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The Language of Architecture by Val Warke, Andrea Simitch

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As alchemists sought inscrutable objectives that included
philosophical and spiritual insights, material transmuta-
tions, astrological projections, and even immortality, they
forged a path that led them to discoveries in sciences
such as chemistry and medicine. Similarly, architects
There is a certain aspect of descriptive geometry that prefigures the visual impact of certain
forms: geometry can present not only what something physically
is
, but projective geometry
can also prefigure
what can be seen
from specific viewpoints, and how complex figures can be
broken down into buildable components.
23
geometry
THE LANGUAGE OF ARCHITECTURE
with diverse utopian aspirations, including
the idealization and optimization of various
spiritual, cultural, aesthetic, material, health,
and environmental goals, have found their
paths most frequently plotted through
geometry.
For thousands of years, most architecture has
been composed of cubes, cylinders, spheres,
cones, and pyramids. Perhaps more than the
development of new materials, new represen-
tational techniques eventually accompanied
by new skills in fabrication have caused
architectural form to develop more elaborate
geometries. Guilds of medieval stonemasons
sharpened their skills as cathedrals reached
higher. In the Renaissance, linear perspective
expanded techniques for the study of
descriptive geometry. Later, in the baroque,
geometries merged and warped as stereo-
tomic techniques were perfected and
craftsmen developed skills in turning wood
and ivory on lathes in fabricating exception-
ally complex objects.
Numbers
Perhaps the most pervasive and persistent
geometries are those based on the golden
ratio. Known since the time of Pythagoras,
this ratio has fascinated mathematicians and
artists for over 2500 years. Golden ratios
and their rectangles have a capacity for
continuous regeneration and subdivision,
and can be found throughout nature, from
nautilus shells to the length of our finger
bones, and it forms the basis for many
investigations into five-fold symmetry
(important in pattern theories). Perhaps
because of its ubiquitousness, artists and
architects have long considered the golden
rectangle to be one of the most visually
pleasing geometric figures.
The golden ratio is closely approximated by
the more finite Fibonacci series—1, 1, 2, 3, 5,
8, 13, and so on—which approaches the
golden ratio of 1: (1.6) as it progresses.
The Fibonacci series forms the basis for
Le Corbusier’s Modulor proportion system
as well as numerous theories of plant and
animal growth.
Religious and governmental architecture
has frequently employed geometries for
their symbolic significance, with equilateral
triangles, squares, pentagons, hexagons,
and so on being used in plan, elevation,
and volumetrically in order to emphasize
the liturgical or historical importance of
certain numbers.
merged with hexagons,
squares embedded in
trapezoids—combined
optimized strategies of
defense with Renaissance
theories of ideal proportion
and universal harmony. As
with most intended utopias,
Palmanova’s idealization has
proven uncongenial to
everyday inhabitation.
use of these proportions
throughout a building would
assure a harmony of the parts
and a sense of human scale
as well as to foster the
development of potential
standards for building
materials and fixtures. It is
here imprinted on his Unité
d’habitation in Marseille,
France, of 1947-52.
cally appear in every aspect
of the building complex,
often combined with the
figure of a tongue, relating
to the legend of St. John’s
martyrdom upon his reputed
refusal to break the silence
of the confessional.
Senatore in Rome (completed
in the seventeenth century),
revealing golden ratios
between the base and upper
stories as well as within the
overall dimensions of the
surface.
Vincenzo Scamozzi’s
Palmanova (designed 1593)
was considered to be the ideal
fortified outpost city of the
Venetian Republic. Its
original ramparts form a
nine-pointed star with its
three entry boulevards
culminating in a hexagonal
central piazza. Its
geometries—nonagons
Le Corbusier’s Modulor 2
proportioning system begins
with the height of a 6-foot
(1.83 m) person—the ideal
English detective hero,
according to Le Corbusier—
with an uplifted arm at 7 feet,
5 inches (2.26 m), subjecting
the increments to subdivision
by means of a Fibonacci
series. His belief was that the
In Jan Blažej Santini’s
exuberant Church of St John
of Nepomuk at Zelená hora in
Žd’ár nad Sázavou (Czech
Republic, 1721), the numbers
five and three—which figure
prominently in the saint’s
hagiography as well as
Christian theology—symboli-
The golden section rectangle
has been used throughout
much of architecture’s history
as a proportioning tool. Here,
it is superimposed on
Michelangelo’s restructured
façade for the Palazzo del
(continued on page 192)

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