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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. [8]
A sphere of radius r has surface area 4πr 2.. The surface area (symbol A) of a solid object is a measure of the total area that the surface of the object occupies. [1] The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc length of one-dimensional curves, or of the surface area for polyhedra (i.e., objects with ...
The square gets sent to a rectangle circumscribing the ellipse. The ratio of the area of the circle to the square is π /4, which means the ratio of the ellipse to the rectangle is also π /4. Suppose a and b are the lengths of the major and minor axes of the ellipse. Since the area of the rectangle is ab, the area of the ellipse is π ab/4.
2. A heavily eroded area along a river featuring steep banks, bluffs, ravines, or gorges. The term is used chiefly in the plural (i.e. breaks) and primarily in the United States and Canada. breaker 1. Another name for a breaking wave. 2. A reef, shoal, bar, skerry, or area of shallow water against which waves routinely break. breaker zone
[12] [13] The modern metropolitan statistical area was created in 1983 amid a large increase in the number of eligible markets, which grew from 172 in 1950 to 288 in 1980; [12] [14] the core based statistical area (CBSA) was introduced in 2000 and defined in 2003 with a minimum population of 10,000 required for micropolitan areas and 50,000 for ...
The area of one acre (red) superposed on an American football field (green) and Association football/soccer pitch (blue) 1 international acre is equal to the following metric units: 0.40468564224 hectare (A square with 100 m sides has an area of 1 hectare.) 4,046.8564224 square metres (or a square with approximately 63.61 m sides)
The area of a triangle can be demonstrated, for example by means of the congruence of triangles, as half of the area of a parallelogram that has the same base length and height. A graphic derivation of the formula T = h 2 b {\displaystyle T={\frac {h}{2}}b} that avoids the usual procedure of doubling the area of the triangle and then halving it.
Below is a list of European countries and dependencies by area in Europe. [1] As a continent , Europe's total geographical area is about 10 million square kilometres. [ 2 ] Transcontinental countries are ranked according to the size of their European part only, excluding Greece due to the not clearly defined boundaries of its islands between ...