The Geometry Of Environment

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.

This book presents a compendium of the urban layout maps of 2-mile square downtown areas of more than one hundred cities in developed and developing countries—all drawn at the same scale using high-resolution satellite images of Google Maps. The book also presents analytic studies using metric geometrical, topological (or network), and fractal measures of these maps. These analytic studies identify ordinaries, extremes, similarities, and differences in these maps; investigate the scaling properties of these maps; and develop precise descriptive categories, types and indicators for multidimensional comparative studies of these maps. The findings of these studies indicate that many geometric relations of the urban layouts of downtown areas follow regular patterns; that despite social, economic, and cultural differences among cities, the geometric measures of downtown areas in cities of developed and developing countries do not show significant differences; and that the geometric possibilities of urban layouts are vastly greater than those that have been realized so far in our cities.

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.

In the past decade, the field of comparative cognition has grown and thrived. No less rigorous than purely behavioristic investigations, examinations of animal intelligence are useful for scientists and psychologists alike in their quest to understand the nature and mechanisms of intelligence. Extensive field research of various species has yielded exciting new areas of research, integrating findings from psychology, behavioral ecology, and ethology in a unique and wide-ranging synthesis of theory and research on animal cognition. The Oxford Handbook of Comparative Cognition contains sections on perception and illusion, attention and search, memory processes, spatial cognition, conceptualization and categorization, problem solving and behavioral flexibility, and social cognition processes including findings in primate tool usage, pattern learning, and counting. The authors have incorporated findings and theoretical approaches that reflect the current state of the field. This comprehensive volume will be a must-read for students and scientists who want to know about the state of the art of the modern science of comparative cognition.

Cities affect every person's life, yet across the traditional divides of class, age, gender and political affiliation, armies of people are united in their dislike of the transformations that cities have undergone in recent times. The physical form of the urban environment is not a designer add-on to 'real' social issues; it is a central aspect of the social world. Yet in many people's experience, the cumulative impacts of recent urban development have created widely un-loved urban places. To work towards better-loved urban environments, we need to understand how current problems have arisen and identify practical action to address them. Urban Transformations examines the crucial issues relating to how cities are formed, how people use these urban environments and how cities can be transformed into better places. Exploring the links between the concrete physicality of the built environment and the complex social, economic, political and cultural processes through which the physical urban form is produced and consumed, Ian Bentley proposes a framework of ideas to provoke and develop current debate and new forms of practice.