This book presents an exploration of the arch from the points of view of architecture, mathematics, engineering, construction history, and cultural symbolism. Leonardo da Vinci described the arch as "two weaknesses which, leaning on each other, become a strength," a metaphor for the way that science and art lean on each other to strengthen our lives.

Leonardo da Vinci was well aware of the fundamental importance of mathematics for architecture. This book examines Leonardo’s knowledge of theoretical mathematics, explores how he used concepts of geometry in his designs for architectural projects, and reports on a real-life construction project using Leonardo’s principles. Authors include Sylvie Duvernoy, Kim Williams, Rinus Roelofs, Biagio Di Carlo, Mark Reynolds, João Pedro Xavier, Vesna Petresin, Christopher Glass, and Jane Burry.

This fourth book in the Nexus series offers papers that further broaden the horizons of studies in architecture and mathematics.

From ancient to modern, architects have looked for fundamental underlying principles of geometry and proportion on which to found their designs. Such principles not only provide an order for the formal elements, they ground the architecture in timeless values and provide an order for the formal elements, they ground the architecture in timeless values and provide a source of cultural meaning. This book illustrates the use of fundamental principles of geometry and proportion in two ancient cultures, the Bronze Age and the Roman Age, as well as in twentieth-century North America.

The purpose of the project is to provide the most up-to-date survey on issues dealing with practical geometry and how it might have been applied in the design of medieval architecture. Chronologically, the topics cover a wide span - from early Medieval through Late Gothic. Geographically, the monuments under discussion range from Early Medieval Florence through Carolingian Germany, Crusader Cyprus, Romanesque France and Gothic England. The applications of both geometry and metrology are considered in this volume, often with illustrations generated by computer-assisted design (CAD) software. The project therefore offers recent scholarship in the field, as well as cutting-edge technology which helps propel the pursuit of such studies. To this end, the project is the first of its kind both in terms of its focus and its comprehensiveness. Such a project is sorely needed to introduce this highly specialized discipline to other historians of art, history, and science of the Middle Ages, as well as historians in most humanistic areas.

The title of this issue of the Nexus Network Journal, "Architecture, Mathematics and Structure," is deliberately ambiguous. At first glance, it might seem to indicate the relationship between what buildings look like and how they stand up. This is indeed one aspect of what we are concerned with here. But on a deeper level, the fundamental concept of structure is what connects architecture to mathematics. Both architecture and mathematics are highly structured formal systems expressed through a symbolic language. For architecture, the generating structure might be geometrical, musical, modular, or fractal. Once we understand the nature of the structure underlying the design, we are able to "read" the meaning inherent in the architectural forms. The papers in this issue all explore themes of structure in different ways.