For each point a of S2, the set of points of S3 whose image by f is the point a (that is, the pre-image of a), which we call the fiber over a, is a circle in S3. What is the connection with the preceding explanation: quite simply that all the points of a line z2= a.z1 are such that z2/z1 is constant (obviously, because it equals a !).
http://www.dimensions-math.org/Dim_CH7_E.htm
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