抄録
The fold-and-cut theorem states that one can find a flat folding of paper, so that one complete straight cut on the folding creates any desired polygon. We extend this problem to curved origami for piecewise C1 simple closed curves. Many of those curves on paper turn out to be cut by a straight plane after we fold the paper into a conical shape—the surface consists of half-lines with a common vertex. Let γ: I → R2 be a piecewise C1 simple closed curve such that there exists a parametrization γ(ψ)= (r(ψ) cos ψ, r(ψ) sin ψ) on ψ ∈ [0,2π) for a Lipschitz continuous function r: R→ (0, ∞). We prove that there exists a conical folding of the plane so that γ can be cut by a plane on the folding if a certain condition on angular total variation holds.
