Every age and every culture has relied on the incorporation of mathematics in their works of architecture to imbue the built environment with meaning and order. Mathematics is also central to the production of architecture, to its methods of measurement, fabrication and analysis. This two-volume edited collection presents a detailed portrait of the ways in which two seemingly different disciplines are interconnected. Over almost 100 chapters it illustrates and examines the relationship between architecture and mathematics. Contributors of these chapters come from a wide range of disciplines and backgrounds: architects, mathematicians, historians, theoreticians, scientists and educators. Through this work, architecture may be seen and understood in a new light, by professionals as well as non-professionals. Volume II covers architecture from the Late Renaissance era, through Baroque, Ottoman, Enlightenment, Modern and contemporary styles and approaches. Key figures covered in this volume include Palladio, Michelangelo, Borromini, Sinan, Wren, Wright, Le Corbusier, Breuer, Niemeyer and Kahn. Mathematical themes which are considered include linear algebra, tiling and fractals and the geographic span of the volume’s content includes works in the United States of America and Australia, in addition to those in Europe and Asia.

This book presents the first detailed mathematical analysis of the social, cognitive and experiential properties of Modernist domestic architecture. The Modern Movement in architecture, which came to prominence during the first half of the twentieth century, may have been famous for its functional forms and machine-made aesthetic, but it also sought to challenge the way people inhabit, understand and experience space. Ludwig Mies van der Rohe’s buildings were not only minimalist and transparent, they were designed to subvert traditional social hierarchies. Frank Lloyd Wright’s organic Modernism not only attempted to negotiate a more responsive relationship between nature and architecture, but also shape the way people experience space. Richard Neutra’s Californian Modernism is traditionally celebrated for its sleek, geometric forms, but his intention was to use design to support a heightened understanding of context. Glenn Murcutt’s pristine pavilions, seemingly the epitome of regional Modernism, actually raise important questions about the socio-spatial structure of architecture. Rather than focussing on form or style in Modernism, this book examines the spatial, social and experiential properties of thirty-seven designs by Wright, Mies, Neutra and Murcutt. The computational and mathematical methods used for this purpose are drawn from space syntax, isovist geometry and graph theory. The specific issues that are examined include: the sensory and emotional appeal of space and form; shifting social and spatial structures in architectural planning; wayfinding and visual understanding; and the relationship between form and program.

A new title in the Architectural Design series that explores the potential of computational mathematics in cutting-edge design Mathematics has always been a vital tool in the architect's trade, but the last fifteen years have seen a sharp rise in the power of computers and has led to computational abilities far beyond anything previously available. Modern design software and computing power have changed the traditional role of geometry in architecture and opened up new possibilities enabled by topology, non-Euclidean geometry, and other areas of mathematics. With insight from a top-notch list of contributors, including such notables as Philippe Morel and Fabien Scheurer, Mathematics in Space discusses how the advent of computation and information technology has affected the work of contemporary architects. This new title in the Architectural Design series updates architectural mathematics since the digital revolution With world-class contributors, this is an essential resource for anyone interested in the ways computation has transformed the discipline The book explores fascinating issues in modern design, most importantly the impact of mathematics on contemporary design creativity For students and practitioners alike, Mathematics in Space covers vital topics in a constantly changing discipline.

Although the disciplines of architecture and structural engineering have both experienced their own historical development, their interaction has resulted in many fascinating and delightful structures. To take this interaction to a higher level, there is a need to stimulate the inventive and creative design of architectural structures and to persua

Buildings are not often thought of as works of art, but the process of designing them can become an art form. Architects such as Frank Lloyd Wright and Zaha Hadid have been internationally recognized for their innovative designs. Through engaging text and full-color photographs, readers learn about the artistic challenges these and other architects face as they attempt to blend form and function in new and exciting ways. Readers are sure to love this detailed look at a kind of art they see around them every day and a career path they can pursue if they are interested in architecture.

Architecture in Formation is the first digital architecture manual that bridges multiple relationships between theory and practice, proposing a vital resource to structure the upcoming second digital revolution. Sixteen essays from practitioners, historians and theorists look at how information processing informs and is informed by architecture. Twenty-nine experimental projects propose radical means to inform the new upcoming digital architecture. Featuring essays by: Pablo Lorenzo-Eiroa, Aaron Sprecher, Georges Teyssot, Mario Carpo, Patrik Schumacher, Bernard Cache, Mark Linder, David Theodore, Evan Douglis, Ingeborg Rocker and Christian Lange, Antoine Picon, Michael Wen-Sen Su, Chris Perry, Alexis Meier, Achim Menges and Martin Bressani. Interviews with: George Legendre, Alessandra Ponte, Karl Chu, CiroNajle, and Greg Lynn. Projects by: Diller Scofidio and Renfro; Mark Burry; Yehuda Kalay; Omar Khan; Jason Kelly Johnson, Future Cities Lab; Alejandro Zaera-Polo and Maider Llaguno Munitxa; Anna Dyson / Bess Krietemeyer, Peter Stark, Center for Architecture, Science and Ecology (CASE); Philippe Rahm; Lydia Kallipoliti and Alexandros Tsamis; Neeraj Bhatia, Infranet Lab; Jenny Sabin, Lab Studio; Luc Courschene, Society for Arts and Technology (SAT); Eisenman Architects; Preston Scott Cohen; Eiroa Architects; Michael Hansmeyer; Open Source Architecture; Andrew Saunders; Nader Tehrani, Office dA; Satoru Sugihara, ATLV and Thom Mayne, Morphosis; Reiser and Umemoto; Roland Snooks, Kokkugia; Philip Beesley; Matias del Campo and Sandra Manninger SPAN; Michael Young; Eric Goldemberg, Monad Studio; Francois Roche; Ruy Klein; Chandler Ahrens and John Carpenter.

Shape grammar and space syntax have been separately developed but rarely combined in any significant way. The first of these is typically used to investigate or generate the formal or geometric properties of architecture, while the second is used to analyze the spatial, topological, or social properties of architecture. Despite the reciprocal relationship between form and space in architecture—it is difficult to conceptualize a completed building without a sense of both of these properties—the two major computational theories have been largely developed and applied in isolation from each another. Grammatical and Syntactical Approaches in Architecture: Emerging Research and Opportunities is a critical scholarly resource that explores the relationship between shape grammar and space syntax for urban planning and architecture and enables the creative discovery of both the formal and spatial features of an architectural style or type. This book, furthermore, presents a new method to selectively capture aspects of both the grammar and syntax of architecture. Featuring a range of topics such as mathematical analysis, spatial configuration, and domestic architecture, this book is essential for architects, policymakers, urban planners, researchers, academicians, and students.

An investigation of mathematics as it was drawn, encoded, imagined, and interpreted by architects on the eve of digitization in the mid-twentieth century. In Formulations, Andrew Witt examines the visual, methodological, and cultural intersections between architecture and mathematics. The linkages Witt explores involve not the mystic transcendence of numbers invoked throughout architectural history, but rather architecture’s encounters with a range of calculational systems—techniques that architects inventively retooled for design. Witt offers a catalog of mid-twentieth-century practices of mathematical drawing and calculation in design that preceded and anticipated digitization as well as an account of the formal compendia that became a cultural currency shared between modern mathematicians and modern architects. Witt presents a series of extensively illustrated “biographies of method”—episodes that chart the myriad ways in which mathematics, particularly the mathematical notion of modeling and drawing, was spliced into the creative practice of design. These include early drawing machines that mechanized curvature; the incorporation of geometric maquettes—“theorems made flesh”—into the toolbox of design; the virtualization of buildings and landscapes through surveyed triangulation and photogrammetry; formal and functional topology; stereoscopic drawing; the economic implications of cubic matrices; and a strange synthesis of the technological, mineral, and biological: crystallographic design. Trained in both architecture and mathematics, Witt uses mathematics as a lens through which to understand the relationship between architecture and a much broader set of sciences and visual techniques. Through an intercultural exchange with other disciplines, he argues, architecture adapted not only the shapes and surfaces of mathematics but also its values and epistemic ideals.

Visual computing and descriptive geometry are multidisciplinary fields addressing the handling of images, 3D models, and other computer graphics. These ideas are experiencing a revival due to emergent technologies and applications available to developers. Based in traditional forms of design and architecture, these fields are currently experiencing a bounty of new research based on old principles. The Handbook of Research on Visual Computing and Emerging Geometrical Design Tools seeks to add to this knowledge base by considering these technologies from a designer’s perspective rather than reiterating the principles of computer science. It combines aspects of geometry and representation with emerging tools for CAD, generation, and visualization while addressing the digital heritage of such fields. This book is an invaluable resource for developers, students of both graphic and computer-generated design, researchers, and designers.