University of Wisconsin-Milwaukee, USA
School of the Art Institute
From the very beginning my T-square
and triangle were an easy media of expression for my geometrical
sense of things.
Frank Lloyd Wright [1946:
There has been an
enormous expression of public interest in Wright in the last
two decades. Publications, exhibits, tours, artifacts, drawings,
documentaries, catalogs of Wright paraphernalia and even an opera
have created new recognitions and appreciation for Wright 's
work well beyond the architectural profession. However, there
remains a gap between the public presence of Wright and the academic
integration of instruction of Wright's use of mathematics and
geometry in architectural institutions. What has been the influence
of Wright in the profession of the late twentieth century and
what is the influence of Wright in the current generation of
architects? This paper describes a seminar that seeks to answer
these questions with evidence of a renaissance of work in the
twenty-first century that emanates or owes allegiance to mathematical
explorations configured in Wright's body of work. This seminar,
The Geometry of Wright, offers students in the state of Wisconsin
the opportunity to learn about Wright's life, those who influenced
him, and those whom he influenced. The combination of history,
theory, mathematics, and design activities in this seminar offer
students an opportunity to become aware of Wright's use of geometry,
understand its roots and precedents, and apply them to a project
of their own. This whole language approach to learning embeds
appreciation of mathematic principles and encourages students
to apply geometric relationships in their own search for proportion
Scully suggests that many twentieth-century historians have marginalized
Wright. "The excellent students who flocked to Gropius and
his associates at Harvard and elsewhere in the forties were indoctrinated
with a deep suspicion of Wright's motives and a kind of sociological
contempt for his buildings" [reference]. Soon the younger
architects were themselves acting as critics in most of the better
architecture schools throughout the country and today are in
leadership positions in many of those same schools. For this
reason, "no serious attempt to teach and develop the principles
of Wright's design concepts have been consistently sustained
in America, outside of Wright's own inbred Taliesins" [reference].
Henry Russell Hitchcock and Philip Johnson eventually refer to
Wright as the Michelangelo of the twentieth century, as the "exception
that illustrates the rule" [Hitchcock and Johnson 1948;
Johnson 1979: 75].
Sixteen buildings have been designated by the American Institute
of Architects to be retained as examples of his architectural
contribution to American culture:
and Studio, Oak Park, IL, 1889-95
- Winslow House,
River Forest, IL, 1893
- Willits House,
Highland Park, IL. 1901
- Unity Temple,
Oak Park, IL, 1906
- Robie House,
Chicago, IL, 1909
- Hollyhock House, Los Angeles, CA, 1917
Spring Green, WI 1911-25
- Johnson Wax Administration Building, Racini, WI,1935
Bear Run, PA, 1936
- Taliesin West,
Scottsdale, AZ, 1937
- Johnson Wax Tower, Racini, WI, 1945
- Unitarian Universalist Meeting House, Madison, WI, 1948
- Price Tower,
Bartlesville, OK, 1948
- Beth Shalom Synagogue, Elkins Park, PA, 1954
- Guggenheim Museum, New York, NY, 1956
This seminar, "The Geometry of
Wright", aims at exploring and building evidence and continuation
of the geometric heritage of Wright's prolific practice to his
influence on practitioners today. The quality of Architecture
is left to interpretion, but geometry is different. Since mathematics
is present in all of physics, and letters are the foundation
of words, geometry must be found in architecture. As we respond
to architecture with emotion, the mathematics of geometry appeals
to our intellect. It is about relationships and the search for
absolute truth just as the architect searches with relationships
for absolute beauty.
This seminar is organized in four parts:
- Introduction to Frank Lloyd Wright's
life (focusing on significant influences on his uses of geometry
- Introduction and analysis of Wright's
use of geometry;
- Review and Research of Current practices
which translate, interpret and innovate from the mathematics
and geometry used by Wright;
- Conceptualization and construction
of an artifact.
1. INTRODUCTION TO FRANK
LLOYD WRIGHT'S LIFE
seminar summarizes key influences from practice, education, and
travel that informed Wright's use of mathematical relationships
and influenced explorations of geometric relationships in possibilities
for habitation, spatial manifestations, and form achieved in
the landscape. Many historians have articulated a series of influences
upon Wright. Vincent Scully , Kevin Nute , Anthony
Alofsin , Robert McCarter , Grant Manson ,
and many others have established the educational process that
Wright found outside of academia. Wright enrolled briefly in
the School of Engineering at the University of Wisconsin in Madison,
but was educated as an architect from childhood education, mentors,
and his contemporaries. The education of Wright is introduced
to draw parallels and highlight differences with the young collegiate
Frank Lloyd Wright was born Frank Lincoln
Wright on June 8, 1867 in Richland Center, Wisconsin. He lived
until 1959 and built close to 500 buildings, with hundreds of
other projects unbuilt. He worked for two architects, first Joseph
Lyman Silsbee and, later, Louis Sullivan at the firm Adler and
Sullivan in Chicago. He lived most of his life in Wisconsin,
also living in Illinois and his winter retreat at Scottsdale,
Arizona. His life was built on reconciling the machine to the
patterns of nature, the rights of the individual to the need
for community, and the cause for American architectural values.
William Cary Wright, his father, was
an English non-Conformist who emigrated to the US. He was an
itinerant Baptist preacher, pianist, and composer who instilled
in the young Wright a reverence for music, and a passion for
Bach and Beethoven. William worked his way through a diverse
range of occupations -- lawyer, administrator, minister, music
teacher, pianist and organist. Anna Lloyd Jones, his mother married
William in 1866. She was the daughter of Welsh immigrants, fifteen
years younger than William. As a schoolteacher, she instilled
in young Wright a reverence for poetry and literature. Frank
was the first of three children. Anna gave Wright copies of Stones
of Venice and The Seven Lamps of Architecture by John
Ruskin, mentor to art and architectural appreciation of the Victorian
Age. At the 1876 Philadelphia Centennial, when Frank was nine
years old, Anna first found the Froebel series of educational
Frederich Froebel, a major childhood
influence to Wright, was a crystallographer before becoming an
educator. The connection in his Education of Man in 1826
says that whether inorganic or organic, crystalline or non-crystalline,
developmental processes all remain the same -- a balance between
inner and outer, or an outward developed from within. He strove
to strengthen the inner forces or natural inclinations and enrich
the outer forces of the environment. The block system that he
designed was to nurture learning about form and relationships
in children from two years old to adolescence. In the kindergarten
education system, four main natural laws apply.
- The Law of Unity, which unites all
- The Law of Opposites, each entity having
- The Law of Development, entity develops
- The Law of Connections forms a continuum
of time from the smallest particle to the cosmos.
The first half of the exercises is called
Gifts, the second half is called Occupations. Altogether,
the gifts form a complete whole with parts that explain each
other. Each part is a complete whole connected to further development.
They cover intuitive and sensory instruction through spatial
instruction. The patterns were not intended to be merely aesthetically
appealing, but to engage the intellect to understand a sense
of harmony. The arrangements are categorized into three types
of forms -- abstractions of familiar objects, principles
of simple mathematics, and forms of beauty from the
infinite variety of symmetrical and asymmetrical balanced forms.
The Gifts move from the concrete to the abstract -- from the
solid to the planar -- in an attempt to reveal the rhythmic structure
in Nature. This comprehensive vision in which aesthetics are
inseparable from the universal principles of form informed Wright's
work throughout the decades.
Wright moved from the rural Unitarian
transcendentalism of south-central Wisconsin to the speed of
the Industrial Revolution in post-Fire Chicago, a city where
a new building was built every eighteen hours after the Great
Fire of 1871. By century's end, the stylistic debate of the nineteenth
century had been eclipsed by the Art Nouveau. In the Midwest,
the greatest contributor to the Art Nouveau was Louis Sullivan,
with his rich integration of ornamentation. As the most direct
and significant influence on Wright, it is important to review
the key Sullivan influences.
In Chicago, the Adler and Sullivan partnership
was in the mainstream of architectural development from 1883
until Adler left in 1895. Wright was made responsible in 1890
for the firm's domestic work. Sullivan had published a transcendentalist
interpretation of the form follows function idiom. H. H. Richardson's
Romanesque designs were a catalyst for early Sullivan work. Then,
Moorish architecture of Muslim form and principles of design
was evident in three commissions between 1890 and 1892 -- the
Getty and Wainwright tombs, and the Transportation Bldg at the
1893 Fair. The Getty Tomb is the first complete application of
his design system of ornamentation. Sullivan progressed to a
naturalism of organic and geometric combinations. However, the
decorations never reached beyond the surface. Wright culminated
his work with ornamental integration turning intellectual theory
Another early influence, Josef Maria
Olbrich was a principle member of Otto Wagner's Vienna Secessionist
movement, in which a rejection of historical forms was declared
as well as a reassertion for principles such as harmony, order,
and symmetry. Wright, William Maher and Robert Spencer visited
the 1904 St. Louis World's Fair where they would have seen Olbrich's
German Pavilion and several interior design installations by
other Secessionist architects and designers.
The Museum of Modern Art's 1937 exhibit
on the International Style presented Wright as a predecessor
to Modernism but a contemporary would be more accurate. Many
of Wright's ideas were contemporary to the Bauhaus of 1925. Each
was concerned with the possibilities of geometries. Froebel has
been acknowledged as an influence on both Wright and the Bauhaus.
Both stressed primary shapes and agreed upon the symbolism of
each. The Bauhaus integrated total design much the way the Frank
Lloyd Wright School of Architecture at Taliesin integrates the
Arts in their curriculum. The Dutch Modernist J. J. P. Oud acknowledged
Wright in the Dutch publication of DeStijl citing "new
plastic architecture, using the primary means of the movement
of planes to open up entirely new aesthetic possibilities for
architecture." "Nature has a practical school beneath
her more obvious forms in which a sense of proportion may be
cultivated..." [Oud 1918].
Wright also looked westward for inspiration.
The Aesthetic Movement of the 1880s had a cult of the Japanesque
and Wright was introduced to authentic Japanese art in prints
and the exhibits at the 1893 Fair in Chicago. The Fair's Ho-o-den
Japanese pavilion contained a cruciform plan, and a repeated
square as basis for proportioning around a central shrine. The
"elimination of the insignificant," a process of simplification
in Japanese prints, was a great resource to Wright in giving
direction to new concepts of space, furnishings, and the detailing
of materials by reducing complex natural forms into their simple
geometrical essence. Wright wrote The Japanese Print 
as a publication on Ukiyo-e, in which he explains the mystery
of the Japanese print. Wright would work through the process
of abstraction to neutralize the subject. Stressing aesthetic
idealism, spirituality, democracy, and organic nature influences
from Japan, Wright understood the complex idea of collapsing
transcendental ideas into architectural form.
Arthur Dow was a teacher of the first
Modernist generation and author of a general system of art education
radically different from the norm. In Dow's text, Introduction
to Composition , the relations of line mass and color,
could not be given by dictation or acquired by reading, but understood
through completion of exercises in creating harmony through composition
dependent on proportion. The five devices are: Opposition, Transition,
Subordination, Repetition, and Symmetry. These aspects were incorporated
into a general theory referred to as pure design. The principles
brought together harmony, balance, and rhythm in art. Abstraction
of form through elemental geometry created simple arithmetic
ratios. All aspects of Wright's work artifacts are treated as
a whole based on a system of design.
2. INTRODUCTION AND ANALYSIS
OF WRIGHT'S USE OF GEOMETRY
This part of the seminar is an introduction of
the relationship of mathematics, in particular geometry, to the
architecture of Frank Lloyd Wright. Students begin their work
with analysis of the geometry of Wright of various sites. We
know that from the visual world to the invisible sub-atomic world,
all forms are made of connected geometric patterns and relationships.
Geometric diagrams are ways to reveal timeless and universal
ideas hidden from our senses. A common mathematical solution
can become a resource for great intellectual and spiritual insight.
The square, rectangle, octagon, triangle,
hexagon, parallelogram, circle, spiral, and arc are keys to the
consistent and systematic quality underlying all of Wright's
work. They allow an ordering of space that encompasses both composition
and construction. Using nature as his mentor and geometry as
his tool he developed what he called organic architecture. He
used number, geometry, proportion, pattern, hierarchy and orientation
in all of his work. Wright used geometry as a formative idea
with the concepts of plane and solid geometry determining the
built form. Besides basic platonic geometries, Wright used combinations,
multiples, derivatives, and manipulations. This structural vocabulary
that was developed throughout his life consists of a three-dimensional
field of lines through which the solid elements of the building
are located enabling the voids to be integral to the whole and
equally meaningful. Architecture was, after all, the space.
To achieve the qualities of repose and
unity, the natural ornament was conventionalized through geometry
to bring out the underlying form- a nature pattern study. Wright
used a range of geometric grammars in which the controlling geometric
unit ordered the plan and drove the detail development. Units
can be equilateral triangles, or four foot squares or a series
of circles. "Planned progressions, thematic evolutions,
the never-ending variety in differentiation of pattern and to
integral ornament always belonging naturally enough to the simplest
statement of the prime idea upon which the superstructure is
based" [Wright 1946: 423].
Seminar sites (vary from year to
- Willits House,
Highland Park, IL. An asymmetrical matte of tartan grid lines
from rectangular rather than square blocks, would express the
grid at all points down to features such as balconies and built-ins,
urns and clustered piers. The simple uniform grid moved to a
symmetrical grid, which in turn moved to an asymmetrical grid.
The line-ideas generate the decorative designs of windows [McCormac
- Cheney House,
Oak Park, IL. Cheney House uses a tartan grid for the entire
site, part of a grid for the city and the whole state. The processional
path to the center of the house moves the viewer through a series
of framed vistas passing planters and steps observing the house
all around the grid. This oriental expression of space prepares
the viewer for the private domain and many the confrontations
of texture the materials and transparency of the public and private
- Jester House
(Pfieffer House), Phoenix, AZ. The tessellation of a singular
unit, either square, hexagon or triangle is used in many of his
works. In the Sundt House of 1938 he used a hexagonal grid with
an overall triangular grid that contains it. In the Life Magazine
Home of the same year, he used a square grid and in the Jester,
a circular system. Mapping out Wright's homes in terms of functions,
many homes are schemed to be identical but look markedly different
due to a change in unit geometry. In these three homes, one arrives
under a carport, passes through a yard area, enters the kitchen
or office, or passes through to the entry area and onto the family
room around which radiate the living, dining and bedrooms.
- Greek Orthodox Church, Wauwatosa, WI. This church sets a concrete
bowl upon a Greek cross structure. The structural system is based
on the same ordering as the textile block. The plan reduces itself
to one dominant entry. The main altar does not lie on the same
axis as the entrance loggia.
- Jacobs I,
Madison, WI. The Usonian houses are natural transformations and
developments from the prairie houses. The diagonal movement experience
of the prairie houses became the primary spatial order of the
Usonian houses. Outside and inside merge with overlapping and
layered spatial definitions. Balance between abstract geometry
and nature is examined in Sargeant [1975 and 1976].
- Hollyhock House, Los Angeles, CA. Poured-in- place concrete
greatly advanced ornament towards structure in helping to modify
or emphasize the lines or planes of a composition. Surface patterns
in bands of stucco or terra cotta panels were exchanged for energetic
three-dimensional devices at the Hollyhock House (Indian princess
surveying her lands) and A D German Warehouse. The Hollyhock
fireplace with reflecting pool, relief mural, and skylight above
incorporate overlapping disks and the square, and ideas unique
to Ms. Barnsdall.
- Guggenheim Museum, New York, NY . The dome of this most important
commission is a web of 6 parabolic arches focused on a central
hexagon framing a central circle. The viewer in the cylinder
identifies with the geometry. The earth and heaven with a column
of light establish the vertical axis. A 1/4-mile gallery at 3%
grade gives a sense of the cosmos of this reversed ziggurat.
- Johnson Wax Administration Headquarters, Racine, WI. The slender monolithic dendriform
shafts stand on metal tips bedded at the floor level. In botanical
terms, it describes the various parts - stem, petal, and calyx.
The innovations allowed the column to be an aesthetic element
and not just a support device. Wright's endeavor to synthesize
technology in a building produced a structured architecture.
The elements of a building can be brought together in a logical
manner, freed from ambiguous meaning, into a form whose character
is governed by a sense of order.
The scholarship grows in this area,
building upon important work from Richard McCormac , Nute
, Sargeant [1975 and 1976], Eaton , Laseau and Tice
, and Koning and Eizenberg .
3. REVIEW AND RESEARCH
OF CURRENT PRACTICES, WHICH TRANSLATE, INTERPRET AND INNOVATE
FROM THE MATHEMATICS AND GEOMETRY USED BY WRIGHT
Part three of this
seminar analyses the work of contemporaries and the first generation
of work after Wright. These architects represent work achieved
in Denmark, Germany, Holland, Belgium, Italy, Spain, England,
France, the United States, Mexico, Canada, Chile, Argentina,
Theo van Doesburg
Greene and Greene
Josef Maria Olbrich
Willem M Dudok
Walter Burley Griffin
Mies van der Rohe
Robert Van t'Hoff
D E Harrington
John Randall MacDonald
Tallmadge & Watson
Marion Mahoney Griffin
Lowe u. Giest
Kuhnert u. Pfiefer
Duiker & Bijvoet
E Fay Jones
Eric Lloyd Wright
Koning and Eizenberg
Wiehle & Carr
Anthony Alofsin  and Heidemarie Kief  both cover
many influences globally but stop short of twenty-first century
4. CONCEPTUALIZATION AND
CONSTRUCTION OF AN ARTIFACT
Students have a chance to apply ideas about geometry
in nature through the ideation, development and construction
of an artifact. Desk lamps, sconces, mobiles, desk organizers,
candleholders, glassworks, fountains, storage units, etc. are
all attempted and achieved through a series of traditional design
studio exercises. Students are evaluated on concept, use of geometry,
geometries expressed, scales, appropriate use of materials and
craftsmanship. Examples of student work are shown below.
Alofsin, Anthony. 1999. Frank Lloyd Wright: Europe
and Beyond. University of California Press.
------. 1993. Frank Lloyd
Wright: The Lost Years. Chicago: University of Chicago Press.
Dow, Arthur. 1998. Introduction
to Composition. University of California Press.
Eaton, Leonard. 1998. "Mathematics
and Music in the Art Glass Windows of Frank Lloyd Wright."
Pp. 57-71 in Nexus III: Architecture and Mathematics.
Kim Williams, ed. (Fucecchio, Florence: Edizioni dell'Erba).
Frederich Froebel. 1826. The
Education of Man. Rpt. 1887, New York: Appleton and Co.
Hitchcock, Henry Russell and
Philip Johnson. 1948. MOMA bulletin 15, 3: pp.
Johnson, Philip. 1979. Writings.
New York: Oxford University Press.
Kief, Heidemarie. 1983. Frank
Lloyd Wright und Europa. K. Kramer, Augs edition.
Koning, Hank and Julie Eisenberg.
. "The Language of the Prairie: Frank Lloyd Wright's
Prairie Houses." Environment and Planning 8,
Laseau, Paul and James Tice.
. Frank Lloyd Wright, Between Principle and Form.
New York: John Wiley and Sons.
Manson, Grant. 1958. Frank
Lloyd Wright to 1910. New York: John Wiley and Sons. (reissued
McCarter, Robert. Frank
Lloyd Wright: A Primer on Architectural Principles. New York:
Princeton Architectural Press.
McCormac, R. . Anatomy
of Wright's Aesthetic. Architectural Review 143 (February
Nute, Kevin. 1997. "Frank
Lloyd Wright and Composition: The Architectural Picture, Plan
and Decorative Design as Organic Line-Ideas." Planning
Perspectives 11, 1 (April): 198-200.
Oud, J. J. P. 1918. DeStijl.
Sargeant, John. 1975. Frank
Lloyd Wright's Usonian Houses. New York: Watson Guptil Publications.
------. 1976. "Woof and
Warp: A Spatial Analysis of Frank Lloyd Wright's Usonian Homes,"
Environment and Planning B 3: 211-224.
Scully, Vincent. 1960. Frank
Lloyd Wright. New York: G. Braziller.
Wright, Frank Lloyd. 1912.
The Japanese Print. New York: Horizon Press.
------. 1946. Autobiography.
New York: Longman's, Green and Co.
Mark Keane and Linda Keane were trained
in the 1970s in an architectural education of modernism transitioning
into post-modernism. Linda received her first architectural degree
along with an environmental design degree from Ball State University,
College of Architecture and Planning. Mark received his first
architectural degree from the University of Illinois at Urbana-Champaign.
Linda's introduction to Wright began in high school art class
with study of the Modern masters, Mies van der Rohe, LeCorbusier,
and Wright. In college, architectural history lectures of the
Robie House in Chicago, the Home and Studio in Oak Park, and
the Guggenheim Museum in New York preceded field trips to these
sites. For Historic American Building Surveys, she completed
documentation of a Wright Usonian home, the Haynes Residence,
in Fort Wayne, Indiana. Her graduate experience in Chicago was
an introduction to the classical language, Chicago's tall buildings,
and critical studies in the process of aesthetics, design, and
architecture. Mark's experience with Wright came from lectures
by Professor Walter Creese at the University of Illinois at Urbana
-Champaign, and tours of Wright's work in Oak Park.
Mark and Linda's first studio of collaborative practice was established
in Oak Park near Wright's Home and Studio, at a time when they
were both teaching in the Department of Interior Architecture
at the School of the Art Institute, whose original founder, Marya
Lilien, was the first female apprentice to Wright at Taliesin.
Linda also team-taught a third year studio at UIC that focused
on disseminating differences in reinterpreting the modern language
of Mies van der Rohe, Le Corbusier, and Frank Lloyd Wright.
In the 1990s Mark and Linda began the Frank Lloyd Wright Initiative
at the University of Wisconsin at Milwaukee. In 1993, the University
of Wisconsin-Milwaukee established an enhanced program that expands
the students' understanding of the importance of Wright as an
architect and as cultural icon. The Frank Lloyd Wright Initiative
has generated graduate level studios, seminar courses on the
impact of Wright on American Heritage, and expanded Historic
American Building Surveys of important Wright structures. A series
of research projects, including Wrightscape: The Geometry of
Wright has been partially supported by the Wright Initiative.
A number of distinguished guests have given public lectures on
the legacy of Frank Lloyd Wright, promoting greater accessibility
and understanding of the work of this master architect.
The correct citation for
this article is:
Keane and Linda Keane, "The Geometry of Frank Lloyd Wright",
Nexus Network Journal, vol. 7 no. 1 (Spring 2005), http://www.nexusjournal.com/Keane.html
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