Ptolemy's table of chords to the arc angle in degrees as is to 3, or more precisely, the ratio can be made as close as desired to ≈ by making "θ" small enough. Thus, for the arc of °, the chord length is slightly more than the arc angle in degrees. As the arc increases, the ratio of the chord to the arc decreases. When the arc reaches 60°, the chord length is exactly equal to the number of degrees in the arc, i.e. chord 60° = 60. For arcs of more than 60°, the chord is less than the arc, until an arc
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,