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In technical drawing an oval (from Latin ovum, 'egg') is a figure constructed from two pairs of arcs, with two different radii (see image on the right). The arcs are join at a point, in which lines tangential to both joining arcs lay 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 ellipse the radius is continously changing.
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Oval in geometry
In geometry, an oval or ovoid 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 much from that of an ellipse, and
- there is at least one axis of symmetry.
The word ovoidal refers to the characteristic of being an ovoid.
Other examples of ovals described elsewhere include:
Egg shape
The shape of an egg is approximately that of half each a prolate (long) and roughly spherical (potentially even minorly 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.
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).
In common English
In common speech 'oval' means a shape rather like an egg or an ellipse, and it may be two-dimensional or three-dimensional.