The Cloisters of Hauterive

Abstract

One of the most typical elements of Gothic architecture, tracery, is exclusively constructed from circular arcs and straight line segments. Traceries appear some 60 years after the first examples of Gothic churches in the 1200s in Reims, where their construction is 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 on Euclid’s Book IV on the regular n-gons carved in stone.

First published as: Benno Artmann , “The Cloisters of Hauterive ”, pp. 15–25 in Nexus I: Architecture and Mathematics, ed. Kim Williams, Fucecchio (Florence): Edizioni dell’Erba, 1996. This chapter originally appeared in The Mathematical Intelligencer, vol. 13, no. 2 (1991), p. 44–49. Reprinted by permission.

Benno Artmann (1933–2010).