Surface

In mathematics, specifically, in topology, a surface is a two-dimensional, topological manifold. The most familiar examples are those that arise as the boundaries of solid objects in ordinary three-dimensional Euclidean space R³, such as a sphere. On the other hand, there are surfaces, such as the Klein bottle, that cannot be embedded in three-dimensional Euclidean space without introducing singularities or self-intersections.

To say that a surface is "two-dimensional" means that, about each point, there is a coordinate patch on which a two-dimensional coordinate system is defined. For example, the surface of the Earth resembles (ideally) a two-dimensional sphere, and latitude and longitude provide two-dimensional coordinates on it (except at the poles and along the 180th meridian).

The concept of surface finds application in physics, engineering, computer graphics, and many other disciplines, primarily in representing the surfaces of physical objects. For example, in analyzing the aerodynamic properties of an airplane, the central consideration is the flow of air along its surface.

Surface (disambiguation)

A surface is a two-dimensional manifold in mathematics.

Surface may also refer to:

See also

Surface (magazine)

Surface is an American design, Architecture, and fashion magazine. The magazine is published 10 times a year. Surface magazine covers in depth design profiles of prominent architects, designers, artists and photographers. Marc Lotenburg is the CEO and Spencer Bailey is the Editor in Chief.

History

Surface was founded in 1993 by Richard Klein and Riley Johndonnell. The magazine was based in San Francisco until 2005, when the main offices moved to New York City.

In 1994, Surface Magazine was one of 10 magazines dubbed as “upstart magazines to watch” by Vanity Fair.

In 1997, Surface introduced its first Avant Guardian issue, which focused on the Avant Guardian Awards, a photography competition that presents an opportunity for up and coming photographers to gain recognition and jumpstart their careers in the fashion editorial world. Winners have gone on to work for world renowned fashion houses and magazines like Giorgio Armani, Hermès, Banana Republic, Nike, IBM and Levi's—as well as magazines like Vogue, Elle, Harper’s Bazaar, Mademoiselle, and The New York Times Magazine. 10 finalists are chosen by heads of fashion and design, and have their work featured in a blowout fashion spread and showcased at a special launch event.

Feint

Feint is a French term that entered English via the discipline of swordsmanship and fencing. Feints are maneuvers designed to distract or mislead, done by giving the impression that a certain maneuver will take place, while in fact another, or even none, will. In military tactics and many types of combat, there are two types of feints: feint attacks and feint retreats.

Attacks

A feint attack is designed to draw defensive action towards the point under assault. It is usually used as a diversion to force the enemy to concentrate more manpower in a given area, to weaken the opposing force in another area. Unlike a related diversionary maneuver, the demonstration, a feint involves actual contact with the enemy.

Retreats

A feint retreat is performed by briefly engaging the enemy, then retreating. It is intended to draw the enemy pursuit into a prepared ambush, or to cause disarray. For example, the Battle of Hastings was lost when Saxons pursued the Norman cavalry. This forfeited the advantage of height and the line was broken, providing the opportunity to fight in single handed combat on a neutral vantage point, a battle for which the Saxons were not ready. The Parthian shot is another example of a feint retreat, where mounted Parthian archers would retreat from a battle and then, while still riding, turn their bodies back to shoot at the pursuing enemy.

The Phantom Agony

The Phantom Agony is the first full-length studio album by Dutch symphonic metal band Epica. It was released in 2003 by the Dutch label Transmission Records. It is the first album recorded by guitarist Mark Jansen after his departure from the band After Forever. On this album, Mark Jansen continues with the collection of songs that make up "The Embrace That Smothers". The first three parts can be found on Prison of Desire (2000), After Forever's debut album, and the following three parts can be found on The Divine Conspiracy (2007), Epica's third album. These songs deal with the dangers of organized religion.

The album was re-released on 23 March 2013, which coincided with Epica’s 10th anniversary Retrospect show, as a 2-disc expanded edition by Epica’s former record label Transmission Records.

Track listings

Personnel

Singles

The Phantom Agony

"The Phantom Agony" was the first single of the eponymous album. It was released in October 2003.

Track listing