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Spiral surfaces enveloped by one-parametric sets of spheres. (English) Zbl 1211.53004

In the present paper, cyclic surfaces in the three-dimensional Euclidean space \(E^3\) generated by spiral motions of a circle are studied. The standard representation of all cyclic spiral surfaces in \(E^3\) which are envelopes of one-parametric set of spheres is found. The theory is illustrated with a nice example.

MSC:

53A05 Surfaces in Euclidean and related spaces
53A17 Differential geometric aspects in kinematics
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