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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. In common English, the term is used in a broader sense; any shape which reminds one of an egg. The 3-dimensional version of an oval is called an ovoid.
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Oval in geometry [link]
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, the common traits that these curves have are:
- 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.
Examples of ovals described elsewhere include:
An ovoid is the 3-dimensional surface generated by rotating an oval curve about one of its axes of symmetry. The word ovoidal refers to the characteristic of being an ovoid and is often used as a synonym for "egg shaped".
Projective geometry [link]
In the theory of projective planes, oval is used to mean 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). See oval (projective plane).
An ovoid in the finite projective geometry PG(3,q), is a set of q2 + 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 [link]
The shape of an egg is approximately half of each prolate (long) and is a roughly spherical (potentially even slightly 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. Refer to the following equation for an approximation of a 3D egg where the letter "a" represents any positive constant:
- Failed to parse (Missing texvc executable; please see math/README to configure.): x^2 + y^2 + z^2(1.5cos((z+a/2)/a))^2 = a\!
Technical Drawing [link]
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), whereas in an ellipse the radius is continuously changing.
In common English [link]
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 oval racing track. This is more correctly, although archaically, described as oblong.[2] Sometimes it can even refer to any rectangle with rounded corners.
See also [link]
- Squoval
- Vesica piscis – a pointed oval
Notes [link]
- ^ When this property makes sense, i.e. when on a differentiable manifold. In more general settings one might only require that there exist 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"
https://wn.com/Oval
Oval, London
Coordinates: 51°28′53″N 0°07′11″W / 51.4813°N 0.1197°W
Oval is a geographically small area of Kennington, south London, in the London Borough of Lambeth. It is situated 2.1 miles (3.38 km) to the south-east of Charing Cross. Oval straddles the border of south-west London and south-east London, and is where the postcode SE11 converges with the postcodes SW8 and SW9. Oval is best known for The Oval cricket ground, the home-ground of Surrey County Cricket Club.
Oval is within the borough constituency of Vauxhall. The Member of Parliament for the area is Kate Hoey of the Labour Party.
History
The land here was, from the seventeenth century, used for a market garden. The name "Oval" emerged from a street layout which was originated in 1790 but never completely built. The Montpelier Cricket Club leased ten acres of land from the Duchy of Cornwall in 1844, and Surrey County Cricket Club was formed soon thereafter at a meeting at the Horns Tavern (since demolished) on Kennington Park Road.
Oval (projective plane)
In mathematics, an oval in a projective plane is a set of points, no three collinear, such that there is a unique tangent line at each point (a tangent line is defined as a line meeting the point set at only one point, also known as a 1-secant). If the projective plane is finite of order q, then the tangent condition can be replaced by the condition that the set contains q+1 points. In other words, an oval in a finite projective plane of order q is a (q+1,2)-arc, or a set of q+1 points, no three collinear. Ovals in the Desarguesian projective plane PG(2,q) for q odd are just the nonsingular conics. Ovals in PG(2,q) for q even have not yet been classified. Ovals may exist in non-Desarguesian planes, and even more abstract ovals are defined which cannot be embedded in any projective plane.
Odd q
In a finite projective plane of odd order q, no sets with more points than q + 1, no three of which are collinear, exist, as first pointed out by Bose in a 1947 paper on applications of this sort of mathematics to statistical design of experiments.
