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arXiv · 2401.17854

Conformal invariants of curves via those for inscribed polygons with circular edges

Harald Dorn
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Abstract

The conformal nature of smooth curves in $\mathbb{R}^3$ is characterised by conformal length, curvature and torsion. We present a derivation of these conformal parameters via a limiting process using inscribed polygons with circular edges . The procedure is based on elementary geometry in $\mathbb{R}^3$ only and similar to the rectification of curves in the metrical case. It seems to be not available in the literature so far.

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Harald Dorn. 2024-01-31. Conformal invariants of curves via those for inscribed polygons with circular edges. https://arxiv.org/abs/2401.17854

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