furniture polish (lemon oil).
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1096 I length, area, and volume ► Leo I
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length, area, and volume Dimensional measures of one-, two-, and three-dimensional geometric objects. All three are magnitudes, represent¬ ing the “size” of an object. Length is the size of a line segment (see dis¬ tance formulas), area is the size of a closed region in a plane, and volume is the size of a solid. Formulas for area and volume are based on lengths. For example, the area of a circle equals 7t times the square of the length of its radius, and the volume of a rectangular box is the product of its three linear dimensions: length, width, and height.
length of a curve Geometrical concept addressed by integral calcu¬ lus. Methods for calculating exact lengths of line segments and arcs of circles have been known since ancient times. Analytic geometry allowed them to be stated as formulas involving coordinates (see coordinate sys¬ tems) of points and measurements of angles. Calculus provided a way to find the length of a curve by breaking it into smaller and smaller line seg¬ ments or arcs of circles. The exact value of a curve’s length is found by combining such a process with the idea of a limit. The entire procedure is summarized by a formula involving the integral of the function describ¬ ing the curve.
Lenin, Vladimir (llich) orig. Vladimir llich Ulyanov (b. April 22, 1870, Simbirsk, Russia—d. Jan. 21, 1924, Gorki, near Moscow) Founder of the Russian Communist Party, leader of the Russian Revolu¬ tion of 1917, and architect and builder of the Soviet state. Born to a middle-class family, he was strongly influenced by his eldest brother, Aleksandr, who was hanged in 1887 for conspiring to assassinate the tsar. He studied law and became a Marxist in 1889 while practicing law. He was arrested as a subversive in 1895 and exiled to Siberia, where he mar¬ ried Nadezhda Krupskaya. They lived in western Europe after 1900. At the 1903 meeting in London of the Russian Social-Democratic Workers' Party, he emerged as the leader of the Bolshevik faction. In several revolution¬ ary newspapers that he founded and edited, he put forth his theory of the party as the vanguard of the proletariat, a centralized body organized around a core of professional revolutionaries; his ideas, later known as Leninism, would be joined with Karl Marx’s theories to form Marxism- Leninism, which became the communist worldview. With the outbreak of the Russian Revolution of 1905, he returned to Russia, but he resumed his exile in 1907 and continued his energetic agitation for the next 10 years. He saw World War I as an opportunity to turn a war of nations into a war of classes, and he returned to Russia with the Russian Revolution of 1917 to lead the Bolshevik coup that overthrew the provisional government of Aleksandr Kerensky. As revolutionary dictator of the Soviet state, he signed the Treaty of Brest-Litovsk with Germany (1918) and repulsed counter¬ revolutionary threats in the Russian Civil War. He founded the Comintern in 1919. His policy of War Communism prevailed until 1921, and to fore¬ stall economic disaster he launched the New Economic Policy. In ill health from 1922, he died of a stroke in 1924.
Leningrad See Saint Petersburg
Leningrad, Siege of (Sept. 8, 1941-Jan. 27, 1944) Prolonged siege of the city of Leningrad (now St. Petersburg) by German forces in World War II. German forces invaded the Soviet Union in June 1941 and approached Leningrad from the west and south while Germany’s Finnish allies came from the north. By November 1941 the city was almost com¬ pletely encircled and its supply lines to the Soviet interior cut off. In 1942 alone, in excess of 650,000 of Leningrad’s citizens died from starvation, disease, and shelling from distant German artillery. Sparse food and fuel supplies reached the city by barge in the summer and by sled in winter across Lake Ladoga. The supplies kept the city’s arms factories operat¬ ing and its two million inhabitants barely alive, while another one mil¬ lion children and sick and elderly people were evacuated. Soviet offensives in 1943 partially broke the German encirclement and were fol¬ lowed in January 1944 by a successful Soviet attack that drove the Ger¬ mans westward from the city’s outskirts, ending the siege.
Leninism Principles expounded by Vladimir Ilich Lenin to guide the tran¬ sition of society from capitalism to communism. The tenets of Marxism, which Lenin embraced, provided no concrete guidelines for the transi¬ tion. Lenin believed that a small, disciplined, professional group of revo¬ lutionaries was needed to violently overthrow the capitalist system, and that a “dictatorship of the proletariat” must guide society until the day when the state would wither away. That day never came, and Leninism in practice meant state control of all aspects of life by the Communist Party and the creation of the first modern totalitarian state. See also Bolshevik, Stalinism, totalitarianism.
Lenni Lenape See Delaware
Lennon, John (Winston) (b. Oct. 9, 1940, Liverpool, Merseyside, Eng.—d. Dec. 8, 1980, New York, N.Y., U.S.) British singer and song¬ writer. He wanted to be a sailor like his father but became a musician after hearing Elvis Presley’s recordings. In 1957 he formed the band that became the Beatles, and in the 1960s he achieved enormous success performing with the group and writing songs with Paul McCartney. In the mid-1960s he began working on side projects in film and music, notably with the Japanese-U.S. avant-garde artist Yoko Ono (b. 1933), whom he married in 1969. Their political activism and social ideals were reflected in much of Lennon’s early solo work, including the hit “Imagine,” and attracted the attention of the U.S. government, which sought to have him deported. After 1975 he withdrew from public life; he and Ono returned with the album Double Fantasy shortly before his murder by a deranged fan. His sons, Julian (b. 1963) and Sean (b. 1975), also became musicians.
lens Piece of glass or other transparent substance that is used to form an image of an object by converging or diverging rays of light from the object. Because of the curvature of its surface, different rays of light are refracted (see refraction) through different angles. A convex lens causes rays to converge on a single point, the focal point. A concave lens causes rays to diverge as though they are coming from a focal point. Both types cause the rays to form a visual image of the object. The image may be real—inverted and photographable or visible on a screen—or it may be virtual—erect and visible only by looking through the lens.
Lent In the Christian church, a period of penitential preparation for Eas¬ ter, observed since apostolic times. Western churches once provided for a 40-day fast (excluding Sundays), in imitation of Jesus' fasting in the wilderness; one meal a day was allowed in the evening, and meat, fish, eggs, and butter were forbidden. These rules have gradually been relaxed, and only Ash Wednesday—the first day of Lent in Western Christianity, when the penitent traditionally have their foreheads marked with ashes— and Good Friday are now kept as Lenten fast days. Rules of fasting are stricter in the Eastern churches.
lentil Small annual legume (Lens esculenta ) and its lens-shaped, protein- rich, edible seed. One of the most ancient of cultivated foods, it is a good source of vitamin B, iron, and phosphorus. Of unknown origin, the lentil is widely cultivated throughout Europe, Asia, and North Africa; though little grown in the Western Hemisphere, its inclusion in the U.S. diet is increas¬ ing. Growing 6-18 in. (15-45 cm) high, the plant has compound leaves and pale blue flowers. Animals are fed the stalks and leaves as fodder.
Lenya, Lotte orig. Karoline Blamauer (b. Oct. 18, 1900, Penzing, Austria—d. Nov. 27, 1981, New York, N.Y., U.S.) Austrian-born U.S. actress-singer. Born into poverty, Lenya worked as a dancer and actress in Zurich and later in Berlin. She married the composer Kurt Weill in 1926 and began appearing in musical dramas by Weill and his longtime col¬ laborator Bertolt Brecht, such as Mahagonny (1927) and The Threepenny Opera (1928; film, 1930). Lenya and Weill fled Nazi Germany for Paris, where she sang in Brecht’s and Weill’s Seven Deadly Sins (1933). The couple moved to New York City in 1935, and Lenya made her U.S. debut in The Eternal Road (1937). After Weill’s death, she lent her inimitably husky voice to revivals throughout the 1950s, including a long-running production of The Threepenny Opera, and she later performed in Brecht on Brecht (1962), Mother Courage and Her Children (1965), and Caba¬ ret (1966), as well as in films.