Abstract. Benno Artman examined the mathematical tracery of the Cloisters of Hauterive at the Nexus 96 conference.

Click here to go to the NNJ homepage

The Cloisters of Hauterive

Benno Artmann
Technische Hochschule, Darmstadt, GERMANY

 Tracery at the Cloisters of Hauterive

 One of the most typical elements of Gothic architecture is the tracery found in windows, on walls, and in many other places in Gothic churches. What is mathematical about it? Tracery is exclusively constructed from circular arcs and straight line segments! It is the most mathematical kind of art known to me. In many of the thousands of Gothic churches and other buildings of that time surviving in Europe you can find nice examples, take photos and analyze them geometrically at home.

Traceries appear some 60 years after the first examples of Gothic churches in the 1200's in Reims. There their construction is, like that of the typical pointed Gothic window, based on the equilateral triangle. In the course of stylistic development, the constructions became more and more elaborate and less determined by geometry until we find whole windows covered by wavy ornaments in the flamboyant late Gothic of about 1500.

Much more than the usual geometric designs of traceries can be found in the cloisters of the Cistercian monastery of Hauterive near Fribourg, Switzerland. Here the theme of the windows is geometry itself. Regular n-gons are shown for n = 3,4,5,6 and 8. Variations of the pentagon show the pentagram and a delicately constructed rose. The whole cloisters seems to be a commentary to Euclid's book IV on the regular n-gons carved in stone.

 The correct citation for this paper is:
Benno Artmann, "The Cloisters of Hauterive", pp. 15-25 in Nexus: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell'Erba, 1996. http://www.nexusjournal.com/conferences/N1996-Artmann.html

1996 Nexus Conference Abstracts Index

 top of page

next abstract

NNJ is an Amazon.com Associate

NNJ Homepage

 Conference Abstracts Index 

Search the NNJ

Order books!

Research Articles

The Geometer's Angle


Book Reviews

Conference and Exhibit Reports

Readers' Queries

The Virtual Library

Submission Guidelines

NNJ Editorial Board

Top of Page