Not antipodean

On the surface of a Sphere, two antipodean points are two opposite points diametrically. An antipodean point is often called a antipode .

Etymology

The term “antipode” comes from plural “antipodes” which traditionally indicated in Europe the areas located on other side of the Earth, like the Oceania (indicated like “Antipodes” or located “at Antipodes”). “Antipodes” comes from a Greek expression literally meaning “opposite feet” (people living there being judicious to go “to back”, since on the other side of the sphere). “Antipode” is an abuse language, the singular of “antipodes” being in Greek “antipous”.

On the Earth

On Earth, only 4% of the surface of the sphere have antipodean points located both on emerged grounds (either thus 14% of those). In 46% of the cases, the two antipodean points are located both on oceans. The 50% remainders are mixed.

There exists an archipelago of the islands Antipodes, located at the South of the New Zealand, thus named because they are located in the antipodean area of the Great Britain (in fact more precisely contrary to Cherbourg, in France).

The Antipode of Mecque is located at the center of the 5 Atoll S which forms the commune of Tureia, in French Polynésie, at the end of 19,845 kilometers of voyage.

Here a small list of cities having another big city like antipode and of the distance to traverse to travel of the one to the other:

Hamilton (Bermuda) and Perth (Australia): 19,946 km,
Asuncion (Paraguay) and Taipei (Taiwan): 19,942 km,
Seville (Spain) and Auckland (New Zealand): 19,926 km,
Tombouctou (Mali) and Suva (Islands Fiji): 19,802 km,
Lima (Peru) and Bangkok (Thailand): 19,699 km,
Buenos Aires (Argentinian) and Shanghai (China): 19,618 km,
Bogota (Colombia) and Jakarta (Indonesia): 19,487 km,
Leon (Spain) and Wellington (New Zealand): 19,312 km,
Santiago (Chile) and Xi' year (China): 19,273 km,

In mathematics

In the domain of the Topology, the concept can be wide on a unspecified Sphère of dimension

S^n

: two points on its surface are known as antipodean if they are symmetrical compared to the center.

The Théorème of Borsuk-Ulam is a result of algebraic Topologie relating to the antipodean points. He affirms that all application continues $S^n$ towards $\ mathbb R^n$ sends necessarily at least a pair of antipodean points of $S^n$ towards the same point of $\ mathbb R^n$ .
a traditional interpretation of this result is the fact that there is always at least a point on the surface of the Earth where the Température and the Pression of the air are identical to those of the antipode.

The antipodean application $A: S^n \ rightarrow S^n$ defined by $A (X) =-x$ sends any point of the sphere towards its antipodean point. It is homotopic with the Application identity if and only if $n$ is odd.

See too

External bonds

antipode

Chart presenting the antipodes for any area of the world
interactive Chart based on Google Maps presenting the antipodes of a given point.

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