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Antipodes
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===Mathematical description=== If the [[geographic coordinate]]s ([[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]]. In terms of the usual way these geographic coordinates are given, this [[Transformation (function)|transformation]] can be expressed symbolically as :''x''° N/S ''y''° E/W <big>↦</big> ''x''° S/N (180 − ''y'')° W/E, that is, for the latitude (the north–south coordinate) the magnitude of the angle remains the same but N is changed to S and vice versa, and for the longitude (the East/West coordinate) the angle is replaced by its [[supplementary angle]] while E is exchanged for W. For example, the antipode of the point in China at {{nowrap|37° N 119° E}} (a few hundred kilometres from [[Beijing]]) is the point in Argentina at {{nowrap|37° S 61° W}} (a few hundred kilometres from [[Buenos Aires]]).
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