The projection of a point x in ℝ3 onto a sphere of radius r centered at the origin is the point p(x) on the sphere in which the line segment from 0 to x intersects the sphere.
(a) Find a formula for p(x), indicating any restrictions on its domain.
(b) The projection of a path x = f(t) onto a sphere is the path x = s(t) on the sphere given by the projection of each point. Write a formula for s(t) in terms of p and f.
(c) Obtain a formula for the projection of the helix x = (cos t, sin t, t), −20π ≤ t ≤ 20π onto the unit sphere and use a graphics program to draw it.
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