On the length of space curves of constant width (Q1315107)

The length of a closed space curve of constant width \(d\) is always greater or equal to \(\pi d\) with equality holding exactly in the plane case. Here an upper bound for the length of such a curve is obtained as a multiple of \(d\). The proof uses methods from spherical integral geometry and the fact that there is an isotopy of every closed space curve of constant width to a spherical one such that the constant width and the length are preserved [cf. the reviewer, Math. Nachr. 53, 337-344 (1972; Zbl 0214.203)].