ABSTRACT
In any quantitative studies of building or environmental geometry it is clearly desirable to be able to describe the forms with some mathematical precision. This chapter begins with a simple modular ‘building block’ description of shape and form. In two dimensions this is a method used in ecology, geography, statistics and urban studies in the form of a square grid or system of quadrats. The American designer, Albert Farwell Bemis, introduced the method systematically into modern architecture through his pioneering work on modular coordination. The modular description serves as a useful introduction to some basic ideas in the theory of sets, in particular, sets of points. For Bemis the building is designed within ‘a total matrix of cubes’, a rectangular outline of space, large enough to include all the physical parts of the building. The voids that constitute rooms, doors and windows can then be defined by the elimination within the house volume of the cubes filling these spaces.
