Oval (geometry)

Encyclopedia : O : OV : OVA : Oval (geometry)

This oval, with only one axis of symmetry, resembles a chicken egg.

A completely rounded rectangle, consisting of two congruent semicircles and two equal and parallel lines, is often called an oval.

In geometry, an oval or ovoid (from Latin ovum, 'egg') is any curve resembling an egg or an ellipse. Unlike other curves, the term 'oval' is not well-defined and many distinct curves are commonly called ovals. These curves have in common that:

they are differentiable (smooth-looking), simple (not self-intersecting), convex, closed, plane curves;
their shape does not depart too much from that of a circle or an ellipse, and
there is at least one axis of symmetry.

Two examples of ovals are shown below. In (a), a semicircle is joined to half an ellipse while in (b), two semicircles are connected with straight line segments. Other ad hoc constructions are often encountered as well.

This second oval shape is called a "rounded rectangle", not really an oval, but racing tracks and sports fields of all sorts are called ovals while being rounded rectangles...

Other examples of ovals described elsewhere include:

Egg shape

The shape of an egg is approximately an oblate ellipsoid, but, while keeping cylindrical symmetry, as illustrated above, there is not quite symmetry in a plane perpendicular to the long axis. The term egg-shaped is typically used taking this asymmetry into account, but it may also simply mean oblate ellipsoid. It can also be used for a 2D shape.

Projective planes

In the theory of projective planes, oval is used to mean a set of q + 1 non-collinear points in PG(2,q), the projective plane over the finite field with q elements. See oval (projective plane).

From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.