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).
Lonely Planet Six Degrees Lonely Planet Six Degrees Lonely Planet Six Degrees is Lonely Planet's flagship travel show, hosted by Asha Gill and Toby Amies. The show is centered on unique people living within locations, rather than simply famous tourist attractions, with one of the hosts meeting with one contact in a specific country, who in turn leads them to another contact, and so on, following the idea of six degrees of separation. In the first season Asha travelled to Mumbai, Buenos Aires, Kuala Lumpur, Melbourne, Auckland, Cape Town, London, and Singapore; while Toby travelled to Sydney, New York City, Havana, Hong Kong, Berlin,