Oval in Geometry
The term oval when used to describe curves in geometry is not well-defined, except in the context of projective geometry. Many distinct curves are commonly called ovals or are said to have an "oval shape". Generally, to be called an oval, a plane curve should resemble the outline of an egg or an ellipse. In particular, the common traits that these curves have are:
- they are differentiable (smooth-looking), simple (not self-intersecting), convex, closed, plane curves;
- their shape does not depart much from that of an ellipse, and
- there is at least one axis of symmetry.
Examples of ovals described elsewhere include:
- Cassini ovals
- elliptic curves
- superellipse
- Cartesian oval
An ovoid is the 3-dimensional surface generated by rotating an oval curve about one of its axes of symmetry. The word ovoidal refers to the characteristic of being an ovoid and is often used as a synonym for "egg shaped".
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