The Polygons of Albrecht Durer -1525

TL;DR

This paper analyzes Albrecht Durer's 1525 geometric constructions for regular polygons, comparing original methods with modern computational approximations and discussing historical and current knowledge of compass and straightedge constructions.

Contribution

It provides a detailed examination of Durer's polygon constructions using original texts, diagrams, and modern computational tools, highlighting historical and mathematical insights.

Findings

Durer's constructions for polygons are largely accurate and insightful.

Mathematica simulations show close approximations to perfect regular polygons.

Durer's angle trisection method is notably precise for its time.

Abstract

The early Renaissance artist Albrecht Durer published a book on geometry a few years before he died. This was intended to be a guide for young craftsmen and artists giving them both practical and mathematical tools for their trade. In the second part of that book, Durer gives compass and straightedge constructions for the 'regular' polygons from the triangle to the 16-gon. We will examine each of these constructions using the original 1525 text and diagrams along with a translation. Then we will use Mathematica to carry out the constructions which are only approximate, in order to compare them with the regular case. In Appendix A, we discuss Durer's approximate trisection method for angles, which is surprisingly accurate. Appendix B outlines what is known currently about compass and straightedge constructions and includes two elegant 19th century constructions.