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.

This textbook provides a thorough introduction to the differential geometry of parametrized curves and surfaces, along with a wealth of applications to specific architectural elements. Geometric elements in architecture respond to practical, physical and aesthetic needs. Proper understanding of the mathematics underlying the geometry provides control over the construction. This book relates the classical mathematical theory of parametrized curves and surfaces to multiple applications in architecture. The presentation is mathematically complete with numerous figures and animations illustrating the theory, and special attention is given to some of the recent trends in the field. Solved exercises are provided to see the theory in practice. Intended as a textbook for lecture courses, Parametric Geometry of Curves and Surfaces is suitable for mathematically-inclined students in engineering, architecture and related fields, and can also serve as a textbook for traditional differential geometry courses to mathematics students. Researchers interested in the mathematics of architecture or computer-aided design will also value its combination of precise mathematics and architectural examples.

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.

This book reports on several advances in architectural graphics, with a special emphasis on education, training, and research. It gathers a selection of contributions to the 19th International Conference on Graphic Design in Architecture, EGA 2022, held on June 2–4, 2022, in Cartagena, Spain, with the motto: "Beyond drawings. The use of architectural graphics".

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.

Volume 2 of History of Construction Cultures contains papers presented at the 7ICCH – Seventh International Congress on Construction History, held at the Lisbon School of Architecture, Portugal, from 12 to 16 July, 2021. The conference has been organized by the Lisbon School of Architecture (FAUL), NOVA School of Social Sciences and Humanities, the Portuguese Society for Construction History Studies and the University of the Azores. The contributions cover the wide interdisciplinary spectrum of Construction History and consist on the most recent advances in theory and practical case studies analysis, following themes such as: - epistemological issues; - building actors; - building materials; - building machines, tools and equipment; - construction processes; - building services and techniques ; -structural theory and analysis ; - political, social and economic aspects; - knowledge transfer and cultural translation of construction cultures. Furthermore, papers presented at thematic sessions aim at covering important problematics, historical periods and different regions of the globe, opening new directions for Construction History research. We are what we build and how we build; thus, the study of Construction History is now more than ever at the centre of current debates as to the shape of a sustainable future for humankind. Therefore, History of Construction Cultures is a critical and indispensable work to expand our understanding of the ways in which everyday building activities have been perceived and experienced in different cultures, from ancient times to our century and all over the world.

This book combines concepts from the history of religions with Byzantine studies in its assessments of kings, symbols, and cities in a diachronic and cross-cultural analysis. The work attests, firstly, that the symbolic art and architecture of ancient cities—commissioned by their monarchs expressing their relationship with their gods—show us that religiosity was inherent to such enterprises. It also demonstrates that what transpired from the first cities in history to Byzantine Christendom is the gradual replacement of the pagan ruler cult—which was inherent to city-building in antiquity—with the ruler becoming subordinate to Christ; exemplified by representations of the latter as the ‘Master of All’ (Pantokrator). Beginning in Mesopotamia, the book continues with an analysis of city-building by rulers in Egypt, Greece, and Rome, before addressing Judaism (specifically, the city of Jerusalem) and Christianity as shifting the emphasis away from pagan-gods and rulers to monotheistic perceptions of God as elevated above worldly kings. It concludes with an assessment of Christian Rome and Constantinople as typifying the evolution from the ancient and classical world to Christendom.

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.

New computational design tools have evolved rapidly and been increasingly applied in the field of design in recent years, complimenting and even replacing the traditional design media and approaches. Design as both the process and product are changing due to the emergence and adoption of these new technologies. Understanding and assessing the impact of these new computational design environments on design and designers is important for advancing design in the contemporary context. Do these new computational environments support or hinder design creativity? How do those tools facilitate designers’ thinking? Such knowledge is also important for the future development of design technologies. Research shows that design is never a mysterious non-understandable process, for example, one general view is that design process shares a common analysis-synthesis-evaluation model, during which designers interact between design problem and solution spaces. Understanding designers’ thinking in different environments is the key to design research, education and practice. This book focuses on emerging computational design environments, whose impact on design and designers have not been comprehensively and systematically studied. It comprises three parts. The history and recent developments of computational design technologies are introduced in Part I. The main categories of technologies cover from computer-aided drafting and modelling tools, to visual programming and scripting tools for algorithmic design, to advanced interfaces and platforms for interactions between designers, between designers and computers, and between the virtual environment and the physical reality. To critically explore design thinking, especially in these new computational design environments, formal approaches to studying design thinking and design cognition are introduced and compared in Part II, drawing on literature and studies from the 70s to the current era. Part III concludes the book by exploring the impact of different computational design technologies on design and designers, using a series of case studies conducted by the author team building on their close collaboration over the past five years. The book offers new insights into designers’ thinking in the rapidly evolving computational design environments, which have not been critically and systematically studied and reported in the current literature. The book is meant for design researchers, educators and students, professional practitioners and consultants, as well as people who are interested in computational design in general.

The Routledge Handbook on the Sciences in Islamicate Societies provides a comprehensive survey on science in the Islamic world from the 8th to the 19th century. Across six sections, a group of subject experts discuss and analyze scientific practices across a wide range of Islamicate societies. The authors take into consideration several contexts in which science was practiced, ranging from intellectual traditions and persuasions to institutions, such as courts, schools, hospitals, and observatories, to the materiality of scientific practices, including the arts and craftsmanship. Chapters also devote attention to scientific practices of minority communities in Muslim majority societies, and Muslim minority groups in societies outside the Islamicate world, thereby allowing readers to better understand the opportunities and constraints of scientific practices under varying local conditions. Through replacing Islam with Islamicate societies, the book opens up ways to explain similarities and differences between diverse societies ruled by Muslim dynasties. This handbook will be an invaluable resource for both established academics and students looking for an introduction to the field. It will appeal to those involved in the study of the history of science, the history of ideas, intellectual history, social or cultural history, Islamic studies, Middle East and African studies including history, and studies of Muslim communities in Europe and South and East Asia.