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Ovoid : ウィキペディア英語版
Oval

An oval (from Latin ''ovum'', "egg") is a closed curve in a plane which "loosely" resembles the outline of an egg. The term is not very specific, but in some areas (projective geometry, technical drawing, etc.) it is given a more precise definition, which may include either one or two axes of symmetry.
In common English, the term is used in a broader sense: any shape which ''reminds'' one of an egg.
The 3-dimensional version of an oval is called an ovoid.
==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),〔When this property makes sense, i.e. when on a differentiable manifold. In more general settings one might only require that there exist a unique tangent line at each point of the curve.〕 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 adjectives ovoidal and ovate mean having the characteristic of being an ovoid, and are often used as synonyms for "egg-shaped".

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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