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).
180 Degrees South: Conquerors of the Useless "Chris Malloy's film strikes so deeply into the heart of Patagonia's wilderness we come to feel at home there". 180 Degrees South: Conquerors of the Useless 180 Degrees South: Conquerors of the Useless, or simply "180° South", is a 2010 documentary directed by Chris Malloy that covers the journey of Jeff Johnson as he travels from Ventura, California to Patagonia, Chile retracing the 1968 trip that Yvon Chouinard and Doug Tompkins took in their Ford E-Series Econoline Van. After finding footage of the 1968 expedition, Johnson decided to make climbing the Corcovado Volcano in Patagonia as his life goal and,