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I'm not sure if this belongs here, but I'm wondering if there is a word for a class of circular shapes?

Thinking about this hierarchically:

* Shape
  * Polygon
    * Square
    * Rectangle
  * ???????
    * Circle
    * Oval

EDIT:

Ok, so mathematically I'm not sure there is a correct answer to my question that's any better than the one Mehper so eloquently explained (round shape). Let's break down what we have so far:

In the blue corner: Noldorin

* Ellipsoid
  * Ellipse
    * Circle
  * Oval

In the red corner: pretty much everyone else

* Oval
  * Ellipse

Now, my question for the red team is: where does a circle fit in? From what I understand a circle can't be an oval, but a circle is an ellipse. Those two facts make the following untrue:

* Oval
  * Ellipse
    * Circle

I'll stick with ellipsoid for now until I hear some better explanation.

Also note this link: http://en.wikipedia.org/wiki/Ellipsoid#Egg_shape

An egg shape, which is an oval (not an ellipse) is comprised of two ellipses. This seems to make an oval a sub-class of an ellipse.

Kindly correct me if I've made any mistakes.

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1  
I love learning new things when my questions get re-tagged. Hypernyms...I love it. –  Bryan Downing Dec 2 '10 at 22:00
    
I suspect you are heading for the problem that you can't classify everything in a tree like taxonomy. e.g. a square is a special case of a rectangle, but it is also a special case of a rhombus –  jk. Jan 25 '11 at 13:09
    
Ellipse and oval are different, but an oval can at times be an ellipse. So you should have {Shape [polygon (square, rectangle)], [ellipse (circle)], [oval]} –  Tester101 Apr 12 '11 at 17:06
    
Oval is egg-shaped, by definition. Ellipsoidal eggs would roll out of the nest and be selected against. Ovals have only one axis of symmetry. –  Malvolio Jul 29 '11 at 19:40

5 Answers 5

up vote 2 down vote accepted

Circles and ovals are both types of ellipses. An 'oval' is really the informal term for an 'ellipse', whereas a 'circle' is an ellipse where the semi-major and semi-minor axes are equal.

If you're talking about higher-dimensions, the word you are looking for is probably ellipsoid. (A sphere is an example.)

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1  
Excellent. It all makes sense now - thanks a lot! –  Bryan Downing Dec 2 '10 at 22:51
5  
I am afraid this answer might be actually wrong, and the comment "in mathematics they're all ellipses" even more so. See Kevin Walker's answer or check Wikipedia. "Any point of an oval belongs to an arc with a constant radius (shorter or longer), whereas in an ellipse the radius is continuously changing." And: "In geometry, an oval or ovoid is any curve resembling an egg or an ellipse, but not an ellipse. Unlike other curves, the term 'oval' is not well-defined and many distinct curves are commonly called ovals." –  RegDwigнt Dec 3 '10 at 10:06
2  
@Noldorin: Every dictionary that I've checked says that you are wrong about an oval being a type of ellipse. Can you cite any dictionaries which agree with you? –  Kevin Walker Dec 4 '10 at 1:23
2  
I have to chime in to say I agree, it is incorrect to say an oval is a type of ellipse. (A circle is a type of ellipse, yes, but that's neither here nor there.) –  Marthaª Dec 7 '10 at 15:14
1  
Holy ellipsoidal ovals Batman! I think this pretty much sums up the argument in Noldorin's favor: en.wikipedia.org/wiki/Ellipsoid#Egg_shape –  Bryan Downing Dec 10 '10 at 3:32

This is mainly a response to Noldorin's answer; I don't have enough reputation points to comment directly.

An oval is not a type of ellipse. It's the other way around: an ellipse is a type of oval. Check a dictionary. Mine defines "oval" as "having a rounded and slightly elongated outline or shape, like that of an egg". It defines "ellipse" as "a regular oval shape, traced by a point moving in a plane so that the sum of its distances from two other points (the foci) is constant".


EDIT:

There has been some dispute in the comments about "oval" versus "ellipse", so I thought I would add some more citations. I claim that defining "oval" to be more general than "ellipse" is common and standard, while defining "ellipse" to be more general than "oval" is rare and non-standard. The definitions I quote above comes from the New Oxford American Dictionary. In addition to that...

dictionary.reference.com agrees: ellipse versus oval

Mathworld agrees: oval

thefreedictionary.com agrees: oval versus ellipse

mathforum.org agrees: "Simply, an ellipse IS an oval, but an oval may or may not be an ellipse."

answers.com agrees: "An ellipse always has two axes of reflection; an oval has one or more."

I've found a relatively few sources which define "ellipse" and "oval" to mean the same thing. I've found no sources at all which say that "ellipse" is more general than "oval".

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@Kevin: Oval is not a mathematical term. It almost always refers to an ellipse. –  Noldorin Dec 3 '10 at 16:01
    
@Rhodri: I'm afraid you're incorrect. That is not what it refers to, go look up the definition please. –  Noldorin Dec 3 '10 at 18:36
3  
@Noldorin: Every dictionary that I've checked says that you are wrong about an oval being a type of ellipse. Can you cite any dictionaries which agree with you? –  Kevin Walker Dec 4 '10 at 1:24
    
@Kevin: Apart from my everyday experience, which counts for a lot... en.wiktionary.org/wiki/oval thefreedictionary.com/oval - I think that proves my point. :) –  Noldorin Dec 4 '10 at 15:43
5  
@Noldorin: Did you mean to say disprove your point? The sources that you yourself cite say that "oval" is more general than "ellipse", not the other way around. –  Kevin Walker Dec 4 '10 at 21:53

Mathematically, you call them "closed curves" although that's not very satisfying. "Ellipse" also covers the two-dimensional shapes you're talking about. (Circle is a subset of ellipse in the same way that square is a subset of rectangle.)

If you just want a general-use word that describes circles and things that aren't perfect circles then you could use "hoop" or "disk" or "ring" or something else depending on the specifics.

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a straight line is also a curve so a polygon can be called as a closed curve as well. :-) –  xport Dec 4 '10 at 9:40
    
@xport: a straight line is a curve only as long as it doesn't have any corners. Kind of hard to draw a polygon without corners, no? –  Marthaª Dec 7 '10 at 15:08
    
@Martha, how can a staight line have a corner? –  xport Dec 7 '10 at 15:11
    
@xport, when you join it to another to start making a polygon, of course. What I'm trying to say is that your "a straight line is also a curve, so a polygon can be called a closed curve as well" statement is wrong. –  Marthaª Dec 7 '10 at 15:18
1  
I'd say the deltoid and the astroid are closed curves... and they do have corners (technically, "cusps"). But certainly they aren't ovals (in the mathematical sense of "oval")! –  user730 Dec 12 '10 at 10:08

Round shape.

A shape that is curved and without sharp angles.

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Convex closed curves?

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