From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Mathematics (Rated B-class, Top-importance)
WikiProject Mathematics
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.
Mathematics rating:
B Class
Top Importance
 Field: Geometry
One of the 500 most frequently viewed mathematics articles.
Wikipedia Version 1.0 Editorial Team / v0.7 / Vital (Rated C-class)
WikiProject icon This article has been reviewed by the Version 1.0 Editorial Team.
C-Class article C  This article has been rated as C-Class on the quality scale.
Checklist icon
 ???  This article has not yet received a rating on the importance scale.


What is the name for the area of overlap of two intersecting circles? (a pointy oval shape) - unsigned

As a symbol, it would be given the name of vesica piscis or mandorla. - Nunh-huh 21:19, 5 Jan 2005 (UTC)

funnily enough in venn diagrams it's called an intersection. and if the circles are named 1 and 2 then it's labeled 1 ∪ 2. Wolfmankurd 22:35, 27 May 2006 (UTC)

shouldnt that be 1 ∩ 2. 1 ∪ 2 is the union of the circles. - unsigned
Yup you're right lol Wolfmankurd 18:32, 15 March 2007 (UTC)

Circle image[edit]

Is it just me, or is the splash image totally unrecognizable as a circle? I don't have a better one to replace it with, though. Reediewes 03:41, May 11, 2005 (UTC)

Which image are you referring to? I find all of them OK, and the bottom ones actually quite nice. Oleg Alexandrov 04:32, 11 May 2005 (UTC)
The top image doesn't seem to display correctly in Internet Explorer. Other viewers I've tried it with don't have a problem with it. The image should either be fixed or reverted to one of the older images that do display in IE. Krellion 13:39, 12 May 2005 (UTC)
I was using Safari when I noted that problem, and referring to the one at the very top. (That image is Circle-1.png now, but it may have been changed as recommended above.) My same computer is having no problem viewing it now. Thanks to all who helped me out. Reediewes 04:52, May 13, 2005 (UTC)the circle is the center of everything and always no matter what the circle is ther ...the circle is what makes everything and no matter whats you do a circle is ther!

I still have a problem with it, using Internet Explorer, doesn't show right at all and all I see is a buncha' dots in the rough shape of a circle. PanzerArizona 23:13, May 17, 2005 (PST)
the 1st image is foo-bar'ed. not showing up correctly. needs to be reverted to an earlier version.

non-Euclidean circle[edit]

I don't see why it shouldn't exist, so perhaps the first sentence should go "In geometry"? --MarSch 13:49, 3 November 2005 (UTC)

ummmm, there's really only one type of truer circle, the other being an oval, so then if circles are euclidian, wouldn't a non-euclidean circle either not exist or be an oval?

The circle is used in Euclid's first four postulates, specifically, his third, which are shared in non-Euclidian geometry, therefore it does exist in other geometries, although not necessarily all of them; I'm not sure of the definition of geometry. Perhaps it should say "In any geometry using Euclid's third postulate ...". Even with the postulate rejected, the circle can still exist, though. — Daniel 23:44, 10 June 2007 (UTC)

The definition of a circle works just as well in a non-Euclidean plane, but the resulting curves have slightly different properties. For example the ratio of the perimeter to the diameter is no longer pi. Perhaps there could be a section on the properties of non-Euclidean circles.--RDBury (talk) 14:31, 27 April 2008 (UTC)


It's easy to integrate from the center of a circle, but I would like to figure out how to integrate

where r is measured from a point not in the center of the circle, i.e.

where c is a constant less than r...

I have a feeling that this is hard.

General derivitive[edit]


and finally:

I might have made an error I was writing this up as I worked. being a circle there are two gradients for any x value consider this when doing the square root

I could easily make this into a general case I did it because I thought the person above wanted the derivitive then I saw he said intgral lol....

using what I have above I got this as the general derivitive for: is:


whilest messing up commons:Category:Curves I added commons:Category:Circles (Geometry) and moved the images used here to commons:Circle (Geometry), because commons:Category:Circles is just so circles ... - I hope, I did no harm. please control it, and correct all my typing, I'm no native EN --W!B: 00:38, 15 December 2005 (UTC)


Why do the other articles on conic sections include an algebraic equation in addition to the Cartesian, and the one on the circle doesn't? What am I missing? thanks


I found this on a disambiguation page, where it doesn't belong. I find it confusing but maybe someone more familiar with circles could dechipher it and find a good place for it. Or toss it: up to you! Ewlyahoocom 08:53, 3 March 2006 (UTC)

In the presence of a circle, a pole is a point that is associated with a line, a polar of the point with respect to the circle. The polar is perpendicular to the line joining the pole with the center of the circle, such that the foot of the perpendicular is the image of the pole under the inversion in the circle.

The origin of 360°[edit]

This was a section added to the article recently. It appears to not assert what its sources are saying. What do you all think? —Mets501 (talk) 03:37, 27 June 2006 (UTC)

Correction and comment[edit]

Hi, there seem to be two issues:

  • As written, the formula is wrong. The regular hexagon inscribed in a unit circle has a perimeter of 6, while the circumference of the unit circle is 2π. So the formula should read

which is a decent approximation (it's too high by ~0.53%).

  • Although interesting, this material doesn't really pertain to circles, but rather to the measurement of angles; see degree (angle), where the same material was posted and signed by the same user. That seems like a more appropriate article for this material, don't you all think so? Perhaps we should delete it here to avoid duplication?

Does the contributor wish to comment? WillowW 09:38, 27 June 2006 (UTC)

We definitely should delete it from circle and move it to degree (angle). I'm doing that now. Thanks for cleaning it up at degree (angle) as well. —Mets501 (talk) 12:24, 27 June 2006 (UTC)

The origin of 360°[edit]

The 360 degree unit of measure for a circle was first derived from the Babylonian method of calculating the circumference of a circle.[1][2]

In the first part of the 19th century, British and French explorers began to rediscover the ruined cities of Babylonia along the banks of the Tigris and Euphrates rivers, which is now southern Iraq. The sophisticated Babylonian cities, which had flourished from 3,000 to 1,000 BCE, had lain unaltered since their gradual demise 19 centuries earlier.

In 1936 a particular mathematical tablet was excavated some 200 miles from Babylon in a city known as Susa.Cite error: The <ref> tag has too many names (see the help page). Cite error: The <ref> tag has too many names (see the help page). The translation of the tablet was partially published in 1950, and states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by the formula:

The Babylonians used the sexagesimal system, i.e., base 60 rather than the modern base 10, which is the reason for the denominators of 60.

The Babylonians apparantly knew that the perimeter of a hexagon is exactly equal to six times the radius of the circumscribed circle, in fact that was evidently the reason why they chose to divide the circle into 360 degrees (6 times their base of 60).

360 degrees is useful for dividing the circle into lots of equal pie slices. 360 has factors of 1, 2, 3, 4, 5, 6, 8, 9, 10, 12. Easy to deal with. Except for 7 and 11. Damn! —Preceding unsigned comment added by (talk) 22:14, 26 September 2007 (UTC)

The answer to why there are 360 degrees in a circle is as simple as why Christmas Day, 25th December is the 360th day of the year. The architects of our modern calendar ensured that we would never forget when the sun begins its journey back to the Equator after the Winter Solstice. To the naked eye, it appears as though the sun never sets at a lower point on the horizon than it does on the first day of a solstice, and then sets at that same point of entry for 3 sunsets (the same period that a full moon appears to last). This happens twice a year, thus the Tropic of Cancer and the Tropic of Capricorn. The total of 6 sunsets during the solstices of 6+ 24 hour periods or 7 days during this period is the basis of why there are 7 days in a week.

In short, to the naked eye, there are 360 different sunset points of entry on the horizon during a calendar year i.e. 90 points / days between Winter Solstice to Equinox, Equinox to Summer Solstice, Summer Solstice to Equinox and then Equinox to Winter Solstice. Sounds like the beginnings of Geometry to me.

There are always simple and practical explanations for these questions, even if it did take me years to figure it out. One simply needs to observe the nature of nature.

Xmasday1963 (talk) 15:25, 14 February 2009 (UTC)

Defining a circle[edit]

I removed the following text from the article:

A circle cannot be defined as the set of all points on a given plane which are equidistant from a fixed point, since a point is a location and has no dimensions. Therefore, any number of points, collectively, will still have zero dimension(s), so cannot form a line of one or more dimensions.

Alternatively, a circle can be defined as the result of any cross-section of a sphere.

The set of all points on a plane equidistant to a fixed point is infinite, and its dimension is 1. So there is no contradiction.

Compare for example the situation where you have all integers in the interval [0, 10]. Since this set is finite, its dimension is 0. However, if you "fill in the gaps", by allowing real numbers, the infinite set consisting of all real numbers in the interval [0, 10] is generated, which has dimension 1, which can be easily verified by transforming it to the set R, which is a known 1 dimensional entity. Shinobu 23:02, 15 August 2006 (UTC)

A circle can be defined as the curve traced out by a point that moves so that its distance from a given point is constant.

Should be

A circle can be defined as the curve traced out by a point that moves in a plane so that its distance from a given point is constant. The point is center of circle and distance is called radius. Rosswante (talk) 12:02, 17 September 2012 (UTC)

How to calculate the crossing points of two intersecting circles?[edit]

This is not in the wiki. Two circles having center points and radius known.

Assume without loss of generality that the center points are (0, 0) and (1, 0).
Solve Sqr(r1^2 - x^2) = Sqr(r2^2 - (1 - x)^2):
r1^2 - x^2 = r2^2 - 1 + 2 * x - x^2
r1 ^ 2 = 1 / 9 + 1 / 4
r2 ^ 2 = 4 / 9 + 1 / 4
This yields 2 * x = 2 / 3, which is correct.
Note that if the circles don't intersect you will still find an x value for the intersection, so always check whether the circles actually intersect.
Fill in to retreive the y value and don't forget the negative one. Please check for errors, this was a half-a-minute post, so there may be bugs. On paper it seems to work, but there may be typos and the like. Shinobu 13:57, 3 October 2006 (UTC)

Chinese area expression[edit]

Shouldn't the Chinese area expression be moved to area of a circle? It strikes me as much too specific for this article. I also strongly doubt this formula is either specifically Chinese (as it's trivial to derive from pi-r-squared, and can be used to sketch an intuitive idea of the workings of the formula) or the form most commonly used in China today (for doing real work that is) as mathematics has homogenised considerably and pi-r-squared is simpler to use in most situations. Shinobu 14:44, 9 October 2006 (UTC)

What is that Chinese area expression and what it looks like? —Preceding unsigned comment added by Sasq777 (talkcontribs) 19:18, 29 February 2008 (UTC)

Triginometry functions[edit]

x = a + r cos(t) 
y = b + r sin(t)

Well, what value is t? Some guy 14:22, 13 October 2006 (UTC)

Any value from 0 to 2pi; it's a parametric variable. EdC 22:44, 24 October 2006 (UTC)
Double redirect on that link. Don't see t on the final page either but I skimmed it. You could have at least added an explanation to the page instead of leaving me to do my best attempt at explaining something I don't know about. Some guy 10:30, 29 October 2006 (UTC)
Would that have been anywhere near as fun? Anyway, parametric variable -> parametrisation -> coordinate system is broken; parametrisation should redirect to parametrization, which has a somewhat better explanation. I'll fix it now. EdC 14:17, 29 October 2006 (UTC)
Now parametric variable redirects to parametric equation, which is what the above equation is. EdC 14:20, 29 October 2006 (UTC)
Just use theta, most people think angle when they see theta don't see why it should be radians, but normally is. Wolfmankurd 18:35, 15 March 2007 (UTC)


Hello, I'm a student of mathematics. I'm Polish, so some language mistakes may occur. I would like to refer to a sentence from the article:

An arc is any continuous portion of a circle.

It is mathematical article, so it should be strict. What means "continuous portion"? We have reliable notion: connected (topology). So, this sentence should be changed to this one:

An arc is any connected portion of a circle.

Well, one of the meanings of continuous is the same as that expressed by the topological notion of connectedness. I wonder whether "connected" would be better, though, given that this article needs to be accessible. Perhaps using "connected" linked to connectedness would be best? EdC 22:44, 24 October 2006 (UTC)

How many sides does a circle have?[edit]

Does a circle have infinity sides or no sides?-- 15:06, 28 October 2006 (UTC)

Since it's a set of points, and points have no spatial dimensions, I'd think infinity, but there's 360 angles, potentially no line segments... No idea! There's a discussion at Math Forum. --Gray PorpoisePhocoenidae, not Delphinidae 15:10, 28 October 2006 (UTC)

It can't possibly be infinite. circles must have an finite amount of sides. something like sides=r²π²360² (totally made up). but then again if circles had a finite number of sides, then including pi would make them have a decimal of sides, that's impossible, and also, tangents would cease to exist, unless they hit a corner. but then again, how would a curve have any sides then? and if it did, wouldn't that make a circle a polygon? if so we would have to rewrite the rules of polygons and geometry, not completely but still.

A circle definately does not have a finite number of line segments. If the two endpoints must be seperate (not in the same place) i.e. a point isn't a line segment, there are no line segments in a circle, because three seperate colinear points can't be equadistant from any other point. If it does count, there are uncountably infinite line segments. If this second definition is true, no line segment shares an endpoint with any other line segments, and therefore no two seperate line segments are connected, directly or indirectly. I doubt it can be considered a side if all the line segments aren't connected.
I think any differentiable (smooth) curve that is not a subset of a larger differentiable curve can be considered a side. There is one of these on a circle. There is an inside and an outside, which are also sides. There's also above, below, to the left, and to the right. I think every angle counts as a side by that definition, and thus there are infinity sides, but I very much doubt you're using that definition. — Daniel 23:23, 10 June 2007 (UTC)

A circle has 360 sides and angles. Now before anyone starts to slam against this, think about it... Let's start with a triangle: 3 angles and 3 sides. A square: 4 angles and 4 sides. Fast forward to a decagon: 10 angles and 10 sides. Have you also noticed that as the number of angles and sides increase, the more of a circle it is becoming? Also, let's look at the degrees of a decagon... Each angle is 144 degrees. Now, imagine using a protractor and drawing from the "0" to the center, then drawing a straight line out to the 144 degree mark. You'd have to draw 10 of these lines/angles to come back to your starting position. Now let's go bigger--the circle. Each angle and side is 1 degree (or 179; however you want to look at your protractor). Now draw your line to the center again, then draw the angle to the opposing side that's either 1 degree or 179 degrees (once again, it's how you look at the protractor). You would have to draw 360 of these angles/sides to come back to the starting point. So no, a circle does not have 0, 1, or infinite angles; instead, it has 360 sides and angles. Still don't believe me? Use a computer to draw a circle, then zoom in as far as possible. If your computer will zoom far enough, you'll be able to see each angle. If your computer does not zoom far enough, refer to the prior sentences. It is not infinite because there is a starting and end point. If it was infinite (which it is not), then the same would hold true for every other polygon because we would not know where the starting or ending point is. The only infinity possible in terms of geometry is a ray that goes on forever. Lines have a starting and ending point. -Ladd Caldwell University of Memphis '14 — Preceding unsigned comment added by (talk) 21:25, 2 November 2015 (UTC)

???? not sure if you try to be funny or to confuse the question, how about polygons that have more than 360 sides , are they rounder than circles? WillemienH (talk) 23:23, 2 November 2015 (UTC)

Zero (yes, I know it's an old post, but the answers so far are all mis-directions). To get an answer to your question you first have to come up with a definition of what a "side" is. Presumably that definition will imply that a side is a line segment of positive length (i.e. not just a point). And then the answer is obviously 0.

If you want to escape this conclusion then you need to define "side" in an unconventional way and/or use non-Euclidean geometry: e.g. a great circle on a sphere could be considered a single "side" (a polygon with one side) if you generalise "line segment" to "geodesic". AlexFekken (talk) 06:57, 30 December 2016 (UTC)


Look, maybe you are no intereted. if you were, please do something...

Auto-intelligence mutilation?: yes, there in es:Círculo (matemática) has begun a voting (insane) to fuse the article with es:Círculo which clearly is wrong (but not too wrong). However, there, someone who feels him as a warrant of true, is blocking my natural improvements toward a better info-contain. That's why i dediced to build es:Círculo (matemática) where i -with respect- add some basic-completely well known facts about the circle. I believe that the friend (who blocks even my editing rights) is abusing his es:bibliotecario powers... that's why i came here to say, to show, to ask for help to put remedy (if we can) to this ridiculus situation. There in es:Círculo (matemática) this same person opened a voting-discussion to fuse with es:Círculo which i will be glad to accept if es:Círculo is updated... Even if you are not spanish-spoken you can help me voting as you believe. Please help-me to raise the planetary intelligence in all of its corners... Greets from Guadalajara.--kiddo 15:53, 1 December 2006 (UTC)

Help again they are smashimg me hard.


Think globaly and act localy. The little context (therein circle) is anyway about topology... and for interior and exterior there are only one possible meaning. And about the links, it just that we have to begin something like bounded and unbounded sets, as we do in math... greets, mathematician--kiddo 20:16, 25 January 2007 (UTC)

Circles in physics/nature/psychology[edit]

Should there be a section on this page about circles occuring naturally in nature, or in function? Some typical noteworthy examples:

  • Ripples in water
  • Bubbles floating on liquid
  • Cornea
  • Group of people sitting down to talk to eachother
  • Path of rotating objects
  • Tree trunk
  • Drain lid
  • Art

etc..etc.. something on the importance and commonness of circles would enhance this page, don't you think?

Totally agree, my opinion is that a section like "Circles on Nature" should be right after the lead. To this list I would add, the Sun and Moon(as they appear to the observer), drops of water, and some every day articles like cups, plates, wheels, and balls. Ricardo sandoval 03:09, 22 April 2007 (UTC)

Yeah. I chose "drain lid" as an "everyday" article, since by being round, it has the essential property of being impossible to drop down the drain, which as far as I'm aware, is unique to a circle (although I don't have a rigorous proof of this).

No, see curve of constant width. Note that most of the rest of the above arise as solutions to the isoperimetric problem. –EdC 17:46, 22 April 2007 (UTC)

Then perhaps something should be written about the isoperimetric problem? Fact is, circles are everywhere, but other "curves of constant width" are less common in nature. Any cross-section of a sphere is a circle. There wouldn't be much point in learning about circles if they didn't have some relevance to everyday life. It is the relevance that should be highlighted.

That could rapidly get bogged down with excessive numbers of examples, though. It might work to add a section describing properties of the circle and how those lead to occurrences in nature, with no more than three examples for each. That would have to go at the end, though, because the properties of the circle are discussed in the main body of the article.
For example:
Isoperimetric property
The circle is the plane curve which encloses maximal area for a given perimeter. Example: bubbles floating on a liquid.
Radial property
The circle is the set of points a fixed distance from a centre. Example: waves from a point source.
Curve of revolution
The circle is the "surface" of revolution of a point around an axis removed from the point. Example: a rainbow.
Maximal symmetry
The circle has maximal symmetry of any plane curve enclosing an area. Example: a wheel.
Conic section
The circle is the conic section with lowest eccentricity. Example: planetary orbits.
Spherical section
The circle is the intersection of a sphere with a plane. Example: appearance of the Moon in the sky.

EdC 20:35, 28 April 2007 (UTC)

Without appearing to be picky actually the "moon in the sky" case looks more like a projection of sphere, even thought there is some distortion. I guess the intersection of a plane with a sphere would be better represented by cutting an orange. And it also illustrates that any plane will do, not just the equatorial one.
The earth itself is a sphere making lots of important circles also.
Good idea separating in sections, and some nice examples there! but I don't think we should be absolute about it since these properties have close relations.
Your sentence "There wouldn't be much point in learning about circles if they didn't have some relevance to everyday life" is a little strong but sums up nicely why we should make this section. I will think more about it later, since i have other problems to solve first. Ricardo sandoval 05:17, 30 April 2007 (UTC)

Error in equation at "Sagitta"[edit]

The equation at "Sagitta" is incorrect. I think that the error is due to using the full length of the chord instead of 1/2 the length of the chord. I am no expert in the simplification of equations, but I worked out the radius of an arch for a wide doorway in my house using trig. The height of the Sagitta is 8.125 inches and the length of the horizontal chord (inside distance between the two framing columns) is 71.875 inches. The radius of the arc is 83.54 inches, which is not the result if the given equation is used.

I found another web site with an equation that does yield the correct radius.



   1. Draw a chord across the Circle, it doesn't have to be a large chord, quite a small one will do.
    2. At the midpoint of the chord draw  at right angles, a sagitta up to the arc.
    3. Measure half the chord and the sagitta.
    4. Add together the square of the sagitta and square of the half chord.
    5. Divide this sum by the sagitta.
    6. The answer will be the DIAMETER of the circle.
Reply. The equation given is correct, and is in agreement with the example you give. The difference is that the given equation uses the chord instead of the half chord, and both sides are divided by two, giving the radius instead of the diameter. Silly rabbit 15:57, 27 May 2007 (UTC)


Not a single claim in this article is cited at all, to say nothing of reliable sources. Someone should try to put those in. 10:45, 10 October 2007 (UTC)

  • Yeah, you're right. I marked some claims as citation needed, but that edit was reverted by Tony Fox. I guess original research is now allowed.
  • Seconded. For example, the Tangent Chord Angle rule/law/whatever was incorrect. See (I don't know how to properly do citations yet, but when I do, I will fix this) (talk) 22:43, 24 May 2009 (UTC)

Wish list[edit]

I'm going to try to add some images and corresponding text to liven up the first few paragraphs. The opening seems like it will be dry for the average person. The article could also use a section on history. --RDBury (talk) 07:02, 5 May 2008 (UTC)

Center vs. Centre[edit]

Can we flip a coin and decide which? Both are being used at the moment which seems a bit sloppy. Is there anything in the style guides that covers this?--RDBury (talk) 22:54, 9 May 2008 (UTC)

I propose we move a lot of content to a new section "Parts of a circle"[edit]

It would be nice to have a every part of a circle (radius, diameter, circumference, arc, chord, sector, tangent, sagitta) in its own subsection alongside a SVG picture highlighting just that. Content would have to be moved from the lead and the tangent section though. Scott Ritchie (talk) 00:49, 16 August 2008 (UTC)

I endorse the above suggestion. I opened this talk page to point out that there's no reference in the text to circular sector which is a fairly basic concept that needs the same treatment as tangent and other other "properties" already in Circle. patsw (talk) 22:25, 4 January 2009 (UTC)

Math articles should not be accessible only to mathematicians.[edit]

This is a general problem with wikipedia articles on mathematical concepts. Most of the time they are explained using mathematical jargon and symbology that is only available to mathematicians. Surely the relevant concepts can be expressed without having to resort to the entire Latex symbol set and in language that the general public should be able to grasp. (talk) 09:17, 12 September 2008 (UTC)

How does this apply to the current article? siℓℓy rabbit (talk) 11:34, 12 September 2008 (UTC)
I believe the consensus is that a general audience article like this one should start at an elementary level without formulas and jargon, but get more technical in the later sections. No article can be everything to everyone but this kind of mixed approach seems to be the best way to meet the needs of both those who are unfamiliar with the subject, and those who are familiar with it and need more detailed information. Keep in mind that this is an encyclopedia article and not a textbook on mathematics so don't expect every concept to be explained in the article, though there should be links for most of them. Also, wikipedia is, and always will be, a work in progress.--RDBury (talk) 12:42, 12 September 2008 (UTC)
Why shouldn't it be a little bit like a textbook? Primary articles can contain a great deal of information on the nature of a thing and include references to other subjects that include it to reduce their native bulk. In essence an encyclopedia is only a shorter version of a textbook, and worse off for brevity in my opinion. Ideally, each page would refer to another, locked page with the correct formulas and interpretive references within some chain of articles alongside. With this, each subject can be suitably classed and modified. Its somewhat ironic that math articles aren't being treated as a logical progression across a system. General audience readers likely cannot accept immediately the classic proof format that these articles seem to take on. IPs are the target audience, and if one can say its wrong, then there are probably thousands who don't even know how to say it is. AcheronSS (talk) 06:47, 26 January 2013 (UTC)

File:Secant-Secant_Theorem.svg may be deleted[edit]

I have tagged File:Secant-Secant_Theorem.svg, which is in use in this article for deletion because it does not have a copyright tag. If a copyright tag is not added within seven days the image will be deleted. --Chris 08:11, 28 April 2009 (UTC)

Apollonius circle[edit]

the definition states that circle is the locus of a point whose distance from 2 fixed points is constant other than unity .if the ratio is one then the locus becomes a straight line

Good point, I adjusted the wording.--RDBury (talk) 16:21, 25 September 2009 (UTC)

area of a circle[edit]

the area is πr2. can somebody please give a simple proof for the area of the circle. —Preceding unsigned comment added by Sidhu 2201 (talkcontribs) 14:13, 30 September 2009 (UTC)

There is an easy picture proof here. I was a bit surprised this doesn't seem to be anywhere on Wikipedia, I thought it was very well known.--RDBury (talk) 13:41, 1 October 2009 (UTC)

that is famous but i was hoping for a more theoretical approach but thanks —Preceding unsigned comment added by Sidhu 2201 (talkcontribs) 17:52, 1 October 2009 (UTC)

circles are unidimensional so they can not have area. Perhaps the best we can talk is of the area bounded by a circle. Instead, in area of a disk you can find all that stuff you think is missing :p--kmath (talk) 01:17, 4 October 2009 (UTC)


the radius of a circle x2+y2+2gx+2fy+c=0

is given by (g2+f2+c)1/2 can somebody upload it for me please . Sidhu 2201 (talk) 14:27, 30 September 2009 (UTC)

Should be -c. I'll check to see if it fits in the article, there is some need to be concerned about having too many miscellaneous formulas though, especially if they can be derived easily from the existing material.--RDBury (talk) 13:48, 1 October 2009 (UTC)

sorry it is -c —Preceding unsigned comment added by Sidhu 2201 (talkcontribs) 17:48, 1 October 2009 (UTC)

Image overlap[edit]

I viewed this article using k-meleon, firefox & IE and the images in the second half of the page all overlap the text, which is pretty annoying. if someone could fix that, it'd greatly imrove the article's readability! —Preceding unsigned comment added by (talk) 23:46, 13 January 2010 (UTC)

Intersection with a line[edit]

How can you talk about chords, secants and tangents without mentioning anything about the line-circle intersection ? —Preceding unsigned comment added by (talk) 06:01, 14 May 2010 (UTC)

Could you expand on what you see as a problem please. What would you say about such intersections? Dmcq (talk) 11:24, 14 May 2010 (UTC)

The (unhappy) ambiguity of usage[edit]

I'm afraid that the term circle is employed in two senses; and the beginning of the article should reflect this.

Sometimes, especially outside mathematics, the word "circle" is used to denote the area enclosed by what I and most mathematicians refer to as a circle. This should be mentioned briefly, even if we dislike this usage. This is a reason for confusion; cf. the section #area of a circle supra; it also explains one use of the word periphery.

A similar divided usage occurs for the word semicircle. Presently, that article only presents the secondary meaning in this case, i.e., it defines a "semicircle" as a half-disc. In that article, too, IMHO, there should be a brief mention of both meanings (1-dimensional and 2-dimensional).

Actually, I'm slightly surprised of finding the 2-dimensional meaning as the only meaning in that article; however, I do not know how "semicircles" are treated in e.g. high school geometry books. JoergenB (talk) 20:48, 28 July 2010 (UTC)

Greek symbols[edit]

I took the liberty of replacing the "\varphi" characters with "\phi" in order to make them appear in the equations as they do in the text. If this leads to incorrect or non-standard usage, please revert, but it would be best if the text and the equation use the same variant of the phi character for those of us not overly familiar with the Greek alphabet or the standard mathematical usages. --Fader (talk) 04:44, 7 August 2010 (UTC)

British spelling restored.[edit]

I'm going to revert edits from the same user for the second time; which is slightly against my 1RR principles. The article was started in British spelling mode. Some edits ago, there was a mixture of the spellings "centre" and "center". A non-inlogged user changed to American spelling consistently, and later complained to a user from England for usung the "misspelling" "centre" when the article was started. I've tried to discuss this with that user, have explained the existence of other standards than the "American heritage dictionary" one, and have warned her/him of my intent to revert. The IP responded politely, but has not commented on the spelling issue.

I take this as a tacit acceptance that the "americanisation" was not a completely good idea. JoergenB (talk) 14:58, 10 August 2010 (UTC)

Back and forth edits[edit]

I've been watching the disagreement on this (which is now taking the form of whether to include a parenthetical statement noting the two spellings) unfold in slow motion for several weeks now. Everyone appears to be acting in good faith, and it's good that it hasn't escalated into an edit war. Fwiw, while I see no real harm in including the parenthetical aside and it may deter the random editor from "correcting" the spelling, I believe it is contrary to precedent and accepted practice. Because the topic of the article is universal and because British spelling was originally used, it is standard operating procedure simply to spell it "centre" and leave it at that. Rivertorch (talk) 04:13, 24 March 2011 (UTC)

I think a parenthetical aside would be a good idea for this article. Considering the number of places where the difference is noted I'd have though the difference was notable in itself, I'd go with WP:IAR for this particular case anyway even if there is something saying otherwise. Dmcq (talk) 08:50, 24 March 2011 (UTC)
I'll try setting up lang-en-us and lang-en-gb templates and see what happens. If an article like Dosa can give various variants in different languages I don't see why English variants can't be given. Dmcq (talk) 08:59, 24 March 2011 (UTC)
They are there already! - I should just have used capitals as in lang-en-GB and lang-en-US Dmcq (talk) 09:01, 24 March 2011 (UTC)
I don't know, Dmcq. It looks awkward on the page, and I'm a little concerned about setting a new precedent here. How many parallel instances are there across Wikipedia? It boggles the mind.

Spelling variants are a pretty common fact of life, and it occurs to me that any "drive-by editor" whose only edit is to change a word from British to American or vice versa either has led a very sheltered life and needs to read more or has an agenda of some sort. At any rate, while I won't object too loudly to your template, I'm guessing the IP editor will revert you. At that point, as much as I hate to say it, there probably should be an RfC. Rivertorch (talk) 16:38, 24 March 2011 (UTC)

The spelling of 'centre' is totally irrelevant to the article about 'circle', and including variant spellings of it is stupid. The people who want to include them must know how stupid they are being because they haven't even remotely attempted to justify themselves, except for saying "it's just three words", which is utterly lame.

Now, if anyone puts back those "just three words", they should go through the article and add an inane template to every word which has different spellings in different variants of English, and then perhaps they'll see how absurd it is. —Preceding unsigned comment added by (talk) 22:01, 28 March 2011 (UTC)

Bingo! (Am I prescient or what?) As stated above, I tend to agree with the general thrust of this argument, although hardly with such vehemence (and certainly not with the tone). RfC time? I can write it up later today if no one else wants to, but we're entering slo-mo edit war territory. Rivertorch (talk) 22:41, 28 March 2011 (UTC)
The alternatives templates are normally only used for the article topic rather than words within an article so has a valid point even if exaggerated to a silly degree. I think center/centre is a special case because of the amount of trouble it causes that a little effort in avoiding drive by reverts is worthwhile. An RFC does sound like the best way of getting a consensus one way or the other. The only real alternative would be to stop ip edits which I really don't think would be right as these ip editors are not being vandals just misguided. Also with an RfC some editor who comes along might have a better idea for dealing with the problem. Dmcq (talk) 10:10, 29 March 2011 (UTC)
Has the trick of putting in a html comment directing people to ENGVAR been done? I'll try that for the moment. Dmcq (talk) 10:21, 29 March 2011 (UTC)
The problem here may go beyond the trouble caused by drive by edits. In some cases there will be a problem with comprehension. Since this is a very basic article whose audience will include young children, some of whom, though knowing the word "center", may not understand what a "centre" is. Paul August 11:52, 29 March 2011 (UTC)
Well, this isn't the Simple Wikipedia. I'd venture a guess that most young children capable of understanding the content of this article will be well aware of regional spelling variations, while their less precocious peers will be quite capable of following the blue link for any word they don't comprehend. I like Dmcq's hidden text, though. Can everyone tentatively agree to that as a compromise? I'm juggling things right now but am still willing to write up the RfC if we don't have consensus. Rivertorch (talk) 18:35, 29 March 2011 (UTC)

I agree that the hidden text is the way to go. Duoduoduo (talk) 18:39, 29 March 2011 (UTC)

Hidden text is the ideal solution, that already works very well in many articles. I do not agree that articles should be written with young children particularly in mind. The Simple English wikipedia is surely the place that should cater for that audience. And how would one ever hope to non-arbitrarily decide which articles are basic enough, and which words confusing enough, to need variants given? —Preceding unsigned comment added by (talk) 23:41, 29 March 2011 (UTC)
Assuming you have a dynamic IP and are the editor who commented above, we seem to be approaching complete consensus. Any thoughts, Paul August? Can we mark this as resolved? Rivertorch (talk) 03:32, 30 March 2011 (UTC)

Parametric form using trigonometric functions[edit]

The equation can be written in parametric form using the trigonometric functions sine and cosine in a polar coordinate system as...

I am confused by the "in a polar coordinate system" part. If this is in fact in polar coordinates should it not be under the polar coordinate subheading? Is this parametrization really in polar coordinates or is it in Cartesian?

where t is a parametric variable, interpreted geometrically as the angle that the ray from the origin to (x, y) makes with the x-axis.

It seems to me that the angle t is the angle by the lines formed between points a,b and x,y and the horizontal that passes through point a,b. Am I correct? Maybe it is just necessary to specify "from the origin of the circle to (x,y)..." If I am correct can someone please correct the article? Alternatively, give me the go ahead and Ill try to do it. I am new to wikipedia editing and dont want to break anything. LE (talk) 22:38, 29 December 2010 (UTC)

I've gone and removed that confused bit. Dmcq (talk) 10:12, 31 March 2011 (UTC)

See also review[edit]

I modified "See also" in a gentle way, yet removed a significant percentage of the links. I hope to rationalize this for the 137 watchers.

The article is about the shape and mathematical concept of circle, so I linked ring to the math and physics section of its disambiguation page Cycle (disambiguation) --> Cycle (disambiguation), and ring to the geometric ring.

This article is not so much about poetic metaphor or thesaurus-like things, so I took out Hoop and Equal. As a consolation, I left loop going to its disambiguation page, and that one does link to hoop, and the like. — CpiralCpiral 01:22, 27 March 2011 (UTC)


You are defining a circumference, not a circle. The circle includes all points inside. Wikipedia article about circumference is inaccurated as well. Good luck.-- (talk) 15:33, 8 July 2012 (UTC)

Disk (mathematics)
In geometry, a disk (also spelled disc) is the region in a plane bounded by a circle.
- Ac44ck (talk) 16:41, 8 July 2012 (UTC)

Merger Proposal[edit]

I propose to merge the article Henagon to this article, Circle. Why? Because I believe its content can be already described in "Circle". Hill Crest's WikiLaser! (BOOM!) 23:12, 22 September 2012 (UTC)

  • Oppose. Henagon is an esoteric topic. I don't believe most readers would be helped by this merger. From the henagon article:
a henagon is usually considered to be an impossible object
I see no reason to describe an "impossible object" in the article about circles. - Ac44ck (talk) 01:04, 24 September 2012 (UTC)
  • Thank you. I realized that this proposal is ridiculous as I don't know what is a henagon. Please close. Hill Crest's WikiLaser! (BOOM!) 20:59, 26 September 2012 (UTC)
I removed the banner. (talk) 03:51, 6 November 2012 (UTC)

An important basic idea...[edit]

The circle of one unit radius of 1 inch (= 2 inches diameter) will have a dimension of its circumference @ 6.28 inches--proof of that will be found by using dental floss on top of the circle line, stretch out the dental floss and measure to see that the line is in fact 6.28 inches long. That 6.28 inches is represented by 2π = 2 (180 degrees) 2 (3.14) = 6.28 inches. Π then will represent 180 degrees or 1/2 (6.28 inches) = 3.14 inches. Π / 2 (or 90 degrees will represent 1.57 inches. (No doubt, a 5th grade math project.)

Maybe this is so self-evident that it needs no explanation, but I suspect lots of trig students are unaware that π or 2π represents real numbers on the x-axis, with the y axis representing 1 and minus 1 for the unit circle. In order to graph a trig sine or cosine function on real number line, one simply multiplies or divides π = 3.14 by the appropriate integer indicated on the unit circle diagram. After watching so many Youtube videos on solving trig functions, none discuss this real aspect of the circle being stretched out on a real number line along the x-axis; it sounds like the trig function is placed on the x-axis by guess or by golly.StevenTorrey (talk) 15:18, 2 October 2012 (UTC)

1234412188.25.110.232 (talk) 09:26, 30 October 2012 (UTC)

Not Hitting line[edit]

In german variant of article is a special definition for a line, that does not cut the circle in any point. It is called "Passante". This is missing in the article and the images. Circle with Passante — Preceding unsigned comment added by (talkcontribs) 09:59, 20 February 2013

Perhaps English-speakers don't care enough to give such a line a special name. —Tamfang (talk) 04:10, 6 July 2013 (UTC)
While I agree that the term is not taught or poorly taught in lower math classes, doing a Google search for "passant line math" or "passant line geometry" results in items like "‎" which has 4 cases of "passant line". I can also see how this line is related to a "skew line" in that it also does not touch the other line, but I also see that the passant line is in the same plane as the circle. John W. Nicholson (talk) 02:26, 10 September 2013 (UTC) "Let Q be any conic in the plane, so that Q has p + 1 tangent lines, (p+1 2) secant lines, and (p 2) passant lines (i.e. lines not meeting Q). That is at least two resent professors which use the term "passant lines" to mean in effect "a coplanar straight line that does not touch the circle." Feel free to reword the definition better, but the word stands. John W. Nicholson (talk) 00:21, 11 September 2013 (UTC)

Can you find a secondary source for the term? If so then cite it. Moorhouse is clearly a primary source. I searched Google for passant in textbooks with Geometry in the title and didn't see anything, the only occurrences were in French (passant=passing) or in the phrase "en passant". In general I'm against cluttering up the article with definitions for jargon that even mathematicians would usually not be familiar with, especially for the level of reader this article is should be written for. Maybe it's a common term in German, or maybe the term should be taken out of that version of the article as well, so I don't take that as a valid argument for including it here. --RDBury (talk) 22:31, 11 September 2013 (UTC)


  1. ^ Ken Williams (1995-01-02). "Why is a Circle 360 Degrees?". Retrieved 2006-06-27.  Check date values in: |date= (help)
  2. ^ Petr Beckmann (1989). A History of Pi. Barnes & Noble Books. ISBN 0880294183. 

Circle with segments[edit]


be used? It would allow the image to be used in every version of Wikipedia world wide, and not just English. It can also hold the English spelling in the caption by both letter-coding and colour-coding (color-coding if you like American English).

John W. Nicholson (talk) 04:42, 5 September 2013 (UTC)

Non-mathematical (but correct) definition of circle[edit]

Anita5192, the shape circle has been understood in the same sense as now for thousands (or rather, millions) of years before Euclid. Even today, all kids know very well what a circle is without knowing the "Mathematical" definition. The word "circle" is used to refer to the same shape by people who don't know mathematics. Is it, then, not necessary to give, along with the mathematical definition which requires people to be aware of the concepts of metric spaces and set theory, a definition which can be understood by people who don't know these terms of mathematics? So I had written the following definition which we all know from childhood.

A circle is a flat shape, all points in which are indistinguishable from each other.

Gameplayer10 (talk) 01:03, 15 March 2016 (UTC)

This is a mathematics article. The definition of circle here should therefore be a mathematical definition, of which there are several. There are common non-mathematical definitions of circle, but they do not belong here. The definition you present is neither a strictly correct mathematical definition, nor does it correspond to any figurative definition that I know of. Hence, it does not belong in this article either. — Anita5192 (talk) 01:55, 15 March 2016 (UTC)
Anita5192, which page on Wikipedia gives information about a circle to non-mathematicians? Further, can you, please, enlighten me on common non-mathematical definitions of circle that you know of?
Also, I don't think that the definition I have given, which people know form childhood, does not define the "mathematical" circle. In fact, a circle (a point in the trivial case) is the only shape (in common language, shapes are bounded and connected) that satisfies the given definition.
Shapes in metric spaces can be defined as equivalence classes of subsets when two subsets are said to be related if one can be obtained by a combination of translations, rotations and uniform scalings of the other. See Equivalence of shapes
Also, we know that two points p1 and p2 in a subset of a metric space belonging to the equivalence class of a shape are indistinguishable if there exists a map from the metric space to itself that preserves mutual distance between all points, and which, applied to the subset, gives the same subset and takes p1 to p2. The definition of circle says that all points in a circle are mutually indistinguishable.
Gameplayer10 (talk) 02:59, 15 March 2016 (UTC)
This definition reminds me of a time, long ago now, when I use to train young math TA's. To provoke a discussion about what not to do in a classroom I would bring up the old saw about how a new TA started off his first recitation in a freshman calculus class by going to the blackboard and writing, "Let M be a differentiable manifold, ...". This always got a laugh. Your definition of a circle is strongly related, it's not wrong, just very inappropriate. Bill Cherowitzo (talk) 04:40, 17 March 2016 (UTC)
Professor Cherowitzo, the words "differential" and "manifold" are not understood by children. Even using the word "smooth" instead of "differential" is useless in a course of Mathematics if you don't know the Mathematics behind it. But the definition I have given for circle can be understood by a kid. Kids can use it to tell a circle from a square (or a polygon, or oval, for that matter). And the definition is perfectly correct mathematically, too. (What kids understand by "smooth" might not be the same as the "smooth" in Mathematics but the concepts of boundedness, shape and distinguishability are the same in mathematics as a kid understands them.) Gameplayer10 (talk) 03:26, 18 March 2016 (UTC)
Although I can see to some extent where you are coming from, I think trying to find a "non-mathematical definition (of a circle)" is like trying to find a "biological classification of unicorns". The best I can come up with, that would be "understood" by a child, would be something like "a circle is the shape of something round and very regular without exceptions". Not really a definition either, of course, but something that might convince a child (or an adult) that it actually does mean something as well as linking the concept of a circle to other concepts (that are just as vaguely defined, but hopefully more familiar).
But I doubt that your "definition", the (by itself) meaningless phrase "A circle is a flat shape, all points in which are indistinguishable from each other" would mean anything at all to a child (I certainly did not have a clue what you meant on first reading, and no: I do not know that definition from childhood). Which is why you had to "explain" it in terms that a child certainly would not understand. And the fact that you feel the need to hyperlink some of the concepts that you use (excluding some that you should have hyperlinked if you had been consistent) shows how aware you are that your definitions are incomplete and not a priori understandable by an adult, let alone a child.
The point I am trying to make is that perhaps a "non-mathematical definition", especially of abstract mathematical concepts, useful as it might be to a wikipedia article, should not even try to go beyond listing a bunch of (hopefully) distinguishing attributes and properties, as well as relationships with other concepts. And without the illusion of actually being a definition rather than a (casual) description. Pictures of a bunch of circles might be even better (or at least complementary) in this case. Attempting to be more formal, without actually trying to be really formal, just becomes ugly really quickly, as if you were trying to open up a can of worms. AlexFekken (talk) 08:58, 30 December 2016 (UTC)

Assessment comment[edit]

The comment(s) below were originally left at Talk:Circle/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

Needs references and a longer lead. Also, the circle seems pretty important in science, society, culture, etc. and there should be more on this (and some history too). Geometry guy 20:41, 9 June 2007 (UTC)

Last edited at 20:41, 9 June 2007 (UTC). Substituted at 11:47, 29 April 2016 (UTC)

Semi-protected edit request: 21 November 2016[edit]

The various secant laws are described using points that do not correspond to the figure. It would be less confusing if the figure's points were used consistently. I'd replace the whole subsection with the following.

Edit comment (FWIW): Use labels in figure where possible. Clarify description of tangent chord angle (since previous theorem involves a tangent and a chord in a different relationship), and secant-secant thm.

I also switched to a script letter ℓ, and swapped entries 2 and 3, but the comment is only so big. (talk) 14:23, 21 November 2016 (UTC)


Secant-secant theorem
  • The chord theorem states that if two chords, CD and EB, intersect at A, then AC × AD = AB × AE.
  • If two secants, AE and AD, also cut the circle at B and C respectively, then AC × AD = AB × AE. (Corollary of the chord theorem.)
  • A tangent can be considered a limiting case of a secant whose ends are coincident. If a tangent from an external point A meets the circle at F and a secant from the external point A meets the circle at C and D respectively, then AF2 = AC × AD. (Tangent-secant theorem.)
  • The angle between a chord and the tangent at one of its endpoints is equal to one half the angle subtended at the centre of the circle, on the opposite side of the chord (Tangent Chord Angle).
  • If the angle subtended by the chord at the centre is 90 degrees then = r √2, where is the length of the chord and r is the radius of the circle.
  • If two secants are inscribed in the circle as shown at right, then the measurement of angle A is equal to one half the difference of the measurements of the enclosed arcs (DE and BC). I.e. 2∠CAB = ∠DOE − ∠BOC, where O is the centre of the circle. This is the secant-secant theorem.
Yes check.svg Done  Paine  u/c 22:56, 21 November 2016 (UTC)

Second request[edit]

File:Circunferencia 10.svg
§ Construct a circle through 3 noncollinear points could use an illustration, like the one to the right of this paragraph. Please add it. (This is the last of a step-by-step series of drawings numbered 01 through 10 available at c:Category:Ruler-and-compass_construction.) (talk) 03:02, 22 November 2016 (UTC)

Yes check.svg Done  Paine  u/c 16:07, 23 November 2016 (UTC)
@Paine Ellsworth: Thanks for both. How's your patience? There are quite a few niggling issues with the article, and should I keep doing this or petition for a protection downgrade to WP:Pending changes? The ones in my pending queue right now are changing π to the italic π (or even π) when referring to the mathematical constant in text; in the "Polar coordinates" section changing the second half of "For a circle centred at the origin, i.e. r0 = 0, this reduces to simply r = a. When r0 = a, or when the origin lies on the circle, the equation becomes" to "...when the origin lies on the circle, i.e. r0 = a, the equation becomes" to clarify that the two definitions are equivalent; and I'm considering adding "circle" to the "Terminology" section. Yes, it repeats what the lead just said, but it really belongs there. Oh, and the definition of "disc" needs to clarify that it means the interior.
Materialscientist is quite right that there were a number of annoying instances of vandalism over several months, but setting an alarm for October 2019 when the protection expires is not a tremendously realistic option. (talk) 14:25, 24 November 2016 (UTC)