On the Gaussian Curvature of Creased Tubes

Keith A. Seffen; Christopher R. Calladine

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arXiv · 2111.13925

On the Gaussian Curvature of Creased Tubes

Keith A. Seffen·Christopher R. Calladine

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Abstract

We calculate the Gaussian curvature of a curved, twisted crease in terms of the rate of change of solid angle along its length; we find that this depends on the fold angle across the crease and on the curvature along it but is independent of twist. We use this result to resolve a paradox concerning the geometry of a creased, twisted-prismatic tube; that there can be no Gaussian curvature overall despite the surface being doubly-curved.

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Keith A. Seffen, Christopher R. Calladine. 2021-11-27. On the Gaussian Curvature of Creased Tubes. https://arxiv.org/abs/2111.13925

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