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

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.