Discusses space in art and mathematics, the geometry of the fourth dimension, pattern recognition, time in space, and spatial concepts

In this insightful book, which is a revisionist math history as well as a revisionist art history, Tony Robbin, well known for his innovative computer visualizations of hyperspace, investigates different models of the fourth dimension and how these are applied in art and physics. Robbin explores the distinction between the slicing, or Flatland, model and the projection, or shadow, model. He compares the history of these two models and their uses and misuses in popular discussions. Robbin breaks new ground with his original argument that Picasso used the projection model to invent cubism, and that Minkowski had four-dimensional projective geometry in mind when he structured special relativity. The discussion is brought to the present with an exposition of the projection model in the most creative ideas about space in contemporary mathematics such as twisters, quasicrystals, and quantum topology. Robbin clarifies these esoteric concepts with understandable drawings and diagrams. Robbin proposes that the powerful role of projective geometry in the development of current mathematical ideas has been long overlooked and that our attachment to the slicing model is essentially a conceptual block that hinders progress in understanding contemporary models of spacetime. He offers a fascinating review of how projective ideas are the source of some of today’s most exciting developments in art, math, physics, and computer visualization.

This sociological analysis of Wright's architecture examines the interaction between people and the spaces they create. Satler shows how Wright explored a new architectural dimension, the space in which we live. Focusing on the Larkin Building (1904) and Unity Temple (1907), works that Wright considered important but that have received little attention, Satler delineates the social nature of space. She provides an analytic framework through which to understand Wright's buildings and his writings, revealing how the history of such works and cultural landscapes offer a basis for making social, political, and spatial choices about the future. Wright's specific architectural works provide a framework for constructing social histories of places and people because his designs represent a natural way to build and to live within a larger social landscape. This original study will appeal to sociologists, architects, urban and architectural historians, urban planners and anthropologists, and those interested in the work of Frank Lloyd Wright.

The Emergence of the Fourth Dimension describes the development and proliferation of the idea of higher dimensional space in the late nineteenth- and early twentieth-centuries. An idea from mathematics that was appropriated by occultist thought, it emerged in the fin de siècle as a staple of genre fiction and influenced a number of important Modernist writers and artists. Providing a context for thinking of space in dimensional terms, the volume describes an active interplay between self-fashioning disciplines and a key moment in the popularisation of science. It offers new research into spiritualism and the Theosophical Society and studies a series of curious hybrid texts. Examining works by Joseph Conrad, Ford Madox Ford, H.G. Wells, Henry James, H. P. Lovecraft, and others, the volume explores how new theories of the possibilities of time and space influenced fiction writers of the period, and how literature shaped, and was in turn shaped by, the reconfiguration of imaginative space occasioned by the n-dimensional turn. A timely study of the interplay between philosophy, literature, culture, and mathematics, it offers a rich resource for readers interested in nineteenth century literature, Modernist studies, science fiction, and gothic scholarship.

Exposition of fourth dimension, concepts of relativity as Flatland characters continue adventures. Topics include curved space time as a higher dimension, special relativity, and shape of space-time. Includes 141 illustrations.

This colorful, visual introduction to the fourth dimension provides a clear explanation of the concepts and numerous illustrations. It is written with a touch of personality that makes this an engaging read instead of a dry math text. The content is very accessible, yet at the same time detailed enough to satisfy the interests of advanced readers. This book is devoted to geometry; there are no spiritual or religious components to this book. May you enjoy your journey into the fascinating world of the fourth dimension! Contents: Introduction Chapter 0: What Is a Dimension? Chapter 1: Dimensions Zero and One Chapter 2: The Second Dimension Chapter 3: Three-Dimensional Space Chapter 4: A Fourth Dimension of Space Chapter 5: Tesseracts and Hypercubes Chapter 6: Hypercube Patterns Chapter 7: Planes and Hyperplanes Chapter 8: Tesseracts in Perspective Chapter 9: Rotations in 4D Space Chapter 10: Unfolding a Tesseract Chapter 11: Cross Sections of a Tesseract Chapter 12: Living in a 4D House Further Reading Glossary About the Author Put on your spacesuit, strap on your safety harness, swallow your anti-nausea medicine, and enjoy this journey into a fourth dimension of space! 10D, 9D, 8D, 7D, 6D, 5D, 4D, 3D, 2D, 1D, 0D. Blast off!

The long-awaited new edition of a groundbreaking work on the impact of alternative concepts of space on modern art. In this groundbreaking study, first published in 1983 and unavailable for over a decade, Linda Dalrymple Henderson demonstrates that two concepts of space beyond immediate perception—the curved spaces of non-Euclidean geometry and, most important, a higher, fourth dimension of space—were central to the development of modern art. The possibility of a spatial fourth dimension suggested that our world might be merely a shadow or section of a higher dimensional existence. That iconoclastic idea encouraged radical innovation by a variety of early twentieth-century artists, ranging from French Cubists, Italian Futurists, and Marcel Duchamp, to Max Weber, Kazimir Malevich, and the artists of De Stijl and Surrealism. In an extensive new Reintroduction, Henderson surveys the impact of interest in higher dimensions of space in art and culture from the 1950s to 2000. Although largely eclipsed by relativity theory beginning in the 1920s, the spatial fourth dimension experienced a resurgence during the later 1950s and 1960s. In a remarkable turn of events, it has returned as an important theme in contemporary culture in the wake of the emergence in the 1980s of both string theory in physics (with its ten- or eleven-dimensional universes) and computer graphics. Henderson demonstrates the importance of this new conception of space for figures ranging from Buckminster Fuller, Robert Smithson, and the Park Place Gallery group in the 1960s to Tony Robbin and digital architect Marcos Novak.

The study of human body measurements on a comparative basis is known as anthropometrics. Its applicability to the design process is seen in the physical fit, or interface, between the human body and the various components of interior space. Human Dimension and Interior Space is the first major anthropometrically based reference book of design standards for use by all those involved with the physical planning and detailing of interiors, including interior designers, architects, furniture designers, builders, industrial designers, and students of design. The use of anthropometric data, although no substitute for good design or sound professional judgment should be viewed as one of the many tools required in the design process. This comprehensive overview of anthropometrics consists of three parts. The first part deals with the theory and application of anthropometrics and includes a special section dealing with physically disabled and elderly people. It provides the designer with the fundamentals of anthropometrics and a basic understanding of how interior design standards are established. The second part contains easy-to-read, illustrated anthropometric tables, which provide the most current data available on human body size, organized by age and percentile groupings. Also included is data relative to the range of joint motion and body sizes of children. The third part contains hundreds of dimensioned drawings, illustrating in plan and section the proper anthropometrically based relationship between user and space. The types of spaces range from residential and commercial to recreational and institutional, and all dimensions include metric conversions. In the Epilogue, the authors challenge the interior design profession, the building industry, and the furniture manufacturer to seriously explore the problem of adjustability in design. They expose the fallacy of designing to accommodate the so-called average man, who, in fact, does not exist. Using government data, including studies prepared by Dr. Howard Stoudt, Dr. Albert Damon, and Dr. Ross McFarland, formerly of the Harvard School of Public Health, and Jean Roberts of the U.S. Public Health Service, Panero and Zelnik have devised a system of interior design reference standards, easily understood through a series of charts and situation drawings. With Human Dimension and Interior Space, these standards are now accessible to all designers of interior environments.

"This new edition ensures that the book will continue to be internationally acknowledged as the standard work on the development of modern architecture." -Walter Gropius "A remarkable accomplishment. . . one of the most valuable reference books for students and professionals concerned with the reshaping of our environment. " -José Luis Sert A milestone in modern thought, Space, Time and Architecture has been reissued many times since its first publication in 1941 and translated into half a dozen languages. In this revised edition of Sigfried Giedion’s classic work, major sections have been added and there are 81 new illustrations. The chapters on leading contemporary architects have been greatly expanded. There is new material on the later development of Frank Lloyd Wright and the more recent buildings of Walter Gropius, particularly his American Embassy in Athens. In his discussion of Le Corbusier, Mr. Giedion provides detailed analyses of the Carpenter Center at Harvard University, Le Corbusier’s only building in the United States, and his Priory of La Tourette near Lyons. There is a section on his relations with his clients and an assessment of his influence on contemporary architecture, including a description of the Le Corbusier Center in Zurich (designed just before his death), which houses his works of art. The chapters on Mies van der Rohe and Alvar Aalto have been brought up to date with examples of their buildings in the sixties. There is an entirely new chapter on the Danish architect Jørn Utzon, whose work, as exemplified in his design for the Sydney Opera House, Mr. Giedion considers representative of post–World War II architectural concepts. A new essay, “Changing Notions of the City,” traces the evolution of the structure of the city throughout history and examines current attempts to deal with urban growth, as shown in the work of such architects as José Luis Sert, Kenzo Tange, and Fumihiko Maki. Mr. Sert’s Peabody Terrace is discussed as an example of the interlocking of the collective and individual spheres. Finally, the conclusion has been enlarged to include a survey of the limits of the organic in architecture.