Charts on SO(3) closed set under composition. This visualization can be extended to a general rotation in 3-dimensional space. The identity rotation is a point, and a small angle of rotation about some axis can be represented as a point on a sphere with a small radius. As the angle of rotation grows, the sphere grows, until the angle of rotation reaches 180 degrees, at which point the sphere begins to shrink, becoming a point as the angle approaches 360 degrees (or zero degrees from the negative direction). This set of expanding and contracting spheres represents a hypersphere in four-dimensional space (a 3-sphere).
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