Are there any differences between "oval" and "ellipse"?
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I believe they can be used interchangeably in common English, but have specific (and different) meanings when used in mathematics.
The online Cambridge dictionary contains the following definitions:
shaped like a circle that is flattened either at one place or at two opposite places, so that it is like either an egg or an ellipse
an oval; a flattened circle
However, in geometry there is a difference. According to the Wikipedia page on ovals:
In geometry, an oval or ovoid is any curve resembling an egg or an ellipse, but not an ellipse.
In addition, from the Math Forum
once the size of an ellipse has been fixed then its exact shape is mathematically determined. In other words, the line forming the perimeter can be drawn in only ONE way. This is distinct from an oval where the perimeter has only to be a concave curve, and there are many possibilities. Simply, an ellipse IS an oval, but an oval may or may not be an ellipse.
- Doctor Sarah, The Math Forum
This is adapted from my answer to another question.
In my experience, "ellipse" usually has a precise, geometric meaning, while "oval" is a more vague and general term. Most dictionaries I've checked agree with this, but a few dictionaries say that the two words can be used interchangeably. The New Oxford American Dictionary 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".
Various other online sources agree:
Mathworld agrees: oval
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".
From what I can tell (looking at my kids' Montessori curriculum), an ellipse is a kind of oval. An ellipse does not have a "pointier" end (is not like an egg), whereas an oval can be pointier at one end, or not.
To me the defining difference is this:
An oval can be made from two radiuses. That is, you can make an oval using your compass (or parts of a circle, if you like). You can never do this with an ellipse. That is, no part of an ellipse will ever make a circle.