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.

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.

In celebration of the 2009 International Year of Astronomy, this issue of the Nexus Network Journal is devoted to relationships between astronomy, mathematics and architecture. Ancient cultures looked to the heavens in order to identify timeless principles for their own creations. Knowledge gained in astronomy was transformed into culture through architecture and design. Papers in this issue look at how astronomy influenced architecture and urban design.

The Winter 2012 (vol. 14 no. 3) issue of the Nexus Network Journal features seven original papers dedicated to the theme “Digital Fabrication”. Digital fabrication is changing architecture in fundamental ways in every phase, from concept to artifact. Projects growing out of research in digital fabrication are dependent on software that is entirely surface-oriented in its underlying mathematics. Decisions made during design, prototyping, fabrication and assembly rely on codes, scripts, parameters, operating systems and software, creating the need for teams with multidisciplinary expertise and different skills, from IT to architecture, design, material engineering, and mathematics, among others The papers grew out of a Lisbon symposium hosted by the ISCTE-Instituto Universitario de Lisboa entitled “Digital Fabrication – A State of the Art”. The issue is completed with four other research papers which address different mathematical instruments applied to architecture, including geometric tracing systems, proportional systems, descriptive geometry and correspondence analysis. The issue concludes with a book review.

The Winter 2012 (vol. 14 no. 1) issue of the Nexus Network Journal is dedicated to the theme “Architecture, Systems Research and Computational Sciences”. This is an outgrowth of the session by the same name which took place during the eighth international, interdisciplinary conference “Nexus 2010: Relationships between Architecture and Mathematics, held in Porto, Portugal, in June 2010. Today computer science is an integral part of even strictly historical investigations, such as those concerning the construction of vaults, where the computer is used to survey the existing building, analyse the data and draw the ideal solution. What the papers in this issue make especially evident is that information technology has had an impact at a much deeper level as well: architecture itself can now be considered as a manifestation of information and as a complex system. The issue is completed with other research papers, conference reports and book reviews.

This issue is dedicated to Mechanics in Architecture. It explores the latest findings in the science of structural mechanics, including the behavior of structures, internal forces, and deformation. It also explores the development of new structural systems designed to resist thrusts resulting from new architectural forms. Some of the papers published in this issue were presented at the Nexus 2006 during a special session dedicated to mechanics.

This volulme features eight original papers dedicated to the theme “Persian Architecture and Mathematics,” guest edited by Reza Sarhangi. All papers were approved through a rigorous process of blind peer review and edited by an interdisciplinary scientific editorial committee. Topics range from symmetry in ancient Persian architecture to the elaborate geometric patterns and complex three-dimensional structures of standing monuments of historical periods, from the expression of mathematical ideas to architectonic structures, and from decorative ornament to the representation of modern group theory and quasi-crystalline patterns. The articles discuss unique monuments Persia, including domed structures and two-dimensional patterns, which have received significant scholarly attention in recent years. This book is a unique contribution to studies of Persian architecture in relation to mathematics.

This book deals with the general concepts in stereotomy and its connection with descriptive geometry, the social background of its practitioners and theoreticians, the general methods and tools of this technology, and the specific procedures for the members built in hewn stone, including arches, squinches, stairs and vaults, ending with a chapter discussing the open problems in this field. Thus, it can be used as a reference book in the subject, but it can also read as a compelling narrative on this subject, one of the main branches of pre-industrial technology. Construction in hewn stone requires the use of geometrical methods and tools to assure that individual stones, either blocks or voussoirs, fit with one another and conform to the general shape of walls, arches or vaults. During the Late Middle Ages and the Renaissance, such techniques and instruments were developed empirically by masons and architects. Later on, learned mathematicians and engineers introduced refinements in these procedures and this branch of knowledge, known as stereotomy, furnished much material to descriptive geometry, a science born with the French Revolution which provided the foundation for projective geometry.

Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along with five celebrated arguments about twentieth-century architecture. Through this process the book offers a unique mathematical insight into the history and theory of design.

CItyMaker presents a method and a set of tools to generate alternative solutions for an urban context. The method proposes the use of a combined set of design patterns encoding typical design moves used by urban designers. The combination of patterns generates different layouts which can be adjusted by manipulating several parameters in relation to updated urban indicators. The patterns were developed from observation of typical urban design procedures, first encoded as discursive grammars and later translated into parametric design patterns. The CItyMaker method and tools allows the designer to compose a design solution from a set of programmatic premises and fine-tune it by pulling parameters whilst checking the changes in urban indicators. These tools improve the designer's awareness of the consequences of their design moves.