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.

Projective plane

In mathematics, a projective plane is a geometric structure that extends the concept of a plane. In the ordinary Euclidean plane, two lines typically intersect in a single point, but there are some pairs of lines (namely, parallel lines) that do not intersect. A projective plane can be thought of as an ordinary plane equipped with additional "points at infinity" where parallel lines intersect. Thus any two lines in a projective plane intersect in one and only one point.

Renaissance artists, in developing the techniques of drawing in perspective, laid the groundwork for this mathematical topic. The archetypical example is the real projective plane, also known as the extended Euclidean plane. This example, in slightly different guises, is important in algebraic geometry, topology and projective geometry where it may be denoted variously by PG(2, R), RP², or P₂(R) among other notations. There are many other projective planes, both infinite, such as the complex projective plane, and finite, such as the Fano plane.

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.

Mini-Con

Mini-Cons are a human-sized race and faction of power-enhancing transforming robots first introduced in various Transformers series. Pioneered for the Transformers: Armada toy line, Mini-Cons have since been sold under the Transformers: Energon, Transformers: Universe, Transformers: Cybertron and Transformers: Classic lines. In some cases, the word may also be spelled "Minicon" and they are known as "Microns" in Japan.

Unicron Trilogy

Mini-Cons are a race of small, roughly human-sized Transformers capable of powerlinxing with a larger Transformer to impart extra abilities or greatly increase their strength. Their origins vary depending on the continuity in which they appear. Sometimes, they are creations of Unicron and other times they are creations of the Last Autobot or the descendants of Micronus Prime. However, there are times where their origins are not explained and are portrayed in different characterizations.

Throughout the different incarnations of the Transformers franchise, the Mini-Cons origins, characteristics and personalities vary, depending on continuity. For example, in the original Armada cartoon, Unicron created the Mini-Cons to be mindless tools, sent to Cybertron as an agitating element to the Transformers' civil war. The power-enhancing "smart tools" would be unleashed upon the populace, who would snap them up and bond with them, and the war would only get more destructive, as Unicron drank in the negative psychic energies from the death and destruction. As the Mini-Cons had been designed to form mental bonds with other life forms, when the human Rad touched the Mini-Con who he knew from the future as High Wire, High Wire apparently formed his bond then, with Rad and through the Mini-Cons' shared "soul dimension", the Linkage, sentience and free will spread throughout the Mini-Cons, forming "souls", and crippling Unicron's plans drastically. Most Mini-Cons had limited verbal capabilities, causing much controversy among fandom.

Plane

Plane or planes may refer to:

Plane or aircraft

Science and technology

Other uses

Plane (tool)

A hand plane is a tool for shaping wood. When powered by electricity, the tool may be called a planer. Planes are used to flatten, reduce the thickness of, and impart a smooth surface to a rough piece of lumber or timber. Planing is used to produce horizontal, vertical, or inclined flat surfaces on workpieces usually too large for shaping. Special types of planes are designed to cut joints or decorative mouldings.

Hand planes are generally the combination of a cutting edge, such as a sharpened metal plate, attached to a firm body, that when moved over a wood surface, take up relatively uniform shavings, by nature of the body riding on the 'high spots' in the wood, and also by providing a relatively constant angle to the cutting edge, render the planed surface very smooth. A cutter which extends below the bottom surface, or sole, of the plane slices off shavings of wood. A large, flat sole on a plane guides the cutter to remove only the highest parts of an imperfect surface, until, after several passes, the surface is flat and smooth. When used for flattening, bench planes with longer soles are preferred for boards with longer longitudinal dimensions. A longer sole registers against a greater portion of the board's face or edge surface which leads to a more consistently flat surface or straighter edge. Conversely, using a smaller plane allows for more localized low or high spots to remain.

Pláně (Plzeň-North District)

Pláně is a village and municipality (obec) in Plzeň-North District in the Plzeň Region of the Czech Republic.

The municipality covers an area of 13.91 square kilometres (5.37 sq mi), and has a population of 259 (as at 3 July 2006).

Pláně lies approximately 23 kilometres (14 mi) north of Plzeň and 82 km (51 mi) west of Prague.

References