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Description
Aristotle would have said that a geometer considers the shapes of things in the natural world, not insofar as shapes are physical, but rather by abstracting the qualities of figure from the things themselves. In a philosophical sense this book by Mr. Arthur is thus one about geometry. The original illustrations go artistically beyond what a reader might expect to find in a textbook, and yet there is still a useful discussion revealing the important secrets of the creative process from a mathematical perspective. As an exploration of symmetry and smoothness, the work exhibits the precision of a draftsman unfettered by the practical constraints of real construction and engineering. Mr. Arthur develops a style of a visual art that is less dependent on the physical coordination of drawing with a pencil or a digital stylus and an art that is more of a purely intellectual nature. Clearly for the mathematical reader at a level of study somewhat exceeding vector calculus, the book pr esents new possibilities of exotic shapes (by their torsion or concavity) still having desirable qualities such as differentiability, self-similarity or compactness. Included in this book are many full-color pictures of tessellations, polyhedrons, unusual curves and surfaces, and fractals, along with their generating equations, coordinates and diagrams. Graphics and images in this book produced with Mathematica. Related Topics Graphics, Recreational |
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