Quaternions and spatial rotation of a circle representing a particular rotation angle will be half of the angle represented by that rotation, since as the point is moved from the north to south pole, the latitude ranges from zero to 180 degrees, while the angle of rotation ranges from 0 to 360 degrees. (the "longitude" of a point then represents a particular axis of rotation.) Note however that this set of rotations is not closed under composition. Two successive rotations with axes in the "xy" plane will not necessarily give a rotation whose axis lies in the "xy" plane, and thus cannot be represented
Six degrees of separation We should select any person from the 1.5 billion inhabitants of the Earth – anyone, anywhere at all. He bet us that, using no more than "five" individuals, one of whom is a personal acquaintance, he could contact the selected individual using nothing except the network of personal acquaintances. This idea both directly and indirectly influenced a great deal of early thought on social networks. Karinthy has been regarded as the originator of the notion of six degrees of separation. A related theory deals with the quality of connections, rather than their existence. The theory of three degrees of influence