Architecture and Mathematics from Antiquity to the Future : Volume II: The 1500s to the Future Part VII: Theories of Representation Part VIII: From 1600 AD to 1900 AD Part IX: 1900 2000 Part X: Contemporary Approaches to Design and Analysis Part XI: Theories and Applications of Computer Sciences Index Acknowledgements The aim of this collection of essays is to present a broad portrait of the ways in which two seemingly different disciplines are interconnected. The diversity and varied texture of the essays richly illustrates the affinity between architecture and mathematics. As the almost 100 papers presented in this two volume publication show every age and every culture has relied on principles of mathematics incorporated in their works of architecture to imbue their built environment with meaning and order. Included are discussions of geometry proportional systems linear algebra periodic and aperiodic tilings fractals perspective computer science and mechanics. Western architecture of every period is examined: Egyptian Roman Medieval Renaissance Baroque Enlightenment twentieth century and beyond as is the architecture of Turkey China India Japan Australia and Islam. The mathematical nature of the architecture of Leon Battista Alberti Andrea Palladio and Frank Lloyd Wright is examined and the philosophical background behind Renaissance architecture is explored. Contributors come from a wide range of disciplines and cultural backgrounds: architects mathematicians historians theoreticians scientists and educators from the world over. Architecture may be seen and understood in a new light by professionals as well as non professionals