分野別セミナー

In Euclidean 3-space R^3, a surface generated by a continuous motion of a line is said to be developable if its Gaussian curvature vanishes identically. Develpable surfaces are well known as mathematical models of bending `paper' without stretching, such as cylinders, cones, and tangential surfaces. A discretization of developable surfaces can be formulated as a line sequence so that any two adjacent lines lie on a common plane in R^3, which was introduced by Sauer in 1970. This formulation discretize the differential geometric property that developable surfaces are locally isometric to R^2. In this talk, we consider the discretization of discrete developable Mobius strips whose centerlines are geodesics or lines of curvature. Moreover, we show the existence of such a discrete developable Mobius strip for any given knot type of centerline and twisting number of a Mobius strip. This result is a discrete version of Kurono-Umehara's theorem.