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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. Dec 2 '10 at 22:00
  • 1
    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. Jul 29 '11 at 19:40
  • An egg is 3-D; its shape is (when idealised, ie no irregularities – never true in real life) 'ovoid', not 'oval'. // An 'oval' is ill-defined: << The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition .... >> [Wikipedia] Feb 19 at 15:46
1

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.)

Edit: I'm not sure what I exactly I was imagining in terms of "oval" at the time, but I was probably wrong to call it a type of ellipse. In fact, it does not have a precise mathematical definition, so saying one is a type of the other doesn't make much sense either way. All it means is, loosely, "egg-like" in shape. A circle, however, is a specific type of ellipse, as mentioned originally.

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    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
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    @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? Dec 4 '10 at 1:23
  • 3
    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
  • 2
    Holy ellipsoidal ovals Batman! I think this pretty much sums up the argument in Noldorin's favor: en.wikipedia.org/wiki/Ellipsoid#Egg_shape Dec 10 '10 at 3:32
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    And yes, "oval" is more general than "ellipse". For instance, we have the classical curves called the Cartesian ovals and Cassinian ovals... which are not ellipses at all.
    – user730
    Dec 12 '10 at 5:38
9

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
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    @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? 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
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    @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. Dec 4 '10 at 21:53
4

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.

6
  • 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
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    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
1

Starting with terms that others have defined the highest class is the superellipse which includes astroids ellipses and the squircle (a shape 'halfway' between a square and a circle) under ellipses you have circles (the case where major axises, or axi are equal.) otherwise you have the word I came up with cyclagon which describes any closed shape (something that doesn't point to infinity) with curved edges like a flower petal or a digon (I pronounce this like di∙jon.) the question does get more interesting in higher dimensions where you have ellipsoids, spheroids and cyclatopes in 3d and glomes in 4d. I used wikipedia for reference and spelling and glome comes from http://hi.gher.space/wiki where you can also find a crind.

0

Round shape.

A shape that is curved and without sharp angles.

0

Convex closed curves?

0

Although oval is often used interchangeably with ellipse in common parlance and even by some matmaticians, I am glad to see that Wolfram now defines oval as that shape constructed from a large circle, a small circle and the pair of tangential arcs that connect them. This retains the etymology of the term oval which derives from the Latin word for egg. Interestingly enough not all eggs are oval; but so many are we ought to have a distinct word for it. Similar to this constructed shape, but not asymmetrically egg-ish, are the constructions draftsmen & architects use to approximate ellipses. Wikipedia now lists these also as a ovals, maintaining the distinction between them and true ellipses; I.e. rounded closed curves. I see this as unfortunate since again it creates ambiguity and we loose the distinct word for the true egg shape. Some mathematicians use the term quadrarc for these constructed rounded shapes (see N. T. Gridgeman, ìQuadrarcs, St. Peter’s, and the Colosseum, The Mathematics Teacher 63 (1970) 209-215). I should point out that although quadrarcs can approximate ellipses, they need not do so or at least no do so very closely, and a quick study of them shows that they can have an identity of their own. This raises an interesting comparison to the whole class of quadrarcs, superelipses, rounded rectangles, and stadia, all of which can be tweaked to appear more like a square/rectangle and less like a rounded shape or oval.

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