Quaternions and spatial rotation the rotation. As the rotation angles become larger, the slice moves in the negative "z" direction, and the circles become larger until the equator of the sphere is reached, which will correspond to a rotation angle of 180 degrees. Continuing southward, the radii of the circles now become smaller (corresponding to the absolute value of the angle of the rotation considered as a negative number). Finally, as the south pole is reached, the circles shrink once more to the identity rotation, which is also specified as the point at the south pole. Notice that a number of characteristics of such
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