Overview

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 presents 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. (Note: the present edition does not publish the source code.)

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9780692262344

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"Here is a brief summary of Mr. Arthur's experience involving mathematics and computer graphics. As a hobby for the high school years, he experimented with ray-tracing and geometric modeling software on his home computer and shared his animation videos with friends. At college, he studied math and worked as an engineering video illustrator, applying what he had learned with the home computer. He received a bachelors degree with honors in math and contributed to a television series about thermodynamics. A virtual reality company later employed him as a graphics programmer, focusing on animation and the interactivity of ""real-time"" content for amusement and business presentation. After that time he was a language teacher, a math teacher, and a student in graduate school where he learned to use LaTeX to write documents about math. For ten years since then, he has been spending some of his time drawing the pictures collected in this book."

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