Six proofs of the F\'ary--Milnor theorem

TL;DR

This paper presents multiple proofs of the Fary--Milnor theorem, illustrating different approaches to understanding the relationship between knot complexity and total curvature.

Contribution

It introduces several distinct proofs of the Fary--Milnor theorem, enhancing understanding through varied mathematical techniques.

Findings

Multiple proofs demonstrate the theorem's robustness.

Different methods highlight various aspects of the theorem.

The work consolidates understanding of knot curvature relationships.

Abstract

We sketch several proofs of F\'ary--Milnor theorem.