OVAL

(Redirected from Oval (geometry))



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.
The word ovoidal refers to the characteristic of being an ovoid.
Other examples of ovals described elsewhere include:

★ Cassini ovals

★ elliptic curves

★ superellipse
A track is known as a stadium, and is actually not a rounded rectangle.

Contents

Egg shape

Projective planes

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).