Oval

An oval (from Latin ovum 'egg') is a closed curve in a plane which 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 of an ellipse. In common English, the term is used in a broader sense: any shape which reminds one of an egg. The three-dimensional version of an oval is called an ovoid.

For other uses, see Oval (disambiguation).

they are (smooth-looking),^[1] simple (not self-intersecting), convex, closed, plane curves;

differentiable

their does not depart much from that of an ellipse, and

shape

an oval would generally have an , but this is not required.

axis of symmetry

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, these are common traits of ovals:

Here are examples of ovals described elsewhere:

An ovoid is the surface in 3-dimensional space 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".

In a a set $Ω$ of points is called an oval, if:

projective plane

For finite planes (i.e. the set of points is finite) there is a more convenient characterization:^[2]

An ovoid in a projective space is a set $Ω$ of points such that:

In the finite case only for dimension 3 there exist ovoids. A convenient characterization is:

Egg shape[edit]

The shape of an egg is approximated by the "long" half of a prolate spheroid, joined to a "short" half of a roughly spherical ellipsoid, or even a slightly oblate spheroid. These are joined at the equator and share a principal axis of rotational symmetry, as illustrated above. Although the term egg-shaped usually implies a lack of reflection symmetry across the equatorial plane, it may also refer to true prolate ellipsoids. It can also be used to describe the 2-dimensional figure that, if revolved around its major axis, produces the 3-dimensional surface.

Ellipse

Ellipsoidal dome

Stadium (geometry)

– a pointed oval

Vesica piscis

Symbolism of domes

Dembowski, Peter (1968), , Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Berlin, New York: Springer-Verlag, ISBN 3-540-61786-8, MR 0233275