# 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 three-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, these are common traits of ovals:

- 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.

Here are examples of ovals described elsewhere:

An **ovoid** is the 2-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".

## Projective geometry

In the theory of projective planes, an **oval** is a set of *n* + 1 points in a projective plane of order *n*, with no three on a common line (no three points are collinear).

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.

## Egg shape

The shape of an egg is approximate by "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 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, if revolved around its major axis, produces the 3-dimensional surface.

## Technical drawing

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), but in an ellipse, the radius is continuously changing.

## In common speech

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 athletics track. However, this is more correctly called a stadium or archaically, an oblong.^{[2]} Sometimes, it can even refer to any rectangle with rounded corners.

The shape lends its name to many well-known places.

## See also

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

## Notes

- ↑ If the property makes sense: on a differentiable manifold. In more general settings one might require only 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