Areas
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Area is a quantity that expresses the extent of a two-dimensional surface or shape in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (m), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus. For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus. Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions. From Wikipedia under the
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GNU Free Documentation License Matching Results for Areas:John HodgmanHe has written two books, The Areas of My Expertise and More Information Than You Require and is a regular contributor to The Daily Show with Jon Stewart. ... Tanya Reinhart Many of the residents of the isolated Israeli settlements that are scattered in these areas are speaking openly in the Israeli media about their wish to leave. ... Suicide If the healthy are granted the right to die, gray areas will inevitably arise. ... does not mean that all areas are gray. Jacob M. Appel, bioethicist, ... From Wikiquote under the
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Regional: Europe: Italy: Geographical Areas This category in other languages: German (58) Italian (83) Italian Lakes - Personal accounts of two English speakers living in the lake district. Itineraries ... Regional: North America: United States: Florida ... See also: Regional: North America: United States: Florida: Business and Economy (216) PRSA - Public Relations Society of America - Tampa Bay Chapter, a membership ... Regional: North America: United States ... The metropolitan San Francisco Bay Area consists of four sub areas: East Bay, North Bay, South Bay and San Francisco. These four sub areas cover nine counties.
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