This carefully researched survey examines how architects now use digital tools and physics to build spatial constructs that would have been inconceivable even ten years ago. Architecture has always relied on mathematics to achieve visual harmony, structural integrity, and logical construction. Now digital tools and an increasing interest in physics have given architects the means to describe and build spatial constructs that would have been inconceivable even ten years ago. This carefully researched survey of forty-six international projects offers an overview of how different strategies are being employed through accessible illustrations and clear text. Each section presents case studies of projects by globally recognized architects in diagrams, photographs, and texts.

Architecture of Mathematics describes the logical structure of Mathematics from its foundations to its real-world applications. It describes the many interweaving relationships between different areas of mathematics and its practical applications, and as such provides unique reading for professional mathematicians and nonmathematicians alike. This book can be a very important resource both for the teaching of mathematics and as a means to outline the research links between different subjects within and beyond the subject. Features All notions and properties are introduced logically and sequentially, to help the reader gradually build understanding. Focusses on illustrative examples that explain the meaning of mathematical objects and their properties. Suitable as a supplementary resource for teaching undergraduate mathematics, and as an aid to interdisciplinary research. Forming the reader's understanding of Mathematics as a unified science, the book helps to increase his general mathematical culture.

This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.

Published in 1923, Toward an Architecture had an immediate impact on architects throughout Europe and remains a foundational text for students and professionals. Le Corbusier urges readers to cease thinking of architecture as a matter of historical styles and instead open their eyes to the modern world. Simultaneously a historian, critic, and prophet, he provocatively juxtaposes views of classical Greece and Renaissance Rome with images of airplanes, cars, and ocean liners. Le Corbusier's slogans--such as "the house is a machine for living in"--and philosophy changed how his contemporaries saw the relationship between architecture, technology, and history. This edition includes a new translation of the original text, a scholarly introduction, and background notes that illuminate the text and illustrations.

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

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 I covers architecture from antiquity through Egyptian, Mayan, Greek, Roman, Medieval, Inkan, Gothic and early Renaissance eras and styles. The themes that are covered range from symbolism and proportion to measurement and structural stability. From Europe to Africa, Asia and South America, the chapters span different countries, cultures and practices.

How a protean mathematical object, the graph, ushered in new images, tools, and infrastructures for design and catalyzed a digital future for architecture. In Graph Vision, Theodora Vardouli offers a fresh history of architecture’s early entanglements with modern mathematics and digital computing by focusing on a hidden protagonist: the graph. Fueled by iconoclastic sentiments and skepticism of geometric depiction, architects, she explains, turned to the skeletal underpinnings of their work, and with it the graph, as a site of representation, operation, and political possibility. Taking the reader on an enthralling journey through a polyvalent mathematical entity, Vardouli combines close readings of graphs’ architectural manifestations as images, tools, and infrastructures for design with original archival work on research centers that spearheaded mathematical and computational approaches to architecture. Structured thematically, Graph Vision weaves together archival findings on influential research groups such as the Land Use Built Form Studies Center at the University of Cambridge, the Center for Environmental Structure at Berkeley, the Architecture Machine Group at the Massachusetts Institute of Technology, among others, as well as important figures who led, or worked in proximity to, these groups, including Lionel March, Christopher Alexander, and Yona Friedman. Together, this material chronicles the emergence of both a new way of seeing and a new prospect for the discipline that prefigured its digital future—of a “graph vision.” Vardouli argues that this vision was one of vacillation toward visual appearance. Digital approaches to architecture, she ultimately reveals, were founded on a profound ambivalence toward the visual realm endemic to mid-twentieth century architectural and mathematical modernisms.

Continuing the themes that have been addressed in The Humanities in Architectural Design and The Cultural Role of Architecture, this book illustrates the important role that a contradiction between form and function plays in compositional strategies in architecture. The contradiction between form and function is seen as a device for poetic expression, for the expression of ideas, in architecture. The book contributes to the project of re-establishing architecture as a humanistic discipline, to re-establish an emphasis on the expression of ideas, and on the ethical role of architecture to engage the intellect of the observer and to represent human identity.

Originally published in 1971 The Geometry of Environment is a fusion of art and mathematics introducing stimulating ideas from modern geometry, using illustrations from architecture and design. The revolution in the teaching of mathematics and the advent of the computer in design challenge traditional ways of appreciating the space about us, and expand the ‘structural’ understanding of our surroundings through such concepts as transformations, symmetry groups, sets and graphs. This book aims to show the relevance of ‘new maths’ and encourages exploration of the widening intellectual horizons of environmental design and architecture.