Antipodal point in the context of N-sphere


Antipodal point in the context of N-sphere

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⭐ Core Definition: Antipodal point

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.

Given any point on a sphere, its antipodal point is the unique point at greatest distance, whether measured intrinsically (great-circle distance on the surface of the sphere) or extrinsically (chordal distance through the sphere's interior). Every great circle on a sphere passing through a point also passes through its antipodal point, and there are infinitely many great circles passing through a pair of antipodal points (unlike the situation for any non-antipodal pair of points, which have a unique great circle passing through both). 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.

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Antipodal point in the context of Tide

Tides are the rise and fall of sea levels caused by the combined effects of the gravitational forces exerted by the Moon (and to a much lesser extent, the Sun) and are also caused by the Earth and Moon orbiting one another.

Tide tables can be used for any given locale to find the predicted times and amplitude (or "tidal range"). The predictions are influenced by many factors including the alignment of the Sun and Moon, the phase and amplitude of the tide (pattern of tides in the deep ocean), the amphidromic systems of the oceans, and the shape of the coastline and near-shore bathymetry (see Timing). They are however only predictions, and the actual time and height of the tide is affected by wind and atmospheric pressure. Many shorelines experience semi-diurnal tides—two nearly equal high and low tides each day. Other locations have a diurnal tide—one high and low tide each day. A "mixed tide"—two uneven magnitude tides a day—is a third regular category.

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Antipodal point in the context of Antipodes

In geography, the antipode (/ˈæntɪˌpd, ænˈtɪpədi/) of any spot on Earth is the point on Earth's surface diametrically opposite to it. A pair of points antipodal (/ænˈtɪpədəl/) to each other are situated such that a straight line connecting the two would pass through Earth's center. Antipodal points are as far away from each other as possible. The North and South Poles are antipodes of each other.

In the Northern Hemisphere, "the Antipodes" may refer to Australia and New Zealand, and Antipodeans to their inhabitants. Geographically, the antipodes of the British Isles are in the Pacific Ocean, south of New Zealand. This gave rise to the name of the Antipodes Islands of New Zealand, which are close to the antipode of London. The antipodes of Australia are in the North Atlantic Ocean, while parts of Spain, Portugal, France and Morocco are antipodal to New Zealand.

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Antipodal point in the context of Maya death gods

The Maya death gods (also Ah Puch, Ah Cimih, Ah Cizin, Hun Ahau, Kimi, or Yum Kimil) known by a variety of names, are two basic types of death gods who are respectively represented by the 16th-century Yucatec deities Hunhau and Uacmitun Ahau mentioned by Spanish Bishop Diego de Landa. Hunhau is the lord of the Underworld. Iconographically, Hunhau and Uacmitun Ahau correspond to the Gods A and A' ("A prime").In recent narratives, particularly in the oral tradition of the Lacandon people, there is only one death god (called "Kisin" in Lacandon), who acts as the antipode of the Upper God in the creation of the world and of the human body and soul. This death god inhabits an Underworld that is also the world of the dead. As a ruler over the world of the dead (Metnal or Xibalba), the principal death god corresponds to the Aztec deity Mictlāntēcutli. The Popol Vuh has two leading death gods, but these two are really one: Both are called "Death," but while one is known as "One Death," the other is called "Seven Death." They were vanquished by the Hero Twins.

The two principal death gods count among the many were-animals and spooks (wayob) inhabiting the Underworld, with the God A way in particular manifesting himself as a head hunter and a deer hunter. Ah Puch was banished after he broke his promise with the Maya king and was sent to the storm that would bring him to earth forever.

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Antipodal point in the context of Opposition (astronomy)

In positional astronomy, two astronomical objects are said to be in opposition when they are on opposite sides of the celestial sphere, as observed from a given body (usually Earth).

A planet (or asteroid or comet) is said to be "in opposition" or "at opposition" when it is in opposition to the Sun. Because most orbits in the Solar System are nearly coplanar to the ecliptic, this occurs when the Sun, Earth, and the body are configured in an approximately straight line, or syzygy; that is, Earth and the body are in the same direction as seen from the Sun. Opposition occurs only for superior planets (see the diagram).

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Antipodal point in the context of North geomagnetic pole

The geomagnetic poles are antipodal points where the axis of a best-fitting dipole intersects the surface of Earth. This theoretical dipole is equivalent to a powerful bar magnet at the center of Earth, and comes closer than any other point dipole model to describing the magnetic field observed at Earth's surface. In contrast, the magnetic poles of the actual Earth are not antipodal; that is, the line on which they lie does not pass through Earth's center.

Owing to the motion of fluid in the Earth's outer core, the actual magnetic poles are constantly moving (secular variation). However, over thousands of years, their direction averages to the Earth's rotation axis. On the order of once every half a million years, the poles reverse (i.e., north switches place with south) although the time frame of this switching can be anywhere from every 10 thousand years to every 50 million years. The poles also swing in an oval of around 50 miles (80 km) in diameter daily due to solar wind deflecting the magnetic field.

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