Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted ABCD.

The square is the n=2 case of the families of n-hypercubes and n-orthoplexes.

A square has Schläfli symbol {4}. A truncated square, t{4}, is an octagon, {8}. An alternated square, h{4}, is a digon, {2}.

Properties

A square is a special case of a rhombus (equal sides, opposite equal angles), a kite (two pairs of adjacent equal sides), a parallelogram (opposite sides parallel), a quadrilateral or tetragon (four-sided polygon), and a rectangle (opposite sides equal, right-angles) and therefore has all the properties of all these shapes, namely:

Geometric group action

In mathematics, specifically geometric group theory, a geometric group action is a certain type of action of a discrete group on a metric space.

Definition

In geometric group theory, a geometry is any proper, geodesic metric space. An action of a finitely-generated group G on a geometry X is geometric if it satisfies the following conditions:

Uniqueness

If a group G acts geometrically upon two geometries X and Y, then X and Y are quasi-isometric. Since any group acts geometrically on its own Cayley graph, any space on which G acts geometrically is quasi-isometric to the Cayley graph of G.

Examples

Cannon's conjecture states that any hyperbolic group with a 2-sphere at infinity acts geometrically on hyperbolic 3-space.

References

Geometry (disambiguation)

Geometry is a branch of mathematics dealing with spatial relationships.

Geometry or geometric may also refer to:

Square (album)

Square is a studio album by Canadian hip hop musician Buck 65. It was released on WEA in 2002. Though it consists of four tracks, each track consists of multiple songs.

It was nominated for the 2003 Juno Awards for Alternative Album of the Year and Album Design of the Year.

Reception

Rollie Pemberton of Pitchfork Media gave Square a 7.0 out of 10 and called it "a melodic mix of folk rock sensibility, smooth early 90s style production, clever lyrical observations and a relatively enjoyable train ride into the mental station of Halifax's best-known emcee." Meanwhile, Clay Jarvis of Stylus Magazine gave the album a grade of B+, saying, "Square is built solely out of his strengths: hazy introspection, sparse snare-and-kick beats and simple, dismal instrumental refrains."

Track listing

References

External links

Square (band)

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Square was a short-lived musical trio from Lincoln, Nebraska who moved to Southern California in early 2000. It was composed of Sean Beste (vocals and keyboards), James Valentine (guitars) and Ryland Steen (drums). Their sound has been described as including elements of rock, pop, and jazz fusion.

The band moved to Orange County after entering an Ernie Ball-sponsored band competition. They won the grand prize, beating 600 other entrants. Shortly after winning the competition, they released their only full-length album, This Magnificent Nonsence, on an indie label called Lucy Smith Music. The band started playing many gigs in the area, including some with local band Kara's Flowers.

In 2001, the members of Kara's Flowers asked Valentine to join their group, an invitation that he accepted, effectively dissolving Square. Kara's Flowers changed its name to Maroon 5 and became one of the most commercially successful acts of the mid-2000s. Steen later joined the established ska band Reel Big Fish. Beste (who was initially upset and unhappy by Valentine's decision to leave Square but says he no longer harbors any ill will) started a band called The Excuse and moved to Portland, Oregon for several years. He has since returned to the Los Angeles area and has done some work with the band Maxeen.

Square (company)

Square Co., Ltd. (株式会社スクウェア, Kabushiki-gaisha Sukuwea) was a Japanese video game company founded in September 1983 by Masashi Miyamoto. It merged with Enix in 2003 and became Square Enix. The company also used SquareSoft as a brand name to refer to their games, and the term is occasionally used to refer to the company itself. In addition, "Squaresoft, Inc" was the name of the company's American arm before the merger, after which it was renamed to "Square Enix, Inc".

History

Square was founded in Yokohama in September 1983 by Masashi Miyamoto after he graduated from Waseda, one of Japan's top universities. Back then, Square was a computer game software division of Den-Yu-Sha, a power line construction company owned by Miyamoto's father. While at the time game development was usually conducted by only one programmer, Miyamoto believed that it would be more efficient to have graphic designers, programmers and professional story writers working together on common projects. Square's first two titles were The Death Trap and its sequel Will: The Death Trap II, both designed by part-time employee Hironobu Sakaguchi and released on the NEC PC-8801.