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|diff4 = https://en.wikipedia.org/w/index.php?title=Angle&diff=582480777&oldid=582479826
|date4 = 05:04, 20 November 2013
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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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: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)
::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)▼
::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)
:::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)▼
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::::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)▼
::::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)
▲:::::[[User:Jacobolus|@Jacobolus]] You are absolutely right ,my bad. [[User:Yuthfghds|Yuthfghds]] ([[User talk:Yuthfghds|talk]]) 15:47, 5 June 2023 (UTC)
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:::[[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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