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Many results in spherical geometry depend on choosing non-antipodal points, and degenerate if antipodal points are allowed; for example, a spherical triangle degenerates to an underspecified lune if two of the vertices are antipodal. The point antipodal to a given point is called its antipodes, from the Greek ἀντίποδες (antípodes ...
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.
Antipodes, points on the Earth's surface that are diametrically opposed; Antipodes Islands, inhospitable volcanic islands south of New Zealand; The Antipodes, a principally British term for Australia and New Zealand (or more broadly the area known as Australasia), based on a rough proximity to the antipode of Britain
For each point p, construct the stereographic projection of s(p) with p as the point of tangency. Then v ( p ) is the displacement vector of this projected point relative to p . According to the hairy ball theorem, there is a p such that v ( p ) = 0 , so that s ( p ) = p .
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.
A polar opposite is the diametrically opposite point of a circle or sphere. It is mathematically known as an antipodal point, or antipode when referring to the Earth. It is also an idiom often used to describe people and ideas that are opposites. Polar Opposite or Polar Opposites may also refer to:
(Every great circle through any point also passes through its antipodal point, so there are infinitely many great circles through two antipodal points.) The shorter of the two great-circle arcs between two distinct points on the sphere is called the minor arc , and is the shortest surface-path between them.
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.