Understanding Geometry and Cathedral Design Through Experiential Learning


The beauty and grandeur of medieval cathedrals lies not only in their sheer size, but also in the harmonious proportions that result from using principles of ancient geometry in their design. This experiential learning project demonstrates the interrelationship of mathematics and design in medieval architecture through the practical application of geometry. Reading assignments (see below) should be completed before the first activity.

In the first activity, students draft a cathedral plan using geometric tools (compass, straight edge, and protractor). The second part of the activity takes place on a campus green space where students physically lay out a scaled cathedral plan, ad quadratum (Latin for “from the square”) following the plan completed in the first activity. The first activity is detailed in the step-by-step guide below, but the second activity is instructed in person, as a master mason would have done, by transmitting information verbally to apprentices and other masons on the building site. In this part, students use the plans they have drawn, but now points on the plan are marked out by wooden stakes and string is used in place of the compass to generate measurements and mark boundaries.

After completing the readings, plan, and layout students will have both a theoretical and experiential understanding of how proportions based on the square root and the Golden Ratio (1:618) find practical application in medieval architecture. As a way to synthesize learning, each student should complete short (2-3 pgs.) reflection paper that consider the ways in which the process of drawing and laying out the plan deepened understanding of the relationship of geometry and design in medieval buildings.

Learning Outcomes

  • Gain a greater understanding of the parts of a cathedral plan and use correct architectural
  • Analyze the interdependence of mathematics (geometry) and aesthetics in the design of cathedral
  • Understand the relationship between the ideal (plan) and real layout of a
  • Develop creative solutions to practical problems through problem
  • Collaborate in a group setting to achieve a common

Reading Assignments

Robert Bork, The Geometry of Creation: Architectural Drawing and the Dynamics of Gothic Design (Ashgate, 2011), 1-27.

Stephen Murray, Notre-Dame, Cathedral of Amiens: The Power of Change in Gothic (Cambridge UP, 1996), 28-43.

Other suggested readings:

Carl F. Barnes, The Portfolio of Villard de Honnecourt (Paris, BnF, MS Fr 19093): A New Critical Edition and Color Fascimile (Ashgate, 2009).

Nicola Coldstream, Medieval Craftsmen: Masons and Sculptors (British Museum Press, 1991).

Nancy Wu, ed. Ad Quadratum: The Practical Application of Geometry in Medieval Architecture (Ashgate, 2002).


Activity Guide (PDF)



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