Shortest closed curve to inspect a sphere
Wenk, James F.
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We show that in Euclidean 3-space any closed curve γ which lies outside the unit sphere and contains the sphere within its convex hull has length ≥ 4π. Equality holds only when γ is composed of 4 semicircles of length π, arranged in the shape of a baseball seam, as conjectured by V. A. Zalgaller in 1996.