In mathematics, a square is the result of multiplying a number by itself. The verb "to square" is used to denote this operation. Squaring is the same as raising to the power 2, and is denoted by a superscript 2; for instance, the square of 3 may be written as 3², which is the number 9. In some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x^2 or x**2 may be used in place of x².

The adjective which corresponds to squaring is quadratic.

The square of an integer may also be called a square number or a perfect square. In algebra, the operation of squaring is often generalized to polynomials, other expressions, or values in systems of mathematical values other than the numbers. For instance, the square of the linear polynomial x + 1 is the quadratic polynomial x² + 2x + 1.

One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its additive inverse −x. That is, the square function satisfies the identity x² = (−x)². This can also be expressed by saying that the squaring function is an even function.

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

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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 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.

In mathematics, and more specifically in abstract algebra, a *-algebra (or involutive algebra) is a mathematical structure consisting of two involutive rings R and A, where R is commutative and A has the structure of an associative algebra over R. Involutive algebras generalize the idea of a number system equipped with conjugation, for example the complex numbers and complex conjugation, matrices over the complex numbers and conjugate transpose, and linear operators over a Hilbert space and Hermitian adjoints.

Terminology

*-ring

In mathematics, a *-ring is a ring with a map * : A → A that is an antiautomorphism and an involution.

More precisely, * is required to satisfy the following properties:

for all x, y in A.

This is also called an involutive ring, involutory ring, and ring with involution. Note that the third axiom is actually redundant, because the second and fourth axioms imply 1* is also a multiplicative identity, and identities are unique.

Algebra (from Arabic "al-jabr" meaning "reunion of broken parts") is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. As such, it includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra, the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians. Much early work in algebra, as the Arabic origin of its name suggests, was done in the Middle East, by mathematicians such as al-Khwārizmī (780 – 850) and Omar Khayyam (1048–1131).

The word 'algebra' is used for various branches and structures of mathematics. For their overview, see Algebra.

The bare word "algebra"

The bare word "algebra" can mean:

In universal algebra, algebra has an axiomatic definition, roughly as an instance of any of a number of algebraic structures, such as groups, rings, etc.

Branches of mathematics

The term is also traditionally used for the field of:

Mathematical structures

Vector space with multiplication

Some notable algebras in this sense are: