Environmental Geometry

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.

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.

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.

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.

Environmental information systems (EIS) are concerned with the management of data about the soil, the water, the air, and the species in the world around us. This first textbook on the topic gives a conceptual framework for EIS by structuring the data flow into 4 phases: data capture, storage, analysis, and metadata management. This flow corresponds to a complex aggregation process gradually transforming the incoming raw data into concise documents suitable for high-level decision support. All relevant concepts are covered, including statistical classification, data fusion, uncertainty management, knowledge based systems, GIS, spatial databases, multidimensional access methods, object-oriented databases, simulation models, and Internet-based information management. Several case studies present EIS in practice.