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 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.

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.

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.

In this fascinating study, architect and Egyptologist Corinna Rossi analyses the relationship between mathematics and architecture in ancient Egypt by exploring the use of numbers and geometrical figures in ancient architectural projects and buildings. While previous architectural studies have searched for abstract 'universal rules' to explain the history of Egyptian architecture, Rossi attempts to reconcile the different approaches of archaeologists, architects and historians of mathematics into a single coherent picture. Using a study of a specific group of monuments, the pyramids, and placing them in the context of their cultural and historical background, Rossi argues that theory and practice of construction must be considered as a continuum, not as two separated fields, in order to allow the original planning process of a building to re-emerge. Highly illustrated with plans, diagrams and figures, this book is essential reading for all scholars of Ancient Egypt and the architecture of ancient cultures.

This volume explores the mathematical character of architectural practice in diverse pre- and early modern contexts. It takes an explicitly interdisciplinary approach, which unites scholarship in early modern architecture with recent work in the history of science, in particular, on the role of practice in the “scientific revolution”. As a contribution to architectural history, the volume contextualizes design and construction in terms of contemporary mathematical knowledge, attendant forms of mathematical practice, and relevant social distinctions between the mathematical professions. As a contribution to the history of science, the volume presents a series of micro-historical studies that highlight issues of process, materiality, and knowledge production in specific, situated, practical contexts. Our approach sees the designer’s studio, the stone-yard, the drawing floor, and construction site not merely as places where the architectural object takes shape, but where mathematical knowledge itself is deployed, exchanged, and amplified among various participants in the building process.

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.

More than a decade in the making, this is a textbook of architecture, useful for every architect: from first-year students, to those taking senior design studio, to graduate students writing a Ph.D. dissertation in architectural theory, to experienced practicing architects. It is very carefully written so that it can be read even by the beginning architecture student. The information contained here is a veritable gold mine of design techniques. This book teaches the reader how to design by adapting to human needs and sensibilities, yet independently of any particular style. Here is a unification of genuine architectural knowledge that brings a new clarity to the discipline. It explains much of what people instinctively know about architecture, and puts that knowledge for the first time in a concise, understandable form. Dr. Salingaros has experience in the organization of the built environment that few practicing architects have. The later chapters of this new book touch on very sensitive topics: what drives architects to produce the forms they build; and why architects use only a very restricted visual vocabulary. Is it personal inventiveness, or is it something more, which perhaps they are not even aware of? There has not been such a book treating the very essence of architecture. The only other author who is capable of raising a similar degree of passion (and controversy) is Christopher Alexander, who happens to be Dr. Salingaros’ friend and architectural mentor. “Surely no voice is more thought-provoking than that of this intriguing, perhaps historically important, new thinker?” From the Preface by His Royal Highness, Charles, The Prince of Wales “A New Vitruvius for 21st-Century Architecture and Urbanism?” Dr. Ashraf SalamaChair, Department of Architecture and Urban Planning, Qatar University, Doha, Qatar “Architecture, Salingaros argues, is governed by universal and intuitively understood principles, which have been exemplified by all successful styles and in all civilizations that have left a record of themselves in their buildings. The solution is not to return to the classical styles… the solution is to return to first principles and build within their constraints… ” Dr. Roger Scruton Philosopher, London, UK “A fundamental text, among the most significant of the past several years.” Dr. Vilma Torselli Architect and Author, Milan, Italy “A Theory of Architecture demonstrates how mathematics and the social sciences offer keys to designing a humane architecture. In this brilliant tome Salingaros explains why many modern buildings are neither beautiful nor harmonious and, alternatively, how architects and patrons can employ scale, materials and mathematical logic to design structures which are exciting, nourishing, and visually delightful.” Duncan G. Stroik Professor of Architecture, University of Notre Dame, Indiana “Salingaros explores ways to clarify and formalize our understanding of aesthetic forms in the built environment, using mathematics, thermodynamics, Darwinism, complexity theory and cognitive sciences. Salingaros’ remarkable observations suggest that concepts of complexity and scale can someday provide a full-bodied explanation for both the practice and the appreciation of architecture.” Kim Sorvig Architecture & Planning, University of New Mexico See this book’s Wikipedia entry http://en.wikipedia.org/wiki/A_Theory_of_Architecture Nikos A. Salingaros is an internationally known urbanist and architectural theorist who has studied the scientific bases underlying architecture for thirty years. Utne Reader ranked him as “One of 50 visionaries who are changing your world”, and Planetizen as 11th among “The top 100 urban thinkers of all time”. He is Professor of Mathematics at the University of Texas at San Antonio.

Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.