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
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,