Lobachevsky wrote Pangeometry in 1855, the year before his death. This memoir is a resume of his work on non-Euclidean geometry and its applications and can be considered his clearest account on the subject. It is also the conclusion of his life's work and the last attempt he made to acquire recognition. The treatise contains basic ideas of hyperbolic geometry, including the trigonometric formulae, the techniques of computation of arc length, of area and of volume, with concrete examples. It also deals with the applications of hyperbolic geometry to the computation of new definite integrals. The techniques are different from those found in most modern books on hyperbolic geometry since they do not use models. Besides its historical importance, Lobachevsky's Pangeometry is a beautiful work, written in a simple and condensed style. The material that it contains is still very alive, and reading this book will be most useful for researchers and for students in geometry and in the history of science. It can be used as a textbook, as a sourcebook, and as a repository of inspiration. The present edition provides the first complete English translation of Pangeometry available in print. It contains facsimiles of both the Russian and the French original versions. The translation is accompanied by notes, followed by a biography of Lobachevky and an extensive commentary.

How psychological ideas of space have profoundly affected architectural and artistic expression in the twentieth century. Beginning with agoraphobia and claustrophobia in the late nineteenth century, followed by shell shock and panic fear after World War I, phobias and anxiety came to be seen as the mental condition of modern life. They became incorporated into the media and arts, in particular the spatial arts of architecture, urbanism, and film. This "spatial warping" is now being reshaped by digitalization and virtual reality. Anthony Vidler is concerned with two forms of warped space. The first, a psychological space, is the repository of neuroses and phobias. This space is not empty but full of disturbing forms, including those of architecture and the city. The second kind of warping is produced when artists break the boundaries of genre to depict space in new ways. Vidler traces the emergence of a psychological idea of space from Pascal and Freud to the identification of agoraphobia and claustrophobia in the nineteenth century to twentieth-century theories of spatial alienation and estrangement in the writings of Georg Simmel, Siegfried Kracauer, and Walter Benjamin. Focusing on current conditions of displacement and placelessness, he examines ways in which contemporary artists and architects have produced new forms of spatial warping. The discussion ranges from theorists such as Jacques Lacan and Gilles Deleuze to artists such as Vito Acconci, Mike Kelley, Martha Rosler, and Rachel Whiteread. Finally, Vidler looks at the architectural experiments of Frank Gehry, Coop Himmelblau, Daniel Libeskind, Greg Lynn, Morphosis, and Eric Owen Moss in the light of new digital techniques that, while relying on traditional perspective, have radically transformed the composition, production, and experience—perhaps even the subject itself—of architecture.

Examines various attempts to prove Euclid's parallel postulate -- by the Greeks, Arabs and Renaissance mathematicians. Ranging through the 17th, 18th, and 19th centuries, it considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, Schweikart, Taurinus, J. Bolyai and Lobachewsky.

"The artist and architect El Lissitzky (1890-1941) is celebrated for his contributions to painting, architecture, photography, and graphic design, and for his role in disseminating Russian and Soviet avant-garde art in Europe during the 1920s. Though he worked in a diversity of media, Lissitzky nonetheless produced the majority of his work on paper in the form of innovative photomontages, architectural drawings, lithographs, typography, books, and photo magazines. This monograph--the first career-spanning archival study of Lissitzky since 1968--reveals that the artist's multiple pursuits arose from his deep commitment to print as the premier medium of public exchange in the young and turbulent twentieth century. Samuel Johnson demonstrates that paper and print media were preoccupations that shaped Lissitzky's worldview, values, politics, and production in ways that have never been fully appreciated. Probing Lissitzky's stance on the problems of distribution and reception, this book offers a compelling and nuanced portrait of Lissitzky as experimenter, visionary designer, technocrat, and propagandist-the very prototype of the twentieth-century artist, with a legacy that remains largely on paper"--

Examines various attempts to prove Euclid's parallel postulate -- by the Greeks, Arabs and Renaissance mathematicians. It considers forerunners and founders such as Saccheri, Lambert, Legendre, W. Bolyai, Gauss, others. Includes 181 diagrams.

Advances in Heat Transfer