Books about Polyhedra from Amazon.com

Leonhard Euler's polyhedron formula describes the structure of many objects--from soccer balls and gemstones to Buckminster Fuller's buildings and giant all-carbon molecules. Yet Euler's formula is so simple it can be explained to a child. Euler's Gem tells the illuminating story of this indispensable mathematical idea.

From ancient Greek geometry to today's cutting-edge research, Euler's Gem celebrates the discovery of Euler's beloved polyhedron formula and its far-reaching impact on topology, the study of shapes. In 1750, Euler observed that any polyhedron composed of V vertices, E edges, and F faces satisfies the equation V-E+F=2. David Richeson tells how the Greeks missed the formula entirely; how Descartes almost discovered it but fell short; how nineteenth-century mathematicians widened the formula's scope in ways that Euler never envisioned by adapting it for use with doughnut shapes, smooth surfaces, and higher dimensional shapes; and how twentieth-century mathematicians discovered that every shape has its own Euler's formula. Using wonderful examples and numerous illustrations, Richeson presents the formula's many elegant and unexpected applications, such as showing why there is always some windless spot on earth, how to measure the acreage of a tree farm by counting trees, and how many crayons are needed to color any map.

Filled with a who's who of brilliant mathematicians who questioned, refined, and contributed to a remarkable theorem's development, Euler's Gem will fascinate every mathematics enthusiast.

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With step-by-step diagrams, detailed instructions and over 70 photographs in vibrant full-color, internationally-renowned origamist and author Tomoko Fuse offers an innovative approach to origami based on assembling separate, multi-dimensional shapes into one structure.
Some of the shapes, like pyramids or four-sided boxes, are simple to master, even for a beginner. Others are quite complex and require much more experience and proficiency. Fuse uses a system to indicate the level of difficulty for each project with one, two or three stars, so the reader knows from the start, how challenging a project is likely to be..
Price: $11.97 [Notify me when price goes down.]

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How can linkages, pieces of paper, and polyhedra be folded? The authors present hundreds of results and over 60 unsolved 'open problems' in this comprehensive look at the mathematics of folding, with an emphasis on algorithmic or computational aspects. Folding and unfolding problems have been implicit since Albrecht Dürer in the early 1500s, but have only recently been studied in the mathematical literature. Over the past decade, there has been a surge of interest in these problems, with applications ranging from robotics to protein folding. A proof shows that it is possible to design a series of jointed bars moving only in a flat plane that can sign a name or trace any other algebraic curve. One remarkable algorithm shows you can fold any straight-line drawing on paper so that the complete drawing can be cut out with one straight scissors cut. Aimed primarily at advanced undergraduate and graduate students in mathematics or computer science, this lavishly illustrated book will fascinate a broad audience, from high school students to researchers..
Price: $34.33 [Notify me when price goes down.]

It was 1976--twenty-five years after R. Buckminster Fuller introduced geodesic domes when literary critic Hugh Kenner published this fully-illustrated practical manual for their construction Now, some twenty-five years later, Geodesic Math and How to Use It again presents a systematic method of design and provides a step-by-step method for producing mathematical specifications for orthodox geodesic domes, as well as for a variety of elliptical, super-elliptical, and other nonspherical contours.
Out of print since 1990, Geodesic Math and How To Use It is California's most requested backlist title. This edition is fully illustrated with complete original appendices..
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Polyhedra have cropped up in many different guises throughout recorded history Recently, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory. This unique text comprehensively documents the many and varied ways that polyhedra have come to the fore throughout the development of mathematics. The author strikes a balance between covering the historical development of the theory surrounding polyhedra and rigorous treatment of the mathematics involved. Attractively illustrated--including 16 color plates--Polyhedra elucidates ideas that have proven difficult to grasp. Mathematicians, as well as historians of mathematics, will find this book fascinating..
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