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For example, assuming the Earth is a sphere of radius 6371 km, the surface area of the arctic (north of the Arctic Circle, at latitude 66.56° as of August 2016 [7]) is 2π ⋅ 6371 2 | sin 90° − sin 66.56° | = 21.04 million km 2 (8.12 million sq mi), or 0.5 ⋅ | sin 90° − sin 66.56° | = 4.125% of the total surface area of the Earth ...
A single Schmidt net can only represent one hemisphere of the earth; typically a pair of Schmidt nets is used to represent both sides of the globe. It is relatively simple to re-plot a gridded map of the world onto a Schmidt net if the azimuth is chosen to be the junction of the equator with any particular meridian from the world-map's grid.
The following is a list of centroids of various two-dimensional and three-dimensional objects. The centroid of an object in -dimensional space is the intersection of all hyperplanes that divide into two parts of equal moment about the hyperplane.
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 view factor is then equal to the differential area dA i times the proportion of the unit circle covered by this projection. The projection onto the hemisphere, giving the solid angle subtended by A j , takes care of the factors cos(θ 2 ) and 1/ r 2 ; the projection onto the circle and the division by its area then takes care of the local ...
The solid angle of an object that is very far away is roughly proportional to the ratio of area to squared distance. Here "area" means the area of the object when projected along the viewing direction. Any area on a sphere which is equal in area to the square of its radius, when observed from its center, subtends precisely one steradian.
Northern Hemisphere: The half that lies north of the Equator. This hemisphere contains approximately 68% of Earth's landmass and is home to about 90% of the global population. [4] It includes North America, Europe, Asia, and most of Africa. Southern Hemisphere: The half that lies south of the Equator. It contains approximately 32% of Earth's ...
Bretschneider's formula generalizes Brahmagupta's formula for the area of a cyclic quadrilateral, which in turn generalizes Heron's formula for the area of a triangle.. The trigonometric adjustment in Bretschneider's formula for non-cyclicality of the quadrilateral can be rewritten non-trigonometrically in terms of the sides and the diagonals e and f to give [2] [3]