Geometry behind the position of stairs: balance in the mind

Abstract

In this paper we examine the link between the human body and architectural design. For this purpose, we combine Cognitive Metaphor Theory (CMT) and geometry. We start from the hypothesis that the organization of space and the positions of stairs within the building floor plan is the result of the embodiment of human mind, which implies that abstract aspects of human thought are grounded in physical aspects of human body. CMT claims that BALANCE is a prototypical schema consisting of countervailing forces acting on a target. This mental structure arises from living in symmetrical bodies which are able to balance two equal halves and maintain erect posture. Having established the metaphorical mapping between the building and the human body (and, consequently, between the stairs and human spine) we examined the position of stairs in the building. We geometrically analyzed floor plans of a set of buildings applying the theoretical framework of Projective geometry and methods of Computational geometry. Our findings reveal that stairwells tend to stretch along the line which divides the building basis in two equal halves.