Antipodal point

Antipodal points on the surface of a sphere are diametrically opposite; on the other side of a globe. For example, "Norway and New Zealand lie in antipodal regions" or "GPS distributes its 12 frequencies amongst its 24 satellites by letting antipodal satellites share a band."

More generally, in mathematics, antipodal points on a sphere of any dimension are those opposite through the centre; for example, taking the centre as origin, they are points with related vectorss v and −v. On a circle, such points are also called diametrically opposite. In other words, each line through the centre intersects the sphere in two points, one for each ray out from the centre. The Borsuk-Ulam theorem is a result from algebraic topology dealing with such pairs of points. If one wants to consider antipodal points as identified, one passes to projective space (see also projective Hilbert space, for this idea as applied in quantum mechanics).

The word Antipodes (pronounced an TIP uh deez) is also used in the United Kingdom to refer to Australia and New Zealand.

An antipodal point is sometimes called an antipode, a back-formed word that originated from the mistaken idea that antipodes is the plural of antipode. In fact antipodes is an adapted Greek plural whose singular is antipous.