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Three people live on the unit sphere and are going to walk from North
Pole (0,0,1) to the South Pole (0,0,−1). The first person walks along the
arc of a great circle that lies in on the coordinate planes. The second
person walks along an arc of a great circle that does not lie in one of the
coordinate planes, and the third walks along a curve that spirals once
around the sphere. Find the parametric equations that describe possible
paths for each person.