Pentagram Map by Euclidean Approach

TL;DR

This paper presents a Euclidean geometric approach to the pentagram map, offering a modern perspective on a classical incidence geometry concept.

Contribution

It introduces a novel Euclidean framework for analyzing the pentagram map, bridging classical geometry with modern insights.

Findings

Provides a new Euclidean geometric formulation of the pentagram map

Enhances understanding of the map's properties through classical geometry

Suggests potential for further geometric analysis of discrete dynamical systems

Abstract

As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an alternative approach based on the setting of the ordinary Euclidean geometry.