Numerical And Logical Analysis Of Visual Forms

The relationship of Mathematics and Architecture is an old topic, changing allthe time during the long history. In ancient time, theories borrowed from mathematicshave turned into the cornerstone of architecture, while during the Industrial Agemathematics lost its impact in architecture. However, since the middle of the lastcentury, mathematics has swarm back into this area under the aid of computer science.Computer science has completely changed our life in a more direct and more rationalway. Correspondingly, mathematical knowledge and logic thinking are indispensiblein creative design, not only from the perspective of modern techniques needed butalso from the perspective of the nature of mathematics. Mathematics is a perfectcombine of logic and beauty, including both the wisdom of human and the beauty ofnature. And one of the purposes of architectural design is to create beauty with humanwisdom.This paper focuses on the relationship of architectural forms and mathematics,mainly on the trends appeared in the last seventy years. Mathematics itself is acomplicated subject which connects closely with many other areas. Although I havetried to give an overall view, considering my limited knowledge, I hope to materializethe discussion through concrete issues. So on one hand, the second chapter goesthrough the history and talks about the relationship of philosophy, mathematics andarchitecture of different period, and the third chapter clarifies how mathematicsinfluence architecture in three facets, space, form and way of thinking. These twochapters are combined to form the foundation of my discussion. And on the otherhand, the forth chapter keeps eyes on several concrete issues according to the way inwhich mathematics works in each topic. Many examples are collected to illustrate.From the view of the classification of mathematics, the first part of this chapterincludes euclidean geometry, cartesian geometry, topology and so forth. From theview of the classification of the potential logic, the second part of this chapterintroduces some algorithms related to Chaos and Complexity.In each issue, basic theories are introduced in the first step and then someexperimental designs, both the trials of others and myself, are adopted to illustrate theissues in the most direct way.