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In geography, the antipode (/ ˈ æ n t ɪ ˌ p oʊ d, æ n ˈ t ɪ p ə d i /) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal (/ æ n ˈ t ɪ p ə d əl /) to each other are situated such that a straight line connecting the two would pass through Earth's center.
The concept of antipodal points is generalized to spheres of any dimension: two points on the sphere are antipodal if they are opposite through the centre.Each line through the centre intersects the sphere in two points, one for each ray emanating from the centre, and these two points are antipodal.
The equal-area projection that results from average of sinusoidal and Mollweide y-coordinates and thereby constraining the x coordinate. 1929 Craster parabolic =Putniņš P4: Pseudocylindrical Equal-area John Craster Meridians are parabolas. Standard parallels at 36°46′N/S; parallels are unequal in spacing and scale; 2:1 aspect. 1949
Coordinate charts are mathematical objects of topological manifolds, and they have multiple applications in theoretical and applied mathematics. When a differentiable structure and a metric are defined, greater structure exists, and this allows the definition of constructs such as integration and geodesics .
On S n, in homogeneous coordinates, (x 1, ..., x n+1), consider the subset U i with x i ≠ 0. Each U i is homeomorphic to the disjoint union of two open unit balls in R n that map to the same subset of RP n and the coordinate transition functions are smooth. This gives RP n a smooth structure.
The time needed to connect power-hungry data centres to the electricity grid could blunt France's advantage using its abundant nuclear power to lure billions of dollars of investment into ...
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
Antipodal. In mathematics, the Borsuk–Ulam theorem states that every continuous function from an n-sphere into Euclidean n-space maps some pair of antipodal points to the same point. Here, two points on a sphere are called antipodal if they are in exactly opposite directions from the sphere's center.