# The $\Lambda$-property of a simple arc

## TL;DR

This paper presents a new proof for a notable property of simple polygonal arcs in the plane and explores several generalizations of this property.

## Contribution

It offers a novel proof of Coulton and Movshovich's property and extends the concept to broader classes of arcs.

## Key findings

- New proof of the $\Lambda$-property for simple arcs
- Generalizations of the property to other arc classes
- Enhanced understanding of polygonal arc characteristics

## Abstract

In 2006 P. Coulton and Y. Movshovich established an unfamilar but note-worthy general property of simple, polygonal, open arcs in the plane. We give a new and quite different proof of this property, and we consider a few generalizations.