Frank Lloyd Wright geometry

The Ross Cottage and a Thesis

My overriding interest in Wright’s is in defining those characteristics that impart what we call beauty to the best of his work. Some works by Wright are universally accepted as being works of art, but the question is why they are so judged. There is also general acceptance that geometry plays a determinative role in Wright’s work. My aim is to explore the role of geometry in the best of his work, designs that display a universal quality of beauty, and do so in a way that is immediately understandable to the professional as well as to the layman.

Fallingwater is the best example of such projects; a truly outstanding work of art. Here is a building whose beauty is understood instinctively and immediately. No explanation is needed, no intellectualization. The beauty is just present in all its glory. If Wright's architecture did not have this enduring quality of art, none of us would today be discussing Wright or his work. However, no amount of intellectualizing about ethics, societal concerns, and the nature of materials, Froebel training, organic architecture, or other related subjects is going to explain why Wright's buildings possess beauty. All of the above are essential ingredients of the unfolded process but only the creative genius of the individual can combine every required element and produce a work of art.

Finally, only history will be the judge as to the lasting quality of any work of art. Wright was one of those individuals who created great art. Since the early work has passed the century mark, I think we can safely say his art will endure.

To a greater or lesser degree depending on the building, why is a Wright building beautiful? That beauty is rooted in the spatial quality of the building, and the space is a function of the geometry of the planes that determine the basic character of the structure. Strong geometry appears first in the floor plans of the earliest work but spatial quality appears, along with geometry, a bit later in the Playroom of 1893 and the Oak Park Studio of 1895, personal spaces for Wright. I make a distinction between spaces that Wright created for himself, ‘personal spaces’, and those he created for clients. He lavished his greatest talent on his own personal environments. He lived in these spaces and molded them to his will until they required no further refinement. I have discussed these particular spaces earlier.

I admit that I came to my basic conclusions quite inadvertently. While reading an essay about the influence of Froebel on the manner in which Wright used geometry, in this case with the Ross cottage, I found myself thinking, “This is sheer nonsense. Wright simply did not think that way.” This raised two obvious questions. The first is, if he didn’t think “that” way, how did he think, and secondly, how did I know how Wright thought? I had been exposed to Wright’s work for some fifty years at this point and obviously drawn some conclusions as to how he proceeded to solve architectural problems. That didn’t mean I approached the problem solving process by intellectual examination, but nevertheless I had concluded, at least in very broad terms, how he approached the architectural design problem. The next step was to examine how he thought, or did not think, about the Ross cottage.

The earliest published drawings of the Ross cottage were drawn especially for Frank Lloyd Wright's Ausgefurte Bauten; the Hitchcock drawings are derivatives of these drawings. They are all right for their intended purpose but are not adequate for serious examination. Neither the preliminary nor working drawings have ever been published, so a visit to the Getty Research Library was in order to examine images of the original drawings. Before I get to the Ross cottage, however, there are precursors to be considered bridging the gap between Wright’s 1889 house for himself and the 1902 Ross Cottage. After all, this is a period of 13 years. A sea change had taken place in Wright’s design vocabulary. The Ross cottage of 1902 is not only fascinating for its geometry, but is also prototypical of almost all the relevant forms common to Wright's residential work from 1902 to the time of his death in 1959.


By 1902, Wright was a major force in the field of architecture with several masterpieces to his credit, including the 1893 playroom added to his 1889 home, the 1895 Studio, the 1896 Romeo and Juliet windmill, the 1900 Bradley and Hickock houses, and in 1902 the Heurtley and Willits houses, the Hillside Home School buildings, and the Ross cottage.

The Ross and other concurrent cottages are of particular importance for their simplicity and originality of concept. They tend to be simple direct solutions to a problem. By 1900, he reached a new plateau of maturity with the Pitkin cottage. Like Wright’s own 1889 house, the Pitkin project is no masterpiece, but the design is important for the ideas that it represents. The most obvious feature of the scheme is the broad rectangular stylobate that serves as a base for the entire structure. The device is similar to the verandas in Wright’s 1889 house, but here is used much more decisively. The main body of the house is a simple rectangle that occupies the center portion of the stylobate and is congruent with it at the back wall. There is an 8’-0” wide cross rectangle defined by two service areas at the outside corners of the stylobate at the back. These alignments create a cross gable at the first floor whose ridge is in-line with the back wall of the second floor. The effect produces a consciously designed relationship that approaches the cruciform: what this cottage is all about. This device is obvious on the elevations, as well as on the floor plan, if you look. The broad chimney mass, which becomes dominant in future work, appears here for the first time and requires a walk through on the second floor, but does emerge as an exterior design element. Also, the first real, but incomplete, unit system makes an appearance. The Swiss Chalet look is out of place in the context of the ideas demonstrated in the concept of the job, which is clearly Wright’s. That look is particularly offensive on the South Elevation. The East Elevation best reveals Wright had in mind.

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Figure 1. Pitkin Cottage First Floor Plan. Frank Lloyd Wright Archives, Drawing  #0005.001 © Frank Lloyd Wright Foundation. Used by permission.
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Figure 2. Pitkin Cottage East Elevation. Frank Lloyd Wright Archives, Drawing 0005.009
© Frank Lloyd Wright Foundation. Used by permission.
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Figure 3. Pitkin Cottage South Elevation. Frank Lloyd Wright Archives, Drawing 0005.007
© Frank Lloyd Wright Foundation. Used by permission.

The George and Walter Gertscottages (Figures 4 and 5, and Figures 6 and 7, respectively) are important for their clarity and elegance of concept. There is nothing unaccounted for in these designs. Each is contained under one big roof, a device that will become a hallmark of Wright’s future work. The unit system is fully developed here, except that he throws an occasional odd unit in each case to accommodate a smaller dimension for the “pier” in the George Gerts cottage. The pier makes a decisive appearance here for the first time. The pier is essentially a masonry form and this presence in a board and batten structure is somewhat problematic, but the arrangement works architecturally to provide visual structural support where needed.

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Figure 4. George Gerts Cottage Floor Plan. Frank Lloyd Wright Archives, Drawing #0202.001.
© Frank Lloyd Wright Foundation. Used by permission.
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Figure 5. George Gerts Cottage Elevations, Frank Lloyd Wright Archives, Drawing  #0202.002. © Frank Lloyd Wright Foundation. Used by permission.
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Figure 6. Walter Gerts Cottage Floor Plan. Frank Lloyd Wright Archives, Drawing  #0203.001.
© Frank Lloyd Wright Foundation. Used by permission.
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Figure 7. Walter Gerts Cottage Elevations. Frank Lloyd Wright Archives, Drawing  #0203.001
© Frank Lloyd Wright Foundation. Used by permission.


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Figure 8. Floor Plans and Photograph. Frank Lloyd Wright, Ausgefuhrte Bauten

The Ross cottage is the last of the structures that has a pronounced stylobate, which here is the primary element of the design. This work is simply amazing for clarity of concept. Wright contemplates an entirely new architectural grammar that he senses only in big overall terms. Any new concept has to start this way. An idea must be worked until the light bulb goes off and understanding occurs. We have all experienced this; possibly in algebra class, or maybe English Literature. Wright was not fully aware of what he had done in this case, and that doesn’t really matter; the essential grammar was evident.

The original drawings are in a somewhat distressed state, but I would like to use them here anyway since they have never before been published and they do provide a lot of information.

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Figure  9. First and Second Floor Plans  Frank Lloyd Wright Archives, Drawing #0206.002.
© Frank Lloyd Wright Foundation. Used by permission.
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Figure 10. Elevations and Details. Frank Lloyd Wright Archives, Drawing #0206.001.
© Frank Lloyd Wright Foundation. Used by permission.

There are also two additional elevation sheets that were obviously drawn much later:

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Figure 11. Elevations. Frank Lloyd Wright Archives, Drawing #0206.003. © Frank Lloyd Wright Foundation. Used by permission.
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Figure 12. Elevations. Frank Lloyd Wright Archives, Drawing #0206.004. © Frank Lloyd Wright Foundation. Used by permission.

The house consists of three basic elements: the stylobate or base on which the house rests, the lower hip roof, and the upper hip roof turned 90 degrees to the lower. This disposition of two equal width hip roof lines at a right angle to each other is the hallmark of Wright's work for years to come and emerges as a major factor in their beauty. The geometry of the plan is as exact as any classical temple. The base is thirteen units square and defined by the six major piers. The lower hip roof, seven units wide and nineteen units deep, centers on the stylobate, overhanging by one unit on the front and extending beyond the stylobate five units on the back. The upper hip roof is also seven units wide and overhangs the stylobate on three sides by one unit, so that the diagonals of the hips coincide with the diagonals of the square stylobate base. The seven, one quarter unit square, visually supporting piers have their diagonals on the diagonal of a hip. The smaller columns determining the exterior closure line of the living room are in line with the two larger columns at the front and have one corner on the diagonal of the base. The chimney has one face on the ridge line of the upper roof and is centered on the ridge line of the lower roof. All this is very geometrically regular but not dull or static (Figure 13).

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Figure 13.  Ross House Schematic Plan.    John W. Geiger

I have chosen to use this plan (drawn August 9, 1986) because it is dated and because it is enhanced by the imprint of a beloved feline friend. I used green to outline the stylobate because it is the closest to earth and blue for the two roof outlines because they are closest to the sky. I find the geometry demonstrated here to be absolutely fascinating for the implications in his future work. As you have probably noticed, I have drawn the stylobate as defined by the six square piers because that is what was uppermost in Wright’s mind. The front railing varies from the basic scheme and was a mistake. Wright trys to do two different things here and the combination doesn’t work.

The stylobate and the lower roof and upper roofs should be considered as parallel horizontal planes. Separated by a story height, they float freely in space, with the additional plane of the earth being considered as the primary plane to which the other planes are related. If you come in one unit line from the roof perimeter and drop a vertical plane, you have the space available for use as enclosed space. This form can be considered for a one or two story space as required. Where more space is needed, either for practical of aesthetic requirements, the enclosing vertical plane can be moved out to the roof edge, but no further. The plane can also be moved inward from the one unit line for similar reasons, as in the living room. The position of the two roofs can also be reversed, as in the two story living room of the Isabel Roberts house.

A space is generated between the plane of the first floor roof and the stylobate. The stylobate continues outside the confines of the lower roof to form a relationship with the next available plane, which is the sky, wherever that happens to be. The second floor roof not only creates a relationship with the two constructed planes below, but where overhanging the stylobate conversely establishes a relationship with the next available plane below, which is the earth. Wright renders a relationship with both earth and sky.

  However, there is one big problem the way in which Wright develops this scheme: the relationship of the front line of the stylobate parapet to the roof above. He moves the parapet off the unit line to the inside face of the wood pier and introduces a projecting stylobate between these piers. This device makes the piers appear to be free standing. The other four piers defining the stylobate are in line with the parapet. The front parapet should also be in line with the front piers and on the unit line. He is trying to do two different things with this front parapet where he should be doing only one. He has already a schematic relationship between the stylobate and the roof plane above through simply overhanging the stylobate by one unit. What he is trying to do with the center projection is the reverse of what he has already achieved; namely to project the stylobate with its attendant parapet one unit beyond the roof line. He does this in a mature way with the Robie house west terrace in 1908. This is 1902, though, and Wright is struggling to invent an entirely new way of looking at architecture as a series of related planes. He pretty much does that schematically with the Ross cottage, but a full realization of what he had done had not yet entered into his conscious thinking. That is understandable, considering the scope of his undertaking.

With Robie he includes the balcony off the living and dining rooms, and the staircase from the terrace down to the first floor is in the equation. The two configurations of the Ross schematic and the Robie west terrace are really the same thing; one being the reverse of the other.

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Figure 14. Robie House Main Floor Plan, with colored overlay by John Geiger.  Sourced from Ausgefuhrte Bauten Frank Lloyd Wright, p. 113.

I am calling this simple relationship the Wright Paradigm, or the WParadigm for short. This basic relationship will occurs again and again in different guises in all of the best work for the rest of his career. I see the relationship as basically between two, or more, horizontal planes, but the vertical plane of the balcony or terrace parapet also plays a secondary role as a vertical plane forming a horizontal to vertical relationship as well.

  I also think that once Wright became aware of the WParadigm, he saw it as a very simple key to produce quality in his work and continued to keep the secret of how he worked from everyone, including the staff.  Maybe he didn't really see this approach as a secret, but simply as his way of working. Possibly it just never occurred to him that he might share the technique with anyone else. He lived in a world of his own creation that was not well populated with friends or enemies; or a wife and children, for that matter. His one big need in life was to be architecturally creative, and the second was for female companionship.

The stylobate of the Ross cottage was to make its last appearance for years to come, but the cruciform roof pattern is the configuration that will have the greatest impact on the work for the next five or six years. The form dominates all the best work. The WParadigm will come later. The Walser, Barton and deRhodes houses of 1903, 1903, and 1906, respectively, are direct developments of the Ross cottage. The 1902 Willits house and the 1904 Martin residence are both extremely sophisticated examples of the cruciform roof pattern. Like Wright’s 1889 for himself, the main roof dominates the composition. In both of these houses Wright takes great care to keep all the major architectural features of the house under outline of the roof. There is no indication of the WParadigm. In the Willits house, Wright extends the living room as a terrace at the front of the house but takes care that the second floor roof has a tight eave with the front elevation. There is no overhang of the terrace by the roof, thus avoiding the WParadigm. Still, the roof pattern is the dominant design consideration. The floor plan had to fit the roof plan.

  The roof plans of the Willits and Martin houses that follow clearly demonstrates the existence, and the importance of, the roof as a geometric pattern, and the subservience of the floor plan to that geometry.

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Figure 15. Willits house roof plan, with colored overlay by John Geiger. Frank Lloyd Wright Archives, Drawing #0208.004. © Frank Lloyd Wright Foundation. Used by permission.
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Figure 16. Martin house roof plan, with colored overlay by John Geiger. Frank Lloyd Wright Archives, Drawing #0405.005. © Frank Lloyd Wright Foundation. Used by permission..

The WParadigm of the Robie house might not seem like a sea change from the Willits and Martin houses, but it is, and as such marks the end of the Oak Park Grammar as well as Wright’s Oak Park life. Here is the beginning of the establishment of a relationship between the floor plane and the roof plane that would pervade Wright’s work for the rest of his life. The Oak Park grammar had run full course and change was in the offing.


To start the giant leap forward, let us draw an imaginary line in the sand. Take the Ross cottage schematic and project the corners of the stylobate and the first floor roof over the line in the sand. Then rechristen that line in the sand a waterfall.

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Figure 17. The Ross schematic, revised. John W. Geiger

And what do you have?

You have Fallingwater.

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Figure 18. Fallingwater, Original Sketch by Wright, with color overlay by John Geiger. Frank Lloyd Wright Archives, Drawing #3509.166.   © Frank Lloyd Wright Foundation. Used by permission.
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Figure 19. Fallingwater, Original Sketch by Wright. Frank Lloyd Wright Archives, Drawing #3602.166. © Frank Lloyd Wright Foundation. Used by permission.

I have repeated the drawing without my intrusion so that you can see that I only enhanced lines already drawn by Wright.

What makes Fallingwater “work” is the overlap of the two constructed planes of the first and second floors with the two natural planes of the top and the bottom of the waterfall; hence the engagement of the fall of the water from one plane to the other; or Fallingwater.

The rest is history.