This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics
The following discussion is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
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)Reply
Nah,Circles don't have sides cuz then it would be a polygon.(I think)
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)Reply
The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
Regions in a circle?
Latest comment: 1 year ago2 comments2 people in discussion
Latest comment: 1 year ago3 comments2 people in discussion
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:
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.
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)Reply
Latest comment: 9 months ago5 comments3 people in discussion
The krikos etymology is absolute crap. A metathesis would imply a "kirkos" form, which definitely does NOT resemble "kyklos", which is instead derived, through Proto-Hellenic, from Proto-Indo-European "*kʷékʷlos", a duplication of an original root "*kʷel-" (meaning "to turn"). On the other hand, the root of krikos is uncertain but most certainly unrelated to kyklos. Please somebody fix this, I can't since the page is protected. ~2025-32295-09 (talk) 12:03, 9 November 2025 (UTC)Reply
I don't know anything about Homeric Greek. Can you propose a better wording?
Aside: Materialscientist indefinitely protected this page in 2020 due to scattered occasional vandalism. I don't think the indefinite protected status is justified. Materialscientist: can you remove the page protection? –jacobolus(t)15:43, 9 November 2025 (UTC)Reply
Something like this could do the job: "The word "circle" derives from Latin "circus", of the same meaning, itself a term likely borrowed from Ancient Greek "κίρκος" ("ring, circle"), [which is of unknown further etymology but has been tentatively connected to the Proto-Indo-European root "*(s)ker-" ("to turn, wind")]." ~2025-32366-53 (talk) 16:17, 9 November 2025 (UTC)Reply
I've already written both etymologies, and that proves there being no relation between κίρκος/κρίκος and κύκλος. Kírkos and kríkos are probably from the Proto-Indo-European root *(s)ker- and kýklos is most definitely from *kʷékʷlos. ~2025-32366-53 (talk) 14:44, 10 November 2025 (UTC)Reply
Too much about math
Latest comment: 8 months ago2 comments2 people in discussion
Obviously the circle is an important concept in mathematics. But it also has had a significant impact, culturally. This article largely ignores such and focuses 95% on math with only a brief mention of anything else in the opener.
Here is some AI slop examples:
Gotcha — here’s a short list you can tack onto the end of your talk post:
Analog clock faces as a circular representation of time, still ubiquitous in public and private settings.
Circular traffic and urban design, such as roundabouts and central plazas.
Circular sports equipment, especially balls used in globally popular games (football/soccer, basketball, etc.).
Rings (especially wedding and engagement rings) as everyday symbols of commitment and unity.
Circular logos and emblems widely used in modern branding and international symbolism.
Circular elements in technology and interfaces, such as buttons, icons, camera lenses and control dials.
To the contrary, there is far too little math in this article, which is missing many important aspects of the geometry of one or more circles. However, you should also feel free to research more about cultural or technological uses of circles. Please do your research in reliable sources rather than asking an LLM. –jacobolus(t)17:14, 28 November 2025 (UTC)Reply
This article is incredibly incomplete, disorganized, poorly sourced, poorly illustrated, etc. It needs probably a hundred or two hours of dedicated effort. Please feel free to do some research and expand it. –jacobolus(t)23:31, 8 March 2026 (UTC)Reply
Informasi ini disarikan dari Wikipedia dan disajikan kembali untuk tujuan edukasi. Konten tersedia di bawah lisensi CC BY-SA 3.0. Kami tidak bertanggung jawab atas ketidakakuratan data yang bersumber dari kontribusi publik tersebut.
The information displayed on this website is sourced in part or in whole from Wikipedia and has been adapted for the purpose of restating it. We strive to provide accurate and relevant information, however:
There is no guarantee of absolute accuracy. Wikipedia is an open, collaborative project that can be edited by anyone, so information is subject to change.
It is not intended to constitute professional advice. The content displayed is for informational and educational purposes only. For important decisions (e.g., medical, legal, or financial), please consult a professional.
Content copyright. Wikipedia is licensed under the Creative Commons Attribution-ShareAlike License (CC BY-SA). This means that content may be reused with appropriate attribution and shared under a similar license.
Responsible use. Any risk arising from the use of information from this website is entirely the responsibility of the user.