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 takes a fresh approach to using educational tools to solve profound problems in societies. The authors bring perspectives from curriculum studies, mathematics education, environmental education, and Indigenous epistemologies to a new consideration of “geometries to think with”. These tools reveal the wealth of resources and interrelationships in our world that have the potential to reconfigure and revitalize education. The transdisciplinary nature of the chapters and authors emphasizes the need for thinking beyond boundaries, while respecting the wisdom inherent in intellectual disciplines and traditions.
An overview of the mechanisms and evolution of spatial cognition, integrating evidence from psychology, neuroscience, cognitive science, and computational geometry. Understanding how we deal with space requires input from many fields, including ethology, neuroscience, psychology, cognitive science, linguistics, geography, and spatial information theory. In From Geometry to Behavior, cognitive neuroscientist Hanspeter A. Mallot provides an overview of the basic mechanisms of spatial behavior in animals and humans, showing how they combine to support higher-level performance. Mallot explores the biological mechanisms of dealing with space, from the perception of visual space to the constructions of large space representations: that is, the cognitive map. The volume is also relevant to the epistemology of spatial knowledge in the philosophy of mind. Mallot aims to establish spatial cognition as a scientific field in its own right. His general approach is psychophysical, in that it focuses on quantitative descriptions of behavioral performance and their real-world determinants, thus connecting to the work of theorists in computational neuroscience, robotics, and computational geometry. After an overview of scientific thinking about space, Mallot covers spatial behavior and its underlying mechanisms in the order of increasing memory involvement. He describes the cognitive processes that underlie advanced spatial behaviors such as directed search, wayfinding, spatial planning, spatial reasoning, object building and manipulation, and communication about space. These mechanisms are part of the larger cognitive apparatus that also serves visual and object cognition; understanding events, actions, and causality; and social cognition, which includes language. Of all of these cognitive domains, spatial cognition most likely occurred first in the course of evolution and is the most widespread throughout the animal kingdom.
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.
Addressing both the literature and the visual arts of Anglo-American modernism, The Geometry of Modernism recovers a crucial development of modernism's early years that until now has received little sustained critical attention: the distinctive idiom composed of geometric forms and metaphors generated within the early modernist movement of Vorticism, formed in London in 1914. Focusing on the work of Wyndham Lewis, leader of the Vorticist movement, as well as Ezra Pound, H.D., and William Butler Yeats, Hickman examines the complex of motives out of which Lewis initially forged the geometric lexicon of Vorticism—and then how Pound, H.D., and Yeats later responded to it and the values that it encoded, enlisting both the geometric vocabulary and its attendant assumptions and ideals, in transmuted form, in their later modernist work. Placing the genesis and appropriation of the geometric idiom in historical context, Hickman explores how despite its brevity as a movement, Vorticism in fact exerted considerable impact on modernist work of the years between the wars, in that its geometric idiom enabled modernist writers to articulate their responses to both personal and political crises of the 1930s and 1940s. Informed by extensive archival research as well as treatment of several of the least-known texts of the modernist milieu, The Geometry of Modernism clarifies and enriches the legacy of this vital period.
