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Beyond the Third Dimension: Geometry, Computer Graphics, and Higher Dimensions
Beyond the Third Dimension Geometry Computer Graphics and Higher Dimensions Author:Thomas F. Banchoff Living in a world of three-dimensional space, we can hardly conceive of phenomena of higher, or lower, dimension. What would a two-dimensional universe be like? How can we even attempt to picture objects of four... five... six dimensions? If we can visualize them, does that mean they are real? Such are the concepts explored in 'Beyond the Third ... more »Dimension, which investigates ways of picturing and understanding dimensions below and above our own. Author Thomas Banchoff, a leader in the study of higher dimensions, is well-known for his creation of computer graphics that let us visualize these previously inaccessible spaces. His images illustrate how the concept of dimensions is a theme that threads its way through mathematics and into the world beyond.
When we realize that a dimension does not have to be spatial, but could represent time, temperature, weight, energy, or other variables, we see that it has practical significance not only in mathematics, but also in physics, geology, medicine, and modern art. Ranging from Egyptian pyramids to the nineteenth-century satire 'Flatland' to the paintings of Salvador Dali, 'Beyond the Third Dimension' recounts our long fascination with extra-dimensional spaces, shapes, and structures.
The author first introduces the ideas of dimension and perspective in a skillful presentation of one and two dimensional worlds -- a journey that allows us to appreciate the relationship of our world to dimension higher than our own. He goes on to explain how geometers, scientists, philosophers, and artists have explored higher dimensions through metaphor, analogy, and more formal methods of coordinate geometry. And he shows how the modern graphics computer enables us to grasp concepts previously beyond our reach.
Liberally illustrated with Banchoff's acclaimed computer images and a colorful collection of photographs, this book expands the visual boundaries of our minds as it imparts a deeper understanding of topics in mathematics and science that are familiar, exotic-and altogether new.« less