Talk:Circle

"🔴" listed at Redirects for discussion

An editor has identified a potential problem with the redirect 🔴 and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 February 11#🔴 until a consensus is reached, and readers of this page are welcome to contribute to the discussion. theleekycauldron (talk • contribs) (she/they) 04:21, 11 February 2022 (UTC)

The distance between any point of the circle and the centre is called the radius.

I see this lead sentence dubious because circle is probably of two elements: round (kružnica) and surface (both define circle at same time). It contains infinite number of points. Radius would be distance from circle's round to center. --5.43.73.144 (talk) 20:12, 29 June 2022 (UTC)

In English circle usually means the perimeter arc, what you call the "round"; not the interior, which is a disc or ball (commonly in informal contexts, but always in mathematics). They each have the same infinite number of points, by the way. —Tamfang (talk) 01:30, 21 May 2023 (UTC)

A circle is a special case of a torus?

Maybe it should be said in the article that a circle is a special case of a torus. !ZanzibarWikiwoowiiBarfuttress (talk) 04:44, 1 May 2023 (UTC)

In geometry, a circle may be considered a degenerate torus; but in topology they are firmly distinct. —Tamfang (talk) 00:38, 21 May 2023 (UTC)

Bad alternative definition

The second sentence of this article currently says:

Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.

This doesn't really work as a definition of a circle. A point can move in a plane in such a way that its distance from a given point remains constant, but not trace out a circle: it might just trace out a circular arc.

This sentence has no cited source. There might be a way to rework this sentence to make it correct, but I'm inclined to just delete it. Thoughts? —Bkell (talk) 01:43, 4 May 2023 (UTC)

It looks like it was introduced in Special:Diff/460034425, revising earlier text that was introduced in Special:Diff/459981433. That wasn't cited either, but it's clearer what the original intent was. Apocheir (talk) 20:39, 4 May 2023 (UTC)

You are correct,the correct definition is :- A circle is a set of all points that are equidistant from a point called centre Yuthfghds (talk) 06:10, 30 May 2023 (UTC)

Personally I have never been keen on the "locus of a moving point" approach to definition of a curve, as opposed to the "set of points" version, but since the locus definition is well established, I initially reluctantly left it in. However, reading the above discussion, indicating that I'm not the only one who doesn't like it, has led me to remove it. I agree with Apocheir that if we are to have the definition in the article the original version was much better, and I won't object if someone decides to restore it, but my preference is to go along with Bkell's "just delete it". Yuthfghds's text is merely a rephrasing of the other definition already in the article, and there's no point in having it in twice. JBW (talk) 14:06, 1 June 2023 (UTC)

@JBW Thank you for your feedback.I think you are correct but locus of a moving point definition is very rough.And set of points is much more defined in mathematics.Like a parabola is defined as:- Parabola is a set of all points that are equidistant from a line and a point here line is called directrix and point is called focus.You see circle comes under conics and in this way the set of points fits in. Yuthfghds (talk) 14:30, 1 June 2023 (UTC)

I think we should use set of points idea in the definition of the circle. Yuthfghds (talk) 14:40, 1 June 2023 (UTC)

A Circle have infinite sides

A Circle have infinite sides.Adding this topic expand our perspective. Yuthfghds (talk) 05:34, 2 July 2023 (UTC)

Usually a circle is taken to be a single smooth curve, that is with one curved "side" if you like. However, it is also true that a circle can also be taken as a limiting case of a regular polygon as the number of sides increases without bound. Perhaps this would be worth mentioning in Circle § Limiting case of other figures. –jacobolus (t) 07:04, 2 July 2023 (UTC)

You know that circle has 0 or Infitite Sides.
Right? 12.171.25.60 (talk) 18:38, 16 November 2023 (UTC)

A circle is usually taken to be a single smooth curve. The word "side" is not really precisely defined in the context of smooth curves, so you'll have to define it before you can decide how many sides a circle has. If you consider "side" to mean a straight portion of a curve, then a circle has no "sides". If you consider a "side" to be a smooth (unkinked) portion of a curve, then a circle has one "side". If you consider a "side" to be a straight line tangent to a curve, then a circle has infinite "sides". Alternately, if you like you can consider the circle to be the limiting case of a regular polygon of fixed apothem as the number of sides increases without bound ("infinite sides"). –jacobolus (t) 19:58, 27 November 2023 (UTC)

lol 12.171.25.60 (talk) 16:29, 6 December 2023 (UTC)

"Meta" sentence in first paragraph

In the first paragraph of this article, it states: "This article is about circles in Euclidean geometry, and, in particular, the Euclidean plane, except where otherwise noted."

It feels really weird to include a meta statement about the article in the article. Disclaimers like this would typically go in the small area below the title of the page. I'm not incredibly familiar with mathematics related pages on Wikipedia, and if this is a common thing, then my bad. It just seems odd is all I'm saying. SpaiceyWarrior (talk) 00:58, 15 September 2023 (UTC)

It seems unusual to me too, and I'm more familiar with math articles on Wikipedia. The closest this page comes to mentioning non-Euclidean geometry is that it links to Geodesic circle in the "Specially named circles" section. I don't think it's necessary, and I've removed the statement.

Really the entire lede section needs a rewrite. Nobody defines a circle using calculus of variations. Apocheir (talk) 03:04, 15 September 2023 (UTC)

I can imagine cases where this kind of disclaimer could be useful, but this is not one of them.

It would be good for this article to discuss other kinds of generalizations of circles, including circles on the sphere and "cycles" in hyperbolic geometry, oriented circles (whether in the Euclidean plane or other contexts, and "circles" (i.e. hyperbolas) in the pseudo-Euclidean plane, etc. –jacobolus (t) 03:13, 15 September 2023 (UTC)

I'd also like to see the first section after the lead discuss other characterizations of circles, including not only the "constant distance from the center" characterization but also the "constant inscribed angle" characterization, the "constant ratio of lengths to two points" characterization, and most importantly the "curve of constant curvature" characterization which leads to the notion of a generalized circle. Possibly also the "image of a line when 3 points of the line are mapped to 3 arbitrary points in the plane via Möbius transformation" characterization, which is related to the inscribed angle characterization (not sure what the most accessible description of this one is, but it's also pretty fundamental; probably should start by saying that there is a unique circle through three arbitrary points). –jacobolus (t) 03:15, 15 September 2023 (UTC)

Regions in a circle?

Would it not be better to move discussion of regions (e.g. segment, sector) to the article on discs? 41.133.90.18 (talk) 15:14, 1 December 2023 (UTC)

We could have it in both articles. ISaveNewspapers (talk) 06:56, 30 August 2024 (UTC)

"360 degrees" redirect

Why is this article the redirect destination for "360 degrees"? Wouldn't Turn (angle) be more natural? ISaveNewspapers (talk) 02:53, 30 August 2024 (UTC)

Well, the redirect was created in 2007, so I doubt anyone remembers the rationale. I'd move 360 degrees (disambiguation) to 360 degrees. Apocheir (talk) 03:23, 30 August 2024 (UTC)

Very well. I will also change the redirect to Turn (angle). ISaveNewspapers (talk) 04:13, 30 August 2024 (UTC)

Wait, I can't change the redirect if I also move the disambiguation page. That makes no sense. Sorry, I didn't think this through.

I'd argue that if someone looks up "360 degrees", then Turn (angle) is most likely the place they want to be, so it should redirect there. ISaveNewspapers (talk) 04:18, 30 August 2024 (UTC)

Radians

I'm surprised that radians aren't mentioned a single time in this article, considering that they're pretty important and they're closely connected to circles. I wrote a draft of a short section about radians. I would like feedback about whether this would fit into the article, and if so, where. Also, this definitely needs an image.

If a circle of radius r is centred at the vertex of an angle, and that angle intercepts an arc of the circle with an arc length of s, then the radian measure 𝜃 of the angle is the ratio of the arc length to the radius:

$\theta ={\frac {s}{r}}$

The circular arc is said to subtend the angle at the centre of the circle. The angle subtended by a complete circle at its centre is a complete angle, which measures 2π radians, 360 degrees, or one turn.

ISaveNewspapers (talk) 14:33, 13 September 2024 (UTC)

I agree that it's a conspicuous omission. Maybe in the first part of Analytic Results with Circumference and Area Enclosed, since the circumference and the area of the circle can be generalized to circular arcs and sectors using radians. Apocheir (talk) 21:50, 13 September 2024 (UTC)

Done. ISaveNewspapers (talk) 03:15, 14 September 2024 (UTC)