The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry
Art and Architecture
The Dual Language of Geometry in Gothic Architecture: The Symbolic Message of Euclidian Geometry versus the Visual Dialogue of Fractal Geometry
Nelly Shafik Ramzy
Recommended Citation
Part of the Ancient; Medieval; Renaissance and Baroque Art and Architecture Commons
The Dual Language of Geometry in Gothic
Architecture: The Symbolic Message of Euclidian
Geometry versus the Visual Dialogue of Fractal
Geometry
1. Introduction
When performing geometrical analysis of historical buildings, it is important to keep in
mind what were the intentions of the originators, even though these intentions have likely changed
many times as the master masons changed. For the medieval builders, geometry in design was a tool
used to structure ideas and aesthetic impulses or perhaps to incorporate into this work a meaningful
system of symbols; it was the internal logic of the building that mattered more than achieving
beauty or following the correct canonical models as was the case in Renaissance era.1 Geometry
was used in Gothic architecture as visual tools for contemplating the mathematical nature of the
Universe, which was directly linked to the Divine, the architect of the Universe as illustrated in the
famous painting of God the Geometer (Austrian National Library, Codex Vindobonensis 2554). To
seek these principles would thus be worshipping God.
The 1390s- Constitutions of Masonry or The Regius Poem opens with: "Here begin the
Constitutions of the art of Geometry according to Euclid."2 Regardless of the accuracy of this
document, the medieval masons clearly understood that the science of Geometry that they used was
received from its inventor: Euclid.
The medieval geometry of Euclid had nothing to do with the geometry that is taught in
schools today; no knowledge of mathematics or theoretical geometry of any kind was required for
the construction process of medieval edifices. Using only a compass and a straight-edge,3 Gothic
masons created myriad lace-like designs, making stone hang in the air and glass seem to chant.
In a similar manner, although they did not know the recently discovered principles of Fractal
geometry, Gothic artists created a style that was based on the geometry of Nature, which contains
myriad of fractal patterns.
Architectural theorists Nikos Salingaros and Christopher Alexander believe that buildings
must convey languages, among them are pattern language and form language; the former is the
basic system for the design of any space, while the latter is what makes the former unique and
beautiful; patterns are general and consistent throughout certain style, while forms are local and
changeable from one building to another.4 Applying this to Gothic architecture, one may say that its
general features, like pointed arches or high spires, are pattern language, while the specific design
of each building and how these patterns came together is the form language. Salingaros also writes
that, with the elimination of the ornaments and details within the range of scales -5mm to 2m or
thereabouts- which corresponds to human scale, the dialogue between architecture and human
beings is also removed.5 Based on this, the paper assumes that the Gothic cathedral, with its
unlimited scale, yet very detailed structure, was an externalization of a dual language that was
meant to address human cognition through its details, while addressing the eye of the Divine
through the overall structure, using what was thought to be the divine language of the Universe. It
discusses the hypothesis that geometry was used in the Gothic style to reproduce forms and patterns
that reflect this dual language. In doing so, master masons distinguished between the abstract
overall proportional lines of plans and elevations (form language), and the organic ornamental
patterns on walls, ceiling, openings, and pavements (pattern language). It is suggested here that
Euclidian geometry was employed for the, usually invisible, proportional or working lines of the
3 Lon
Shelby, Gothic Design Techniques, 1977
: 82–83.
4 Nikos Salingaros, Twelve Lectures on Architecture, 2010: 26.
5 Nikos Salingaros, Architecture, Patterns, and Mathematics, 1999: 61-72.
former, which are perceived only by the designer himself or by analytical view of the drawings with
a mesh of imaginary lines; while Fractal Geometry, was used for the visible details of the latter, at
which the worshipers can gaze and wonder about and may establish a "visual dialogue"; the former
is to address the eye of the Divine, while the latter is to address the earthly eye of humans.
This paper will test this hypothesis by finding the actual logic and context (proportional
lines, decorating pattern, invisible line, visible details, etc), with which these two types of geometry
were used in Gothic buildings, locating the settings (in structural elements, in plans, in decoration
elements, …etc.), in which they functioned in these buildings. It also aims to find the b (...truncated)