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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.
If the geographic coordinates (latitude and longitude) of a point on the Earth's surface are (φ, θ), then the coordinates of the antipodal point are (−φ, θ ± 180°). This relation holds true whether the Earth is approximated as a perfect sphere or as a reference ellipsoid.
Like the North Magnetic Pole, the North Geomagnetic Pole attracts the north pole of a bar magnet and so is in a physical sense actually a magnetic south pole. It is the center of the 'open' magnetic field lines which connect to the interplanetary magnetic field and provide a direct route for the solar wind to reach the ionosphere.
Points in the polar coordinate system with pole O and polar axis L. In green, the point with radial coordinate 3 and angular coordinate 60 degrees or (3, 60°). In blue, the point (4, 210°). In mathematics, the polar coordinate system specifies a given point in a plane by using a distance and an angle as its two coordinates. These are
The Bloch sphere is a unit 2-sphere, with antipodal points corresponding to a pair of mutually orthogonal state vectors. The north and south poles of the Bloch sphere are typically chosen to correspond to the standard basis vectors | 0 {\displaystyle |0\rangle } and | 1 {\displaystyle |1\rangle } , respectively, which in turn might correspond e ...
If the azimuthal equidistant projection map is centered about a point whose antipodal point lies on land and the map is extended to the maximum distance of 20,000 km (12,427 mi) the antipode point smears into a large circle.
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.