Form and Numbers: Mathematical Patterns and Ordering Elements in Design

In America, buildings are often constructed with the intent of being utile only 30-40 years. All over the world though, there are buildings that are hundreds of years old that are still very functional. Historically, architecture was a part of mathematics, and in many periods of the past, the two were indistinguishable. Architects were often required to be also mathematicians in ancient times. The idea of this thesis is to identify the relationship between mathematics and architecture and to reintroduce them in order to create a module for successful design . Presence of mathematical boundaries help to attain visual consistency by relating a small scale to a larger scale. Spaces which meet these criteria are subconsciously realized as sharing critical qualities with natural and biological forms. Accordingly, they are perceived as more comfortable psychologically. Scaling coherence is a common element of traditional and vernacular architectures, but is often extensively deficient from contemporary architecture. Architecture has used proportional systems to create, or limit, the forms in building since its inception. In almost every building tradition, there exists a system of mathematical relations which governs the relationships between elements of design. These are often quite simple: whole number ratios or easily constructed geometric shapes. Many types of revival architecture have been employed in recent years, therefore it would be critical to identify why they have achieved a resurgence in popularity. However, historical allusions are generally superficial. No authentic scale or systems are used and the formerly unique qualities are not explored spatially. The attraction to, and association with, forms possessing harmonic proportions is a mitigating factor in design that needs to be addressed. The natural beauty stemming from proportion, mathematics, and the proper relationship of elements to the whole is what renders a building aesthetically and experientially pleasing to a human. Post-Modern architecture is all but going in the opposite direction of achieving this goal. The idea that a building should scale down to dimensions humans can relate to and reveal its stature in the experiential qualities must be extracted from traditional architecture and employed in contemporary techniques