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We find bounds on the difference between the writhing numbers of a smooth curve and a polygonal curve inscribed within. The proof is based on an extension of Fuller's difference of writhe formula to the case of polygonal curves. The results establish error bounds useful in the numerical computation of writhe in terms of bounds on the edge lengths of the polygon and the derivatives of the curve. The bounds are "adaptive" in the sense that they improve when regions of the smooth curve with larger derivatives are approximated by shorter edges of the polygon.

On Comparing the Writhe of a Smooth Curve to the Writhe of an Inscribed Polygon