Ellipse

In mathematics, an ellipse is a curve on a plane that surrounds two focal points such that the sum of the distances to the two focal points is constant for every point on the curve. As such, it is a generalization of a circle, which is a special type of an ellipse that has both focal points at the same location. The shape of an ellipse (how 'elongated' it is) is represented by its eccentricity, which for an ellipse can be any number from 0 (the limiting case of a circle) to arbitrarily close to but less than 1.

Ellipses are the closed type of conic section: a plane curve that results from the intersection of a cone by a plane. (See figure to the right.) Ellipses have many similarities with the other two forms of conic sections: the parabolas and the hyperbolas, both of which are open and unbounded. The cross section of a cylinder is an ellipse, unless the section is parallel to the axis of the cylinder.

Analytically, an ellipse can also be defined as the set of points such that the ratio of the distance of each point on the curve from a given point (called a focus or focal point) to the distance from that same point on the curve to a given line (called the directrix) is a constant, called the eccentricity of the ellipse.

Ellipsis (linguistics)

In linguistics, ellipsis (from the Greek: ἔλλειψις, élleipsis, "omission") or elliptical construction refers to the omission from a clause of one or more words that are nevertheless understood in the context of the remaining elements. There are numerous distinct types of ellipsis acknowledged in theoretical syntax. This article provides an overview of them. Theoretical accounts of ellipsis can vary greatly depending in part upon whether a constituency-based or a dependency-based theory of syntactic structure is pursued.

Preliminary comments

Varieties of ellipsis have long formed a central explicandum for linguistic theory, since elliptical phenomena seem to be able to shed light on basic questions of form–meaning correspondence: in particular, the usual mechanisms of grasping a meaning from a form seem to be bypassed or supplanted in the interpretation of elliptical structures, ones in which there is meaning without form. In generative linguistics, the term ellipsis has been applied to a range of phenomena in which a perceived interpretation is fuller than that which would be expected based solely on the presence of linguistic forms.

Ellipse (album)

Ellipse is the third studio album from Grammy Award-winning British singer-songwriter Imogen Heap. After returning from a round the world writing trip, Heap completed the album at her childhood home in Essex, converting her old playroom in the basement into a studio. The album got its name from the distinctive elliptical shape of the house. The album's title was confirmed by Heap via her Twitter page on 25 April 2009, after being leaked onto the internet on 23 April. On 15 June, Heap confirmed that the album would be released on 24 August 2009 in the United Kingdom on Megaphonic Records and 25 August in the United States/Canada on RCA Victor Records. International release date was also 24 August.

Subject matter in the songs includes post break-up malaise ("Wait It Out"), domestic boredom ("Little Bird"), body image issues ("Bad Body Double") and a common Heap theme, unrequited love ("Swoon" and "Half Life").

Background

In July 2009, a promotional copy of the album (designed by Andy Hau) appeared on eBay; Heap in return placed a bid of £10,000,000 to try to reclaim the album, which eBay rejected. As of 8 July, eBay had ended the auction. On 14 July, the first single "First Train Home" was released, and a digital pre-order for the album became available on iTunes in two versions.