Computables of Architectural Design: The Quantitative Basis and Invisible Structure of Architectural Form

Earl Mark, Architecture

1996 TTI Fellow

Project website: http://urban.arch.virginia.edu/~arch548/

This project is developed on the World Wide Web to revise an undergraduate course at the School of Architecture at the University of Virginia. It explores the perception of beauty and the comprehension of mathematical order in architectural form.On the one hand, the beauty of architectural form may be thought of as a phenomenon that one must experience and intuit. On the other hand, there is a long tradition of thought, going back at least as far as the Pythagorean School, that attributes aesthetic properties to the mathematics which describe form. As a well known example, the Parthenon at Athens fits the proportions of the golden rectangle. More recently here at the University of Virginia, Jefferson made extensive use of pure geometric elements (e.g., arcs, circles, spheres) in designing the buildings and plan of the Lawn which is acknowledged widely to be a pleasure to experience. Over the span of this century, however, the relationship between the study of mathematics and the experience of geometrical form has had a decreasing emphasis in architectural education. It is evident especially in the decreased presence of descriptive geometry, a subject no longer typically taught within Schools of Architecture in the United States.The project is intended to rejuvenate the weakened tradition of mathematical education in architecture. Students are taught to understand what is referred to as the"computables of architecture." With the aid of three-dimensional computer-aided design or "CAD," software, students do not simply design architectural forms by picking from a menu of pre-defined geometrical modeling options; rather, they create them by writing programs to describe their mathematical order. By doing so, the connection between aesthetic experience and mathematical formulation is direct: there is no need to argue the point, since students can immediately perceive the results of tinkering with the equations that generate forms. By interactively observing the relationship between the mathematical and formal composition, students gain an appreciation of and facility to work with the geometric basis of many forms found in architecture and nature.Because of the speed with which the computer processes can graphically represent complex mathematical equations, the project is intended in part to push beyond the mundane application of geometry to architecture. For example, students can demonstrate that some of the unusual organic forms of Antonio Gaudi's architecture have a mathematical basis. Students can also employ the relatively new field of fractal geometry to show that even apparently chaotic forms, such as those found in nature, have a computable basis and comprehensible mathematical order. Through these kinds of case studies, students do not employ the computer in a way that lowers the threshold of what skill is needed to generate mathematically complex forms. That is, the computer is not a substitute for mathematical reasoning, but serves a catalyst for students to directly work with the underlying algebra which can be used to describe forms found in nature and architecture. This use of the computer suggests that mathematical descriptions can become the means of connecting contemporary architects to their lost Classical roots.