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 patent Zynga and Tribe.net for $700,000 at an auction in 2003. When explaining his reasoning for purchasing the Six Degrees patent, Hoffman stated, "Right now you're hearing a lot of spurious patent threats (...) And that's why I moved quickly to get a patent that was foundational." He also commented on other entrepreneurs' views of social networking: "The general attitude among entrepreneurial people is that they think that they were first and that there is no history to what they are doing (...) Both Mark and I had tracked six degrees as an intellectual precursor to our own businesses." Andrew Katz