Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball, (viz., analogous to a circular object in two dimensions). Like a circle, which geometrically is a two-dimensional object, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space. This distance r is the radius of the ball, and the given point is the center of the mathematical ball. The longest straight line through the ball, connecting two points of the sphere, passes through the center and its length is thus twice the radius; it is a diameter of the ball.

While outside mathematics the terms "sphere" and "ball" are sometimes used interchangeably, in mathematics a distinction is made between the sphere (a two-dimensional closed surface embedded in three-dimensional Euclidean space) and the ball (a three-dimensional shape that includes the sphere as well as everything inside the sphere). The ball and the sphere share the same radius, diameter, and center.

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.