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For other uses, see Oval (disambiguation).

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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**.

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),
^{[1]}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:

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".

In the theory of projective planes, * oval* is used to mean a set of

An **ovoid** in the finite projective geometry PG(3,q), is a set of *q*^{2} + 1 points such that no three points are collinear. At each point of an ovoid all the tangent lines to the ovoid lie in a single plane.

The shape of an egg is approximately half of each of a prolate (long) and a roughly spherical (potentially even slightly oblate/short) ellipsoid joined at the equator, sharing 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, revolved around its major axis, produces the 3-dimensional surface. Refer to the following equation for an approximation of a 3D egg where the letter "a" represents any positive constant:

In technical drawing, an **oval** is a figure constructed from two pairs of arcs, with two different radii (see image on the right). The arcs are joined at a point, in which lines tangential to both joining arcs lie on the same line, thus making the joint smooth. Any point of an oval belongs to an arc with a constant radius (shorter or longer), whereas in an ellipse the radius is continuously changing.

In common speech "oval" means a shape rather like an egg or an ellipse, which may be two-dimensional or three-dimensional. It also often refers to a figure that resembles two semicircles joined by a rectangle, like a cricket infield or oval racing track. This is more correctly, although archaically, described as oblong.^{[2]} Sometimes it can even refer to any rectangle with rounded corners.

The shape lends its name to many well-known places (see Oval (disambiguation)).

- Vesica piscis – a pointed oval
- Ellipse
- Stadium (geometry)

**^**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.**^**"Oblong".*Oxford English Dictionary*. 1933. "**A***adj.***1.**Elongated in one direction (usually as a deviation from an exact square or circular form): having the chief axis considerably longer than the transverse diameter"