Oval

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, which may include either one or two axes of symmetry. 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.

Oval in geometry

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:

Oval, London

Coordinates: 51°28′53″N 0°07′11″W / 51.4813°N 0.1197°W / 51.4813; -0.1197

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.