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The Story: Greek and Roman Architecture
Greek and Roman Architecture
Just as the triangular form of Egyptian pyramids represents a visual model of that period, triangles can also be used to represent some of the theories of Classical architecture. The treatise "On Architecture" written in retirement by the Roman military engineer and architect Vitruvius Pollio during the period of 31 B.C. to 14 A.D. [Raeburn, 1980, p. 60] expressed ideas, which form the basis for many architectural theorizing and controversy. He recognized that there are three different requirements for a building:
Firmitas: it should be structurally sound : Structure
Utilitas: it must have a practical function : Function
Venustas: it should be beautiful : Aesthetics
According to Raeburn, "Vitruvius' book was written principally about Greek architecture. The most important themes that derive from his book are the definitions of the classical Orders, theories of proportion based on modular system, on simple geometry and on the human body, and aesthetic definitions relating to harmony and proportions such as 'disposition', 'distribution', 'symmetry' and 'eurhythmy'. Over fifty manuscript copies of the book have survived from the Middle Ages, and it seems that it was used as a textbook by medieval architects, largely for the geometric ideas it contains." [Raeburn, 1980, p. 9-12]
Today the triad relationship of Structure-Function-Aesthetics is a fundamental part of architecture. Architects throughout the classical, modernist and postmodernist periods referenced Vitruviusí ideas. Today the minimum five years formal education are close to the definitions set by Vitruvius for what constituted an architect. He stated that architects should have amongst others, the following attributes:
Should have an imagination
An understanding of the theoretical and practical aspects of Construction
Should be versed in:
    Letters
    Drawings
    Geometrical Instruments
    Optics
    Arithmetic
    History
    Philosophy
    Music
    Medicine
    Law
    Astronomy
The emphasis on theory ensured that the architectural profession throughout the ages endured - surviving even the buildings and physical structures of their construction. Through recorded trial and error and the ideals of what should be, a body of knowledge has been placed before us, which can benefit many contemporary architecture-intensive disciplines.
The role of the architect was more prominent in Greek architecture than in Roman. Greek architects were considered artists - balancing community, religion and civic institutions - whereas Roman architects were technicians and engineers. [Foster, 1983, p.18]. The progress of Greek architecture was described as "an empirical search for form. The development of Greek temple architecture had little to do with either structure or function. Nor was it much concerned with internal space; since the main rituals took place outside, the exterior form dominated architects' thinking." [Foster, 1983, p.43]. This may seem to have been a contradiction of Vitruvius, but the answer lies in the Greek interpretation of structure and function and in their understanding of mathematical and geometric laws. While the Greeks pursued the triad of structure-function-aesthetics, their mental models of geometry and mathematics limited them.
In 1945 William Mills Irvin Jr., a retired curator of the Metropolitan Museum of Art, wrote his controversial study on "Art and Geometry". It was controversial because it argued against the supremacy of the Greek culture, which was regarded as the foundation of Western civilization. He concluded that Greeks were "tactile-thinkers" as opposed to "visual-thinkers". Their perceptions of space were based not on a three-dimensional view but on their sense of touch. Today, it is recognize that of the three learning methods (auditory, visual and kinaesthetic or tactile), tactile learning is the most challenging for modern educators. Unfortunately, there is an unjustified perception or social stigma that tactile learning is associated with slow learners.
Irvin was not attacking the Greeks, he was merely placing the evidence of his study, "Basically, the Greeks thought about their geometry in terms of an unexpressed chalk line or yard stick which they held in their two hands." Irvin demonstrated how Euclid derived his basic theorem of parallel lines and concluded that "Euclid's geometry was based on the tactile-muscular intuitions" and that neither Euclid nor his successors made any use of proof of abstract ideas such as "infinity", because it was beyond their notions of handling and measurement [Irvin, 1946, p.40-42].
Many architectural historians noted, but without the same theoretical examination as Irvin, who wrote, "The simple fact of the matter is that the figures of Greek sculpture are abstract, ideological conformations, devoid of physical, mental or spiritual histories. Such little emotion or movement as they have has no relation to emotional or volitional states." [Irvin, 1946, p.23]
Theory in the triad relationship between theory-design-construction is more than just about a treatise, it is about a way of thinking - much of which is in the form of tacit knowledge. The evidence that theory is manifested through design into construction is evident throughout architectural history, of which Greek architecture was no exception. Almost all of Greek architecture is based on the post-lintel system or horizontal beams carried by vertical supports. This was a structural model applied irrespective of construction material - wood or stone. The Greeks showed no evidence of improvement in technical design although they were competent technically. They had an understanding of a beam's strength relative to height and thickness, which seems to confirm a tactile approach, but they showed no evidence of a theoretical understanding of structure [Raeburn, 1980, p.47-48].
In 1452 the Italian, Leon Battista Alberti, produced the treatise De Re Aedificatoria with the object of presenting the works of Vitruvius to his contemporaries. Earlier in 1435 he produced De Pictura , which emphasized painting as the basis for architecture. However, it was his treatise, which was the most influential in architectural history. It "imbued a strong sense of social function of architecture in creating a happy and well-ordered state" [Raeburn, 1980, p.132]. The most important aspect of Alberti's book which was a turning point from Greek architecture and which inspired an age of enlightenment or the Italian Renaissance, was "the geometrical scheme for depicting objects in a unified space, or in other words what we today call perspective." [Irvin, 1946, p.68]
Perspective and three-dimensional geometry re-defined the focus of architecture. Architecture began to deal with the internal living space and addressed the problems of space as a whole. It was a dramatic shift from the external view of Greek architecture. The shape of the square and rectangle as a fundamental structure of the grid would become a foundation for many visual concepts in modernism.
Interestingly, the shapes of triangles, circles and squares (and rectangles) seemed to gain increasing significance. In religious abstract conception, the circle was considered a perfect symbol. It embodied the concept of the church as representative of the cosmos. In De Re Aedificatoria , Alberti identified nine ideal plan-forms based on a circle, and eight polygons derived from the circle. It reinforced the ideal of church construction with a dome as a central location for the altar and sacrament [Risebero, 1997, p.127]. The Church would play a dominant role in architecture throughout the Italian Renaissance, the Middle Ages and the Reformation.
 
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