square, magic: see magic square.

square root: see root, in mathematics.

square, closed plane figure bounded by four straight line segments of equal length and meeting at right angles. The points of intersection of the lines, or sides, are called vertices. The diagonals of a square are the two lines joining opposite vertices; they are of equal length and are the perpendicular bisectors of one another. The perimeter of a square is the sum of the lengths of its sides, or P=4s, where s is the length of a side. The area enclosed by a square is A=s². The square is one of the commonest geometric figures and has long had various symbolic meanings in religion and art.

magic square, a square divided into parts with letters or numbers inscribed therein that, whether combined vertically, horizontally, or diagonally, form the same sum or the same word. In ancient times such squares were thought to have magic properties, perhaps connected with the stars. Magic squares have been found in such widely divergent cultures as ancient China, Egypt, and India, as well as W Europe. Example:

chi-square test: see statistics.

Trafalgar Square, in Westminster, London, England, named for Lord Nelson's victory at the battle of Trafalgar. The statue surmounting the Nelson memorial column (185 ft/56 m high) was sculpted (1840-43) by E. H. Baily. On the northern side of the square stand the National Gallery and the Church of St. Martin-in-the-Fields. Trafalgar Square is a frequent site of political rallies.

Times Square, in New York City. Formed by the intersection of Broadway, Seventh Ave., and 42d St., this famous square was named (1904) for the building there that formerly belonged to the New York Times. The building, located in the center of the square, is still famous for the outdoor news "zipper" that displays up-to-the-minute news. Times Square and the adjacent area form one of the most concentrated entertainment districts in the nation, featuring legitimate theaters, motion picture houses, shops, newsstands, bars, and restaurants. During the 1970s and 80s, the area became notorious for pornographic theaters and general tawdriness, but it was cleaned up and revived in the 1990s. Broadway at Times Square, jammed with traffic and illuminated by a profusion of enormous electrical signs, is known as the "Great White Way." On New Year's Eve, close to a million people congregate there to celebrate.

Tiananmen Square, large public square in Beijing, China, on the southern edge of the Inner or Tatar City. The square, named for its Gate of Heavenly Peace (Tiananmen), contains the monument to the heroes of the revolution, the Great Hall of the People, the museum of history and revolution, and the Chairman Mao Zedong Memorial Hall (with Mao's embalmed body). Mao Zedong proclaimed the founding of the People's Republic in the square on Oct. 1, 1949, an anniversary still observed there. A massive demonstration for democratic reform, begun there by Chinese students in Apr., 1989, was brutally repressed on June 3 and 4. It was initiated to demand the posthumous rehabilitation of former Communist Party Chairman Hu Yaobang. The government was tolerant until after his funeral; then Deng Xiaoping denounced the protests. The demonstrators were joined by workers, intellectuals, and civil servants, until over a million people filled the square. General Secretary Zhao Ziyang expressed sympathy, but lost out to Deng, who supported the use of military suppression. Martial law was declared on May 20. The protesters demanded that the leadership resign, but the government answered on the nights of June 3 and 4 with troops and tanks, killing thousands to quell a "counterrevolutionary rebellion." Zhao was dismissed and a number of the student leaders were arrested.

Haymarket Square riot, outbreak of violence in Chicago on May 4, 1886. Demands for an eight-hour working day became increasingly widespread among American laborers in the 1880s. A demonstration, largely staged by a small group of anarchists, caused a crowd of some 1,500 people to gather at Haymarket Square. When policemen attempted to disperse the meeting, a bomb exploded and the police opened fire on the crowd. Seven policemen and four other persons were killed, and more than 100 persons were wounded. Public indignation rose rapidly, and punishment was demanded. Eight anarchist leaders were tried, but no evidence was produced that they had made or thrown the bomb. They were, however, convicted of inciting violence, although no evidence was presented that they knew the bomber, who was never discovered. Four were hanged, one committed suicide, and the remaining three—after having served in prison for seven years—were pardoned (1893) by John P. Altgeld, governor of Illinois, on the ground that the trial had been patently unjust. The incident was frequently used by the adversaries of organized labor to discredit the waning Knights of Labor movement.

Franklin Square, uninc. city (1990 pop. 28,205), Nassau co., SE N.Y., on Long Island. Although it is chiefly residential, there is significant manufacturing, including fire extinguishers, dye castings, electrical machinery, and lighting fixtures.

Geometrical representation of the traditional logical relations of opposition (contradictories, contraries, subalterns) among the four types of propositions (universal affirmative or A-proposition, universal negative or E, particular affirmative or I, particular negative or O) in the Aristotelian doctrine of the syllogism. At the top left is the A; at the top right is the E; below the A is the I; and below the E is the O. The A and the O, like the E and I, are contradictories (diagonal relations); the A and the E are contraries; and the I is subaltern to (hence implied by) the A, the O subaltern to the E. Whereas contradictories have opposite truth-values (one true, the other false), contraries cannot both be true but can both be false.

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Dance for sets of four couples standing in square formation. The most popular type of U.S. folk dance, it derived from the quadrille and was originally called a square dance to distinguish it from the contra, or longways, dance (for a double line of couples) and the round dance (for a circle of couples). The U.S. square dance progresses through specific patterns called or sung out to the dancers by a caller and accompanied by lively music played on instruments such as fiddle, banjo, accordion, guitar, and piano.

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In measurement, a device consisting of two straightedges set at a right angle. It is used by carpenters and machinists to check the correctness of right angles, as a guide when drawing lines on materials before cutting, or for locating holes. In mechanical drawing or drafting, a T-shaped instrument known as a T square is used to establish a horizontal reference on the drafting board.

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One of the largest public squares in the world, originally designed and built in Beijing in 1651 and enlarged in 1958. It is named for the massive stone “Gate of Heavenly Peace” (Tiananmen) at its northern end. It contains and is surrounded by halls, museums, and monuments, including the Mao Zedong Memorial Hall, where Mao's body rests in state. Tiananmen Square is the site of numerous parades and other celebrations. It has also been the rallying point for political demonstrations, including events during the May Fourth Movement in 1919 and during May–June 1989.

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