Talk:Circle

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==Tangent==at 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 15 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)

Contents

[edit] Circle image

Is it just me, or is the splash imaysge 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.

[edit] non-Euclidean circle

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)

[edit] Integration

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

\int_0^{2\pi} \frac{1}{r^2} d\theta.

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

r2 = x2 + (y − c)2

where c is a constant less than r...

I have a feeling that this is hard.

[edit] General derivitive

r2 = x2 + y2 − 2cy + c2
0 = 2x + 2y\frac{dy}{dx} - 2c\frac{dy}{dx}
-2x = \frac{dy}{dx}(2y - 2c)
\frac{-2x}{2y - 2c} = \frac{dy}{dx}
y = \sqrt (r^2 - x^2) + c

giving:

\frac{dy}{dx} = \frac{-2x}{2(\sqrt (r^2 - x^2) + c) - 2c}
\frac{dy}{dx} = \frac{-2x}{2\sqrt (r^2 - x^2) + 2c - 2c}
\frac{dy}{dx} = \frac{-2x}{2 \sqrt (r^2 - x^2)}

and finally:

\frac{dy}{dx} = \frac{-x}{\sqrt (r^2 - x^2)}

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: (x + a)2 + (y + b)2 = r2 is: \frac{dy}{dx} = - \frac{x + a}{\sqrt (r^2 - (x + a)^2)}

[edit] Commons

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)

[edit] equations

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

[edit] "Pole"?

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.

[edit] The origin of 360°

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)

[edit] Correction and comment

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
\frac{6}{2\pi} = \frac{3}{\pi} = 0.954929\ldots \approx \frac{57}{60} + \frac{36}{60^2} = 0.96

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)

[edit] The origin of 360°

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.[3][4] 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:

\pi = \frac{57}{60} + \frac{36}{60^2}

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 137.229.184.166 (talk) 22:14, 26 September 2007 (UTC)

[edit] Your Signature

Please sign your contributions and comments, by using 4 ~ signs. Prof.rick 21:02, 15 August 2006 (UTC)

[edit] Defining a circle

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)

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

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
Example:
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)

[edit] Chinese area expression

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 (talk • contribs) 19:18, 29 February 2008 (UTC)

[edit] Triginometry functions

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)

[edit] Phrasing

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)

[edit] How many sides does a circle have?

Does a circle have infinity sides or no sides?--67.10.200.101 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)

[edit] Help

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.

[edit] Doctormath

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)

[edit] Circles in physics/nature/psychology

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)

[edit] Error in equation at "Sagitta"

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.

Quote: http://members.tripod.com/hew_frank/id34.htm

EXAMPLE 1:-

   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)

[edit] JUST MATH?!

Circles have incredibly varied symbolic meanings across many cultures and time periods. I can't find this information anywhere on wikipedia. What's up with this?

[edit] Cites?

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)

[edit] Wish list

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)

[edit] Center vs. Centre

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)