Unexpected Sense of Symmetry Inside the Projection

Abstract

Aim of this work is to focus on some aspects of symmetry in the light of a projective ap- proach not strictly metrics oriented. What seems to be permitted by etymology, since as we know, more than to metrics itself, the word symmetry refers to relations (syn = together with) by, or, in metrics (metron = measure). Regarding architectural design and construction, despite the dominant idea (and practice) for long mainly based on axial and polar metric mirroring, emphasis on sym- metry as a relationship among components of architectural spaces considered as systems was al- ready at the base of the classic compositional approach. From this side, metric-based symmetry may be seen as a subset of the overall symmetry. Inspiration came from Projective Geometry and its applications to architectural survey and design, where the relationship between space and image gets the stage. And the research question arose: if thousands of images (projections) can be gener- ated from one space (physical or theoretical), is it allowed, and in which way, to look for a ‘sense of symmetry’ inside those interrelated graphic representations? Answering this question would have implied thinking about symmetry as a transformation in a wider sense and going beyond the classic Euclidean borders according to the modern concept of space. Then we entered the projec- tive world looking at its relational more than metric side, where homology seemed to offer a valid vessel to sail onboard.