Closed Space Curves of Constant Curvature Consisting of Arcs of Circular Helices
نویسندگان
چکیده
A closed κ0-curve is a closed regular curve of class C r (r ≥ 2) in the Euclidean 3-space having constant curvature κ0 > 0. We present various examples of nonplanar closed κ0-curves of class C , which are composed of n arcs of circular helices. The construction of c starts from the spherical image (= tangent indicatrix) c of c, which then has to be a closed regular curve of class C on the unit sphere S consisting of n circular arcs and having the center O of S as its center of gravity. The case c ⊆ S ∩ Π is studied in detail, assuming that Π is a cube, or, more generally, a regular polyhedron the edges of which are tangent to S. In order to describe and to visualize the curves c and c, and to derive c from c, projection methods of Descriptive Geometry are used.
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