Party Game for a 500th Anniversary

TL;DR

This paper celebrates Durer’s 500th anniversary by exploring the enigmatic polyhedron in Melencolia I, demonstrating how the cross ratio can be used as an invariant to analyze its geometric and symbolic properties.

Contribution

It introduces the cross ratio as a tool for analyzing perspective and shape in art, providing a new method for interpreting complex geometric figures in historical artworks.

Findings

Cross ratio acts as a projectively invariant shape parameter.

The method aids in evaluating different theories of the polyhedron.

Demonstrates the application of projective geometry in art analysis.

Abstract

On the 500th anniversary of Albrecht D\"urer's copperplate engraving Melencolia I, we invite readers to join in a time-honored "party game" that has attracted art historians and scientists for many years: guessing the nature and meaning of the composition's enigmatic stone polyhedron. Our main purpose is to demonstrate the usefulness of the cross ratio in the analysis of works in perspective. We show how the cross ratio works as a projectively invariant "shape parameter" of the polyhedron, and how it can be used in analyzing various theories of this figure.