OVAL

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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).