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Geometry in Architecture

Geometry in Architecture
Texas Buildings Yesterday and Today
Foreword by Louis Kahn; original edition photography by Maryann Heimsath; revised edition photography coordinated by Lisa Hardaway

How geometric forms are used in historic and modern buildings.

July 2002
180 pages | 8.5 x 11 | 370 photos, 37 line drawings |

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Pioneer Texas Buildings opened people's eyes when it was first published in 1968. At a time when "progress" meant tearing down the weathered houses, barns, churches, and stores built by the original settlers of Central Texas, this book taught people to see the beauty, simplicity, and order expressed in the unadorned geometric forms of early Texas buildings. It inspired the preservation and restoration of many of the remaining pioneer buildings, as well as the design of modern buildings that employ the same simple geometries.

This revised edition of Pioneer Texas Buildings juxtaposes the historic structures with works by twenty contemporary architects who are inspired by the pioneer tradition to show how seamlessly the basic geometries translate from one era to another. As in the first edition, sketches and brief commentary by Clovis Heimsath explain how squares, triangles, and circles take shape in the cubic, triangular, and cylindrical forms that comprise houses and other buildings. Then black-and-white photographs, the heart of the book, illustrate these geometric forms in historic and modern buildings. The book also includes two essays in which Heimsath discusses the factors that led him and his wife Maryann to document early Texas buildings and the results in historic preservation and timeless architectural designs that have followed from their efforts.

  • About This Book
  • Acknowledgments
  • Foreword by Louis I. Kahn
  • Introduction to Pioneer Texas Buildings, 1968
  • Introduction to the Revised Edition
  • Geometry
  • Porches
  • Stairs
  • Chimneys
  • Steeples
  • Materials
  • Barns
  • Buildings Together

Clovis Heimsath, FAIA, the founding partner of Clovis Heimsath Architects, is now Senior Designer with Maryann Heimsath in Heimsath Architects of Austin, owned and managed by their son, Ben Heimsath, AIA.


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This book updates and expands Pioneer Texas Buildings: A Geometry Lesson, published by the University of Texas Press in 1968. Thirty-four years ago it was ahead of its time, for it celebrated the simple geometry of early Texas buildings at a time when they were considered by many to be of no historic significance, and were routinely torn down.

Fortunately the climate of opinion has changed over the last thirty-four years. Not only are the remaining buildings cherished for the heritage they preserve, but also Texas architects continue to design with simple geometry, straightforward structures, and local materials to address today's programs.

It is the realization that the geometry lesson of Pioneer Texas Buildings is alive today that led the University of Texas Press to publish an updated edition of the book. In the process of revising the book I have contacted many architects across the state and included their work as an example, today, of the principles of design so clear in the early Texas buildings. While the projects presented are only a small sampling of what has been built by these and many other architects, the reader does not have to guess how a building today would look if it were built in the pioneer Texas tradition: there are photos of current work in the book that answer this question. Lisa Hardaway, of Hester + Hardaway, architectural photographers, has coordinated the acquisition of appropriate photographs of recent work.

The format of the book remains the same. Each section reproduces the original photographs by Maryann Heimsath and simple text of the first edition along with photographs of current work by Texas architects designing in this tradition. The transition is seamless. The continuity in design is broadly interpreted to include a wide range of geometric forms applicable to today's programs and materials.

Clovis Heimsath

(Note: This essay appeared as a postscript in the 1968 edition of Pioneer Texas Buildings.)

Early Texas buildings brought me back to Texas. A hundred times I drove down dusty roads through bleak countryside and discovered again a hundred different moods of homes and towns. A hundred moods sprang up from this remembrance, and I had to come home. We can talk about the geometry of these early Texas buildings, and that is their glory, but it is the poignancy of the environment they create, set in the Hill Country, that is the "why" of this book. It would be so easy to forget that, first and foremost, architecture is a reality; it must be dissected to understand how it is formed, so that it can be seen, so that we can learn to see. But the end, the reason, the adventure is the feeling of it; it is the mood it creates; it is the reality of responding to a man-made form, a man-made space.

Early Texas buildings brought me back to Texas. It took me five years to discover it. As this book grew, it became clear to me that these houses had been speaking to me since I had first known them as a child; they had been telling me something about simplicity, order, geometry, about how Texas was a hundred years ago. I have felt the need to say something about architecture; suddenly, in these houses, I found that it was about them I wanted to speak. This book lets it out; this book lets me go on; this book helps me see architecture in basic terms, and I want it to speak to others. Architecture is a great adventure, and when we see it, when we respond to it, we are richer.

I want these houses to speak out against the sham of current American domestic architecture. The fraud is so appalling, it becomes the aesthetic sin of the age by its very magnitude; that we snug Americans can live in our endless four-square rooms with our endless eight-foot-high ceilings while the outsides say everything stylistically under the sun is a fraud—we want it, so we have it. But it damages our spirit to acknowledge this fraud. Our eyes are dulled to the things of architecture, for they accept window trimming, the memory overlay of decoration, in place of significant form, significant space, or the synthesis of the two. A Polynesian broken-eaves roof has the same stuffings inside as a French Provincial mansard-roof façade, or an Old English façade. We are building townhouses today with a Disneyland disregard for form; no one calls fraud when he sees fake plywood chimneys popped on top of gingerbread roof forms. No one calls fraud about a row of townhouses in alternate styles: one French, one Spanish, one Early American. At least we could have the aesthetic decency to admit that all the townhouses in France were French, in England, English, and in Spain, Spanish. With formal fraud on top of formal fraud, no wonder we have so much trouble seeing architecture; no wonder our eyes are dimmed. And the fraud is institutionalized; each Sunday across the country a Home Building Section appears, calling these stylistic frauds beautiful, elegant, classic, and well balanced. A generation is growing up believing only the fraud, believing their parents live in a beautiful home because the paper says that a large, aluminum-windowed, two-carred, interior-bathed, vinyl-floored "Early Colonial" is beautiful.

Do we have a problem? We have a problem.

Let's try to see architecture again. Let's start out again; let's see if our eyes can lead our hearts to a new adventure. It doesn't have terms; it has no style; it is a way of seeing. In a world that wants to be "tuned in" and in an age that wants real experience, don't forget the glory, the reality of architecture.

A building is space and form. It is a strange and wonderful duality. It is the only form we experience both inside and out; not even in the cave do we really experience the duality, for we can conceive the space within but not the mountain. Outside, a building is an object which can be seen from a distance, small enough to put in our pocket. If we want to control a building visually, we need only walk away from it; sooner or later it's small enough for our ego and we can stop; we've mastered it. Come closer and we're in trouble; any building begins to grow up to overpower us, blank out the sky, and then all at once the moment of visual truth—we step through! No Alice in Wonderland looking glass was ever more exciting than this adventure we experience a thousand times a day. We pass through, space-to-space outside, then space-to-space from outside to inside. We're jaded or it would stop us; we're jaded or the wonder of it would haunt us; we're jaded or the two environments—the one outside we control, the one inside that controls us—would intrigue us. Not many years ago men felt this mystery of entering; through history man has made his entry point impressive; he has given it dignity. To look in or out was an act as worthy; the windows, the holes slashed in this form-giving skin, were gracious in size, decorated to entice the eye. Whatever the style, whatever the material, whatever the age, man will move through space, man will continue the mystery of entering and leaving form. And he'll do it from a five-foot, two-inch-high eye level. He'll walk through space or drive, but the measure of man will be the same as it had been through history. Incredible, it's architecture.

There are really four things that architecture does. It creates interior space that envelops us. It creates an exterior object, the formal husk of the space within. It creates exterior spaces by the grouping of objects in space (call them buildings if you must) which leave a space in between. Finally, by superimposed buildings it creates corporate forms like the skyline of a city. With these simple things to do, architecture makes our environment. If thoughtfully done, if architecturally done, it enhances our mood. Our environment speaks to us, gives us something of our inner longing to be masters of our world, of our short life, of the incredible endless mystery. Without architecture, without thought, the forms still act on us, but the mood is fragmented, it builds nowhere; it becomes an environmental limbo, as most of our environs are today. Our junkyard of thoughtlessly formed cities and our sloppy countrysides are not wrong unless mediocrity is wrong; they are not evil unless it's evil to deprive man of art; they are not worth changing unless to know something of the power of form is important.

Thus, when you find simply stated geometric truths in houses, set quietly in the pensively rugged countryside of Texas, it is important. Architecture is space/form. It is a space within and an object without. When this inner form and outer form are one-one (the form expresses completely the space within) it's refreshing to say the least! In pioneer Texas buildings all the space is used: If the roof is a shed form, the space inside is a shed form; if the roof outside is a pitch form, the space inside is a pitched-ceiling space. Delightfully, the porches do all sorts of things: they are added forms; they are cut-out voids; they turn corners; they are dog-runs dividing the form into two parts—a thousand variations on the same theme, using interior spaces, exterior porches, and clear, related geometries.

Clusters of these forms make farms or towns. Many of the early towns are around a square, like Gonzales, Halletsville, or New Braunfels. Sometimes the square is immense, as at Castroville, or minute, as at Round Top. Sometimes there is a sequence of squares, as in Anderson. It's not St. Mark's Square, but it's real; it works on you just the same. Sometimes a town hall is dropped into the middle of the square, the space is lost, and the object of the pretentious town hall is so big that you wonder what they had in mind. For me, it's the ribbon of storefronts as in Comfort, Waelder, or Schulenburg that makes the statement for exterior space. These fronts become a wall, a line, often paralleling the train track with a ghost wall on the other side almost too far away to be felt. It's a ribbon space, a passing-through space, and it seems entirely appropriate to Texas, where going through takes more of your time than stopping. You are always going through town. It's the farm that is the cul-de-sac place to stop. In Texas, space is endless; you leave the passed-through town, end at the arrived-at farm. The most wonderful example of this is visiting Lange's Mill outside of Fredericksburg. There is a special magic world behind that farm with the waterfall, the farmhouse, and the space across to the enclosing barns downhill.

We live by moods—a thousand times a day we feel them. Most don't stick and become a part of the fabric; when they do, they become part of our person, our reality. I rather think in an afterlife we will remember them still—if so, would they not be religious? Such a mood I relate to this farm. I felt the mood there keenly and can recall it clearly as a precious remembrance.

Architecture is geometry/structure. All forms have form—sounds simple-minded, but it leads somewhere. Forms must be sorted out and stacked in our minds in order for them to have meaning for us; rather, in order for us to understand our visual world through the symbol of these forms. Forms must be categorized for survival. Natural forms we can break out easily, partly by what they are not. They are not geometric; geometry gives us mastery over forms, for we can conceive of them, use them, make building blocks out of them. As I write, I'm looking outside at the nongeometric, uncontrollable, "formless" forms of trees. The leaves shift, the light makes patches, the forms recede. Try as I might, I cannot control them. Luckily, I have the view ordered by the geometric square of the window.

Buildings are basic geometries because it is through systems of mathematical order that we transcribe form, that we order our physical environment. To talk about an x-x axis and a y-y axis makes as much sense in the geometry of form as it does in the geometry of electromagnetic fields. Geometry is an ordered projection of our thought patterns; it expresses how we think about the concrete. Love isn't geometric, but science is.

But we have to build buildings that stand up—at least for a while. Geometry and structure become cosponsors of form when the buildings is unselfconscious and the relationship is one-one. Forms are added together in a simple geometry, and they translate the loads to the ground. All the fine architectural forms we find in brick and stone buildings express this form-structure duality nicely, since a curve is the structural path of a load carried by small members in compression. They aren't the designed arches we pop onto our pseudo-Spanish façades to look round and pretty; they are structural arches that carry the load of the wall. Often, today, we don't need the arches to carry the load (for we have steel to span across lintels; we have wood walls behind the brick to carry the weight of the brick and roof to the ground). Why aren't we using the freedom today, opening the walls as never before? Why not go beyond the structural limitations and find a new reason for ripping through the enclosing skin?

Pioneer buildings in Central Texas are a geometry lesson. The forms are simply put together; there is a clear if uncomplicated structural integrity behind them (in the wood houses it is merely responding to the plainer quality of wood frame construction). These simple geometries are expressive of the space within in a simple one-one way. Yet the buildings relate to the special features of their sites, to settings almost as undisturbed as any in America. The environment is saying something to us, much as it did to men who lived simple lives a hundred years ago. In the book, I have stayed out of the cities, stayed apart from the Spanish influences, although these are important in Texas and carry a strong mood quotient. I have wanted to stay where the problem is a simple one, without a style overlay, without the encrustation of change brought on by time. It is in the predominantly German towns of Central Texas that this kind of architecture says its simple piece over and over again.

How did it happen that we have this treasure? Texas history spells it out, and these houses are there to affirm it.

There is a path running from the Gulf of Mexico to Dallas, with settlements dropped as cut-ants drop leaves along the way. It is in this area that houses are clustered. As inevitable as the geometry of architecture is the geometry of nature and man's response to it. He came from Europe, across a different substance than he could walk on, and so he used a boat—incidentally, it may be the other form we experience as an object and as a space, at least a boat in drydock where we can see all of it; it is rather exciting to think of a boat as a house covered almost halfway by water. A boat is a house on its side so the porch is on top and you must run down into the rooms. Or perhaps a house is a boat set on its side so you can run out. But the tyranny of physical geometry controlled our immigrant arrivals as much as the tyranny of that enclosing skin that separates the inside and the outside of our houses. The best they could do was arrive in Texas by the Gulf. First arrivals were explorers, the historians of newness who left us their names for the mystical thing they did here: La Salle, arriving in Matagorda Bay in 1685, making it all right for German immigrants to come to the same bay in the 1840's, more than 150 years later; Coronado, De Soto, now relegated to automobiles, were the giants in space, the astronauts of another age. I knew an astronaut very well, one who died; did I know La Salle a little bit, or Coronado, or the incredible Franciscan priests who set up shop on this moon of yesterday? Have I ever known the cruel, incredible Hernando Cortez, who tramped over the Aztecs in 1519, a hundred years before the explorers started. Who was Cortez?

Who were the Germans who landed in thousands in the 1840's? I know them, for one of them was named Heimsath. Whatever social, interpersonal tyrannies drove him from Germany—perhaps the dictator Metternich, perhaps the potato famines sweeping Europe in those years—he came, and thousands more. He exchanged an interpersonal tyranny for a natural one. He arrived in Galveston, and then went to Indianola for a trek across Texas, to a land grant somewhere above Fredericksburg. In 1846 he saw his friends die of cholera. In any of the other years he fought Comanches, he heard of bandit raids, he lived with the interpersonal tyrannies of the New World on top of the droughts of Texas.

Before 1836 and Texas independence, Mexico promoted colonies. The most successful were led by Stephen F. Austin and Green C. DeWitt. In 1836 Texas armies defeated Santa Anna in some treacherous coastal plain geography, won independence, and intensified immigration. Read the story of the Adelsverein, a society of German princes set up to properly handle the German immigration and to protect their countrymen in the New World. It tells us why New Braunfels is where it is, and Fredericksburg and many of the other German settlements from the Gulf northward. For sheer incompetence it was unparalleled; yet it got land deeded, it drummed up Texas in Germany, it inspired my forefathers to get out before things in Germany got worse. I would like to keep alive the historical fiction that Central Texas is all German. Actually, only a small portion, say 20 percent, of the immigrants came from Germany, but they came early and in organized lots and they settled their cities first. They helped establish the format of the cities, gave them their names, often German, as New Braunfels, Weimar, Frelsberg, New Ulm, Boerne. Polish settlers and already-Americanized settlers from the other states made up the vast part of the other newcomers. Fortunately, for Texas and for this latter-day look, the economy on the whole was not slave. There were few slaves in this central area, so studying pioneer homes has no problem of social guilt, something I wrestle with in affirming plantation architecture.

Life in Central Texas in the second half of the nineteenth century was isolated, rugged, simple, and hard. The houses reflect the virtue of this life. In our age, jaded by a plethora of forms, by visual stimuli screaming to be heard, it is an experience aesthetically and spiritually to follow again a dusty road, to find again the simple form of pioneer Texas houses. Perhaps twilight is the best time—when a nightly form dismemberment takes place, if our eyes are tuned to see it and our minds can rejoice in discovering. The form of the object, expressing the space within, dissolves little by little into the nature that encompasses it, the nature that encompasses the house, the house that encompasses you—unless you must break through the skin of enclosing form and sit outside on the defined exterior space of the porch, unless you feel the anxiety of the quiet upon you and you must leave the house entirely and stand under the form of the sky, surrounded only by the now no longer amorphous form that is the mountains, and wonder about the stars.

I am typing this new introduction on my laptop, sitting on an open porch on the square in Fayetteville, Texas, listening to the rustle of the leaves, noting the people as they pass into Orsaks Cafe, delighted to have this chance to speak again about the magic of Texas vernacular architecture.

Much has transpired in thirty-four years: in my life and career, in architecture in general ,and in the influence of Pioneer Texas Buildings. Maryann and I have five wonderful children, they were brought up for ten years in this small Czech town, are graduates of this extraordinary small town school (total enrollment 185, kindergarten through twelfth grade), and are well into to their exciting lives. We launched a recognized architecture firm and succeeded in producing another architect—Ben Heimsath, who graduated from Columbia University and went on to earn a Master of Architecture from Harvard (where he spent as much time as possible in the Business School to learn how to actually run an architectural firm). Now, Ben and his partner, Richard Calloway, own Heimsath Architects, and Maryann and I work for them!

Since I wrote the introduction (postscript) to the first edition there have been three positive surprises. First, Texans have increasingly grown in their respect for early Texas buildings. Second, Texas architects have used and evolved the geometry lesson of these buildings in their work. Third, the computer revolution visually defines the geometry of a building in three dimensions. The designers, by using newly developed computer technology to define geometries in three dimensions, can have much more ability to use the forms in their designs.

Respect for Architectural Heritage

The first surprise is the change in the climate of opinion in Texas about old buildings. Today anyone tearing down an old structure needs to justify the need to do so. This is a radical change from thirty-four years ago. Statewide examples of the change of attitude about historic buildings include the restoration of the King William and La Villita areas in San Antonio, the Swiss Avenue restoration in Dallas, and the redevelopment of the Montrose area in Houston. The list goes on and on. For me the change is personalized by two episodes in Fayetteville, Texas, my rural retreat and pulse-taking city.

There is a historic red brick schoolhouse in Fayetteville, built at the turn of the century and still standing. This doesn't sound like such a big deal unless you understand Fayetteville. A state inspector suggested to the Fayetteville School Board that the building could not be used for classrooms in its present condition. He should have explained that ramps and an elevator were needed if the second floor was to be upgraded to meet disability access standards. The Fayetteville School Board interpreted the report as a condemnation of the building and was prepared to tear it down. A groundswell of support for the building developed from former students who remembered the building fondly, and they prevailed. It has been saved as a major landmark celebrating Fayetteville's past.

In a similar instance, the Fayetteville Bank purchased an adjacent property, including a small hundred-year-old house, to provide a parking lot for its employees. Thirty-four years ago it would have been a goner. Today the change in attitude toward our Texas heritage made it difficult for the bank, a good neighbor, to tear it down. Instead, a bank board member bought the house from the bank and moved it to a new location in town. It is part of the surprise of Fayetteville itself, rebuilding its town center, encouraging people to move back to town as a result.


The second surprise is seeing Texas architecture develop in the last thirty-four years. Much of the best architecture in the state is an evolution of the geometry lesson of Pioneer Texas Buildings!

It was with some trepidation that I contacted architects in Texas whose work seemed to express the geometry lesson of Pioneer Texas Buildings. I was afraid they would think it was stretching the concept to include their current work in the new edition. To my delight I found that many of the architects were familiar with the original edition and had used it in their practice as a reference. One architect remembered O'Neil Ford, the dean of Texas architecture, bringing the book into the drafting room to inspire this architect, then a draftsman. Another architect told me that his client insisted that he duplicate a stair shown in the book (a photo of the stair is included in the expanded Stair section).

By contacting architects across the state I learned a great deal about the last thirty-four years of Texas architecture. Architects have expanded the geometries used in Texas buildings, while still maintaining the integrity of the forms. Many stunning buildings rely only on interlocking rectangular volumes, without the typical triangular roof form. Others combine rectangular and curved geometries in amazing ways. As I filled out the book with new work, the seamless transition from old and new became clear. Contemporary and traditional are terms that fade away when you read the geometry of these buildings.

It is also apparent as the geometry lesson evolves that there are many scales of geometry used today, from the grand scale of the geometry of structures holding up buildings to the geometric detail of railings and sun screens. The geometry lesson of Pioneer Texas Buildings is not only alive and well today but has blossomed in many dimensions.

Computer Technology

The third surprise is the computer and what it can do to show the geometry of buildings in three dimensions. Thirty-four years ago a computer was an expensive and somewhat bizarre instrument. Special rooms built with double floors and insulation to maintain a constant temperature were designed for these extremely expensive machines, and draftsmen were sent away for weeks to learn how to use them. What a contrast to today, when the staff at Heimsath Architects is networked to a server, working in two dimensions and three dimensions interchangeably.

With the computer the architect can see a building before it is built. I can remember spending half a day laying out one perspective. If the owner wanted a different view, it meant another half-day before I could return with the drawing. Now I can develop a three-dimensional model of the building and instantly move around and through it. The importance of this change in design cannot be overstated. We can see the whole building and make changes to improve it before construction begins.

There are other exciting developments. In developing the extraordinary double-curvature splayed roofs and walls at Bilbao, the architect was evolving a geometry that could scarcely be drawn using traditional techniques. I remember reading about Le Corbusier developing molded roof forms for the Paris pavilion in the 1940s. He was forced to build up sand to the form he wanted and them use the sand as forms for the reinforced concrete roof.

In 1958 I studied curvilinear forms in architecture for a Fulbright thesis in Italy. I was able to define the geometries of basic curved forms by building cardboard models and slicing the curved forms into many planes. Today it is not only possible to draw double curvature (that is curves that go in two directions at once) but it is possible for the architect to send the computer analysis directly to the subcontractor who will use the same computer images to construct the forms. When the cost of such construction becomes economical, it will offer architects the ability to expand the geometry of buildings even further.

In the last analysis the geometry lesson of Pioneer Texas Buildings / Geometry in Architecture is a base for architecture. As opportunities for change increase, it is important to return again to such a base, where the geometry is clear, the structure has a one-one relationship of outside to inside, and the materials are locally available.

Change will occur, but people will continue to be drawn to central Texas and the magic of the pioneer Texas buildings.



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