nonantipodal

Nonantipodal refers to a condition where two points on a sphere are not diametrically opposite. In spherical geometry and topology, antipodal points are pairs of points that are directly across from each other through the center of the sphere. For example, the North Pole and the South Pole are antipodal points on Earth.

If two points are nonantipodal, it means that a straight line segment connecting them does not pass through the center of the sphere. Consequently, the distance between nonantipodal points is less than the diameter of the sphere. The concept of antipodal points is fundamental in various fields, including geometry, physics (especially in describing states of quantum systems), and cartography.

The negation of antipodal, therefore, simply describes the vast majority of possible point pairings on a sphere. Any two points chosen at random on a sphere are highly likely to be nonantipodal. Understanding the distinction between antipodal and nonantipodal points is crucial when discussing concepts like geodesics, which are the shortest paths between points on a curved surface, or when considering symmetries of spherical objects.