Osculating curves: around the Tait-Kneser Theorem

TL;DR

This paper explores the Tait-Kneser theorem, detailing its implications for osculating circles of plane curves with monotonic curvature and examining various related variations.

Contribution

It provides a comprehensive discussion of the Tait-Kneser theorem and introduces several variations, expanding understanding of osculating circle properties.

Findings

Osculating circles are pairwise disjoint and nested for curves with monotonic curvature.

The paper discusses multiple variations of the Tait-Kneser theorem.

Insights into geometric properties of plane curves with monotonic curvature.

Abstract

The Tait-Kneser theorem states that the osculating circles of a plane curve with monotonic curvature are pairwise disjoint and nested. We discuss this theorem and a number of its variations.