IJUP08 - Universidade do Porto

Geometry and Space Conception the importance of the processes
of representation to Architecture
Bruno Russo 1 and João Pedro Xavier 2
1 Faculty of Architecture, University of Porto, Portugal.
2 Doctor, Professor of Geometry, Faculty of Architecture, University of Porto, Portugal.
What is the nature of space? What is our concept of space? Has it been unchangeable over
time? And how do the architects use this concept, or concepts, in order to create
architecture, the organization of space? The search for the idea of space starts at the
crossroads of Geometry and Architecture. If the latter is its organization and management,
the first, more than the science that studies space, is its very language, the ultimate tool for
the architect, even if sometimes he’s not aware of it. Geometry and Architecture have
evolved through time and their paths have often crossed, causing echoes on the individual
development of each.
Starting at Euclid’s Elements, the cornerstone of the western knowledge on geometry, and
following the major breakthroughs of this science of space, we try to understand the
influence they set on architectural production. On the other hand, by identifying turning
points on Architecture’s theory and/or practice we’ll search for reverberations on the
representation processes in particular, and on Geometry in general.
Architecture owes Geometry what Vitruvius called dispositio – the representation
processes. And since the ancient Greeks those processes have evolved: Euclid thought of
an infinite and plane space (Euclidean Space), Brunelleschi, Alberti and Piero della
Francesca invented the Perspectiva Artificialis, Desargues and Poncelet developed the
Projective Geometry, Monge codified a double-projection system, Lobachevsky, Bolyai
and others discovered the non-euclidean geometries, used by Einstein to re-design our
model of the Universe and finally, at the turn of the millennium, the computer-based
design knows mass use and becomes the only tool for many young architects.
The architects used the tools Geometry provided them, and “tuned” them. We cannot sever
perspective or Monge’s system from Architecture, and certainly can’t dissociate the
classical orders from Pythagoras’ view of the World. Nowadays we get entangled in an
overwhelming variety of forms and geometries, in a lack of “order” for the architect to
follow. Architecture pursued geometric values on the search of beauty and order for many
centuries, but now it seems these values have changed. Or have they not?
We think that the relationship between Architecture and Geometry is a symbiosis that can’t
be easily broken. We believe that the study of the history of Geometry can help us
understand the history of Architecture. Today we have more knowledge, more technology,
advanced engineering and higher levels of education. We need to know better the tools at
our disposal in order to produce better architecture. Geometry has always been our
premium tool but now, with the automation of the processes brought to light by the
personal computer, we tend to distance ourselves from the geometric definition of space
and form. And this can lead to a poorer comprehension of space, preventing Architecture
from achieving higher goals.
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