An Introduction to the Vesica Piscis, the Reuleaux Triangle and Related Geometric Constructions in Modern Architecture

Abstract

The focus of this paper is the Vesica Piscis, a symbol made from the intersection of two circles of the same radius and where the centre of each circle lies on the circumference of the other. The origin of the Vesica Piscis is uncertain, but it can be found in different cultures throughout many historical periods. The Christian religion was most likely responsible for its spread, first as a fish symbol, then as an architectural niche surrounding sculptures and drawings of Christ, and finally as the Gothic pointed arch. A related geometric construction is the Reuleaux Triangle, which uses three intersected circumferences. In the second half of the twentieth century several architects rediscovered both types of geometrical constructions, producing variations of each. This paper commences with an overview of the history and construction of these geometric forms, and then analyses existing buildings which use them, before discussing different design strategies to develop new mathematical models based on ancient designs.