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In mathematics, two points of a sphere (or n-sphere, including a circle) are called antipodal or diametrically opposite if they are the endpoints of a diameter, a straight line segment between two points on a sphere and passing through its center.
Antipodal point, the point diametrically opposite to another point on a sphere, such that a line drawn between them passes through the centre of the sphere and forms a true diameter; Conjugate point, any point that can almost be joined to another by a 1-parameter family of geodesics (e.g., the antipodes of a sphere, which are linkable by any ...
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.
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: Polar Opposite, a 2011 EP by Sick Puppies
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
Any two great circles intersect in two diametrically opposite points, called antipodal points. Any two points that are not antipodal points determine a unique great circle. There is a natural unit of angle measurement (based on a revolution), a natural unit of length (based on the circumference of a great circle) and a natural unit of area ...
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An area formula for spherical triangles analogous to the formula for planar triangles. Given a fixed base , an arc of a great circle on a sphere, and two apex points and on the same side of great circle , Lexell's theorem holds that the surface area of the spherical triangle is equal to that of if and only if lies on the small-circle arc , where and are the points antipodal to and , respectively.