editor please avoid my faults.I still need feedback from your kind of editors.
::Thank you
::Yuthfghds [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 05:49, 5 June 2023 (UTC)
:::I still do not understand what you are trying to say. What is the difference between "linear angles" vs. "circular degree measure"? This article does discuss degrees, minutes, and seconds. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 06:03, 5 June 2023 (UTC)
::::[[User:Jacobolus|@Jacobolus]]
::::Linear Angles:
::::Linear angles are measured in degrees or radians and represent the amount of rotation or deviation between two lines or line segments.
::::They are used to measure angles in two-dimensional space, such as in geometry or trigonometry.
::::Linear angles have a fixed starting point (usually a reference line) and are measured in a straight line.
::::Linear angles range from 0° to 180° (or 0 to π radians) in a half-circle and extend up to 360° (or 2π radians) in a full circle.
::::Circular Angles:
::::Circular angles are measured in terms of arc length or fraction of a circle and are used to describe rotational positions or displacements.
::::They are commonly used in applications that involve circular or periodic motion, such as physics, engineering, or navigation.
::::Circular angles are based on the concept of a full circle, where one complete revolution is equal to 360 degrees or 2π radians.
::::Circular angles can exceed 360° or 2π radians, representing multiple revolutions or fractional parts of a revolution. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 06:17, 5 June 2023 (UTC)
:::::"Linear angles" is not a term used in technical literature or curriculum that I have seen. Most of the results in a search for "linear angle" seem to be using it as a synonym for "straight angle" (i.e. a half turn, 180°). Where did you get these names? Do you have a source? I would call this instead something like "angular distance" or "angular separation" (or just "angle"). I agree that this article should do a better job about talking about different concepts of angle, and I have started gathering sources for hopefully an eventual rewrite/rework. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 06:45, 5 June 2023 (UTC)
::::::[[User:Jacobolus|@Jacobolus]] Sir, here are some references for linear and circular angles:- help you.
::::::Linear Angle:
::::::Elementary Geometry for College Students by Daniel C. Alexander and Geralyn M. Koeberlein.
::::::Chapter 1: Basic Geometry Concepts.
::::::Chapter 2: Reasoning and Proof.
::::::Geometry: A Comprehensive Course by Dan Pedoe.
::::::Chapter 2: Angles.
::::::Circular Angle:
::::::Trigonometry by James Stewart, Lothar Redlin, and Saleem Watson.
::::::Chapter 1: Trigonometric Functions.
::::::Trigonometry by I.M. Gelfand and Mark Saul.
::::::Chapter 1: Angles.
::::::Elementary Trigonometry by H. S. Hall and S. R. Knight.
::::::Chapter 1: Trigonometrical Ratios of Acute Angles.
::::::sir if you still have some queries please question me.Thanks for feedback.
::::::Yuthfghds [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 07:25, 5 June 2023 (UTC)
{{dedent|6}} Unless I am doing something wrong with my text searches at the internet archive, the term "linear angle" does not appear in either of the books you listed by [https://archive.org/details/elementarygeomet0000alex_o5k5_4ed/page/6/mode/2up?q=%22linear+angle%22 Alexander] or [https://archive.org/details/geometrycomprehe0000pedo/page/n5/mode/2up?view=theater&q=%22linear+angle%22 Pedoe]. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 11:13, 5 June 2023 (UTC)
:[[User:Jacobolus|@Jacobolus]] Please recheck,if you still don't find it I can't do anything.Because I don't have those books that I mentioned you.Because I red those books few years ago.And I think linear angle is informal term mentioned by the author.And I argued here so it's my fault but still we can add these topics in this article.If I tell you the definition of linear angle and circular angle it would be like this:-
:linear angle- Angle measured between two rays in degrees.
:circular angle- Angle measured between two rays also in degrees but including minutes and hours. Technically angles that are placed inside a unit circle with 3 divisions namely degrees, minutes and hours.
:I am glad that you understand my perspective and debate over this topic. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 13:03, 5 June 2023 (UTC)
::The angle between two rays does not depend on whether or not a circle is drawn around their vertex! — When you say "including minutes and hours", are you referring to [[right ascension]] (part of the coordinates of a star in the sky) which is at least sometimes given in hours? — The subdivisions of a degree are called ''minutes'' and ''seconds''. As far as I know, hours and degrees are never used together, partly because of the confusion between two kinds of "minutes". —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 21:01, 7 July 2023 (UTC)
:::@[[User:Tamfang|Tamfang]] You are absolutely right.These are just "informal" terms to distinguish between trigonometric angles and geometric angles. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 05:25, 9 July 2023 (UTC)
::::Why do they need distinguishing? Is there ever a circumstance in which mistaking a trigonometric angle for a geometric angle (or vice versa) or a linear angle for a circular angle (or vice versa) (are these the same distinction?) would lead to wrong results? —[[User:Tamfang|Tamfang]] ([[User talk:Tamfang|talk]]) 20:08, 5 August 2023 (UTC)
:As I mentioned above linear angle is an informal term referred to angles that are measured in only degrees like in protector when we measure angle we say 12.5° or 45.2° just because we can't expand it but in circular angles we expand this system.linear angles are helpful in geometry but circular angles are helpful in trigo [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 13:12, 5 June 2023 (UTC)
:well the references that I mentioned you are generated by Chatgpt.But I red the book by padeo don't know linear angle is in that book or not but I red somewhere about linear angle in a random book but when Ai generated that book I thought it cover that topic sorry for the inconvenience that you suffered but still together we can make this article near excellence. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 14:14, 5 June 2023 (UTC)
::Please don't ever ask ChatGPT for help writing Wikipedia, and be careful using it for any other purpose. It will confidently make up total nonsense. ChatGPT is a statistical language model, not a reference librarian. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 15:36, 5 June 2023 (UTC)
:::[[User:Jacobolus|@Jacobolus]] You are absolutely right ,my bad. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 15:47, 5 June 2023 (UTC)
== Negative angle definition ==
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]]. [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 23:03, 9 November 2023 (UTC)
: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. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 00:45, 10 November 2023 (UTC)
Thank you for those sources on directed angle. The issue of angle definition came to a head in 1893 in Chicago when Felix Klein shot down Alexander Macfarlane’s paper on the topic which was presented to the mathematical congress held in connection with the [[Columbia Exposition]]. The paper was included in ''Papers in Space Analysis'' (1894) as the ''Proceedings'' of the congress only noted the title. The notion of an area-based definition referring to the sector of a circle was included in ''The Elements of Plane Trigonometry'' (1892) by R. Levitt & C. Davison (page 158). [[Robert Baldwin Hayward]] noted the complete analogy between the circular and hyperbolic cases when area of sectors are used to define the circular and hyperbolic angles. — [[User:Rgdboer|Rgdboer]] ([[User talk:Rgdboer|talk]]) 01:19, 12 November 2023 (UTC)
: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. –[[user:jacobolus|jacobolus]] [[User_talk:jacobolus|(t)]] 02:25, 12 November 2023 (UTC)
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