On comparing the writhe of a smooth curve to the writhe of an inscribed polygon

TL;DR

This paper establishes bounds on the difference in writhe between smooth curves and inscribed polygons, extending Fuller's formula to polygonal curves to aid in accurate writhe computation.

Contribution

It introduces an extension of Fuller's writhe difference formula to polygonal curves, providing new error bounds for computational purposes.

Findings

Derived bounds on writhe difference between smooth and polygonal curves

Extended Fuller's formula to polygonal curves

Provided error estimates for writhe calculations

Abstract

We find bounds on the difference between the writhing number of a smooth curve, and the writhing number of a polygon 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 computation of writhe.