Problems in the Cultural History of the Ellipse

Abstract

There are a number of problems relating to the history of the ellipse in Western culture that may make interesting research topics for readers of this journal. The two basic questions may be phrased as follows: Did the ellipse exist in architecture during the classical period? If not, when did architects first begin to use it? Answers to these questions would improve our information concerning the level of mathematical sophistication in Western society at various times in the past. Architects, as far as we know, have generally been neither academic mathematicians nor persons entirely without culture, so the knowledge available to them would give an indication of the permeation of mathematical concepts throughout the society. The test case for architectural applications of the ellipse in the classical period is the Roman amphitheater, which is normally oval in shape. Whether such structures were ever laid out as true ellipses remains, as far as I can tell, an open question. J. A. Wright, in his analysis of the plan of the amphitheater at Caerleon, finds that the arena was laid out as a series of curves that are segments of circles. The area from the edge of the arena to the external wall of the amphitheater is irregular, and Wright speculates that the surveyor may have left the layout of this area to the construction gangs. Wright also notes that the amphitheater at Trier was laid out much as was the one at Caerleon. A. Broch, however, in his analysis of the amphitheater at Pola, finds that the curve of the external wall describes an ellipse. It should be noted that Wright, in his discussion of Caerleon, does not rule out the possibility that some amphitheaters may in fact have elliptical plans.1