Learning from the Medieval Master Masons: A Geometric Journey through the Labyrinth

Summary

Introduction

In recent years, there has been a resurgence in understanding, constructing, and walking mazes and labyrinths, many originating from the Middle Ages. For the student of mathematics, these novel geometric objects can be an experience in the power, beauty and utility of mathematics.

These qualities of mathematics were well appreciated by medieval master masons, the designers and builders of the great pavement labyrinths in some of the medieval churches and cathedrals. Master masons worked their way up the ranks of stonemasonry starting with demanding years of apprenticeship. There were many tools for stone cutting and sculpting to master. The key and emblematic tools for stonemasonry were large compass-dividers, set square [Figure 1], and measuring rod. These tools underscore the master masons' skill in practical geometry, not in theoretical mathematics involving axioms, theorems and proofs [1]. Common mathematical and geometrical motifs of the master masons [2] were:

1. a) a square rotated a half of a right angle about its center,

2. b) the square's side to its diagonal (in modern terms, unknown to the medieval mason, 1:,

3. c) the equilateral triangle's half-side to its altitude (in modern terms 1:,

4. d) the regular pentagon's side to its diagonal (in modern terms the ‘golden section’ and, and

5. e) simple whole number ratios, e.g., 1 : 1, 1 : 2, and 3 : 4.

Designs were translated to full-scale templates, made of cloth and wood, for the cutting of limestone, sandstone, and marble [3].