Is there a word for a class of circular shapes?

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.

Solution 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.

Solution 2:

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".

Solution 3:

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.

Solution 4:

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.