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Alan Holden

Shapes, Space, and Symmetry (Dover Books on Mathematics)

by Alan Holden (Author)

4.5 38 ratings

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"Altogether a most instructive, entertaining, and esthetically pleasing book." — Science.
Since the ancient Greeks, the visualization of space has been a challenge that has intrigued men of learning. Through centuries of thoughtful looking, a number of three-dimensional figures or polyhedral, as the Greeks called them, have been discovered, admired, and wondered at for their mathematical elegance and beauty. And they have been put to use in remarkably diverse ways by engineers and builders, chemists and crystallographers, architects and sculptors.
This book describes very clearly and simply, and illustrates with beautiful photographs of models, a great number of three-dimensional figures, all but a few consisting of plane faces bounded by straight lines. It examines the nine regular solids — the five commonly called Platonic, described by Theaetetus in the fourth century B.C., and the four called Kepler-Poinsot, two each of which were discovered by Kepler and Poinsot many centuries later. And it examines many variations obtained by truncation, stellation, dualization, and compounding.
Writing for the layman as well as the student or professional in mathematics, Alan Holden explains the structure of the figures and demonstrates how they can be used to explain mathematics visually rather than by symbol systems, an effort hailed by Scientific American magazine as "a victory of clear, connected thinking over the theorematic method." At the end of the book the author includes a section containing instructions for constructing cardboard models.

ISBN-10

0486268519
ISBN-13

978-0486268514
Publisher

Dover Publications
Publication date

March 14, 2012
Language

English
Dimensions

5.9 x 0.6 x 8.9 inches
Print length

208 pages
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Product details

Publisher ‏ : ‎ Dover Publications (March 14, 2012)
Language ‏ : ‎ English
Paperback ‏ : ‎ 208 pages
ISBN-10 ‏ : ‎ 0486268519
ISBN-13 ‏ : ‎ 978-0486268514
Item Weight ‏ : ‎ 12.6 ounces
Dimensions ‏ : ‎ 5.9 x 0.6 x 8.9 inches

Best Sellers Rank: #864,767 in Books (See Top 100 in Books)
- #211 in Geometry
- #672 in Geometry & Topology (Books)

Customer Reviews:
4.5 38 ratings

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4.5 out of 5

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S. Fay

Plenty of inspiration

Reviewed in the United States on October 16, 2008

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This book is beautiful. It is easy to read and the ideas are beautifully illustrated through photos of models created by the author, a real feat given the 3D subject. A guide for building the models is included; as the author states, the best way to learn about these shapes is to build them. The book carefully and succinctly guides the non-mathematician through fascinating and illuminating transformations of regular polyhedra using their symmetries and duality.

For the artist or craftsman who wants to make something inspired by polyhedra, this book is perfect. This is one of my favorite books because every time I pick it up I have a new idea for something to make.

3 people found this helpful

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Tanis Coralee Leonhardi

High quality geometry fodder

Reviewed in the United States on January 12, 2020

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I love this book. I got it thinking I wouldn’t like it and was pleasantly surprised by how good it is. The concepts covered are well explained both with words and visuals and the concepts covered flow coherently throughout the whole book. One I am proud to have in my geometry collection.

One person found this helpful

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synaptic

How did I miss this book?

Reviewed in the United States on December 6, 2018

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This is a fascinating book if you're doing a deep dive on geometry. Good complement to Synergetics and a fantastic addition for anybody with a 3d printer. I was personally interested in the concept of "nolids" and this book describes them in some detail. I was so happy with this book, I bought a copy for a friend as a gift.

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Michelle C.

Good book on overlooked topic

Reviewed in the United States on December 27, 2015

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Filled with photos and good information on polyhedra. Since most math courses in high school do not discuss these shapes, this book was perfect for learning about the topic.

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Nosedive

This man will make you feel lazy

Reviewed in the United States on February 19, 2013

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Detailed text, many photographs of a large collection of well made models and clear figures bound together by concise, casual text. If you are interested in solid geometry for any reason, this book belongs in your collection.

One person found this helpful

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Dan V

pictorial journey through the foundations of regular solids

Reviewed in the United States on May 16, 2014

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gave me a much better understanding of the variety of 3D forms. Very methodical. Shame the cover doesnt do it justice. Look inside !

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Viktor Blasjo

Quite charming book on polyhedra

Reviewed in the United States on November 23, 2006

This book illustrates many beautiful ideas through photographs of paper models with concise commentary. First the regular polyhedra, of course, followed by variations of the models that brings out their duality and symmetry properties. We also study how the regular polyhedra can be compounded, inscribed in each-other, and pasted together along a common cross-section ("when halves of the Platonic solids having the same cross-sections come together, monsters are born"). We also study truncating the regular polyhedra to obtain the semi-regular polyhedra, stellating to obtain non-convex regular solids, and faceting to obtain non-convex semi-regular polyhedra. There is a deplorably short but somewhat useful section with practical advice on building models. "Suitable cardboard is of the sort used for mounting photographs, and suitable glue is a 'white glue' of the sort exemplified by 'Elmer's Glue-all' ... For several hours the joints remain sufficiently flexible to permit adjustment of the dihedral angle". It's a pity that we are advised to construct the sides of the regular polyhedra by unromantic means; equilateral triangles are to be made using "a draftsman's 30-60-90 triangle" and the construction of a regular pentagon "requires a guide made of heavier cardboard, such as an illustration board, with two edges meeting at the desired angle"---obviously you will want to construct the faces using ruler-and-compass constructions.

6 people found this helpful

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Andrew MacDonald

Little Gem

Reviewed in the United States on January 19, 2002

Alan Holden must be a very dedicated man. This short book on polyhedra is filled with pictures of intricate paper models, all made by the author. In the final section, showing how to construct similar models, one can see a photo of his workshop with hundreds of models arrayed neatly on shelves behind him. This book was clearly a work of love.
Most of the book is occupied with a treatment of regular and semiregular polyhedra, prisms and antiprisms. These are examined in some depth--for example, all nine regular polyhedra are constructed. The last fifty pages introduce other topics, such as packing, lattices, and knots; the treatment here is very brief, somewhat disappointing and leaving a desire for more depth. The same can be said of the final section, on construction--Holden gives general guidelines but leaves the reader to compute the dimensions of all the faces of his models himself.
The prose is clear and concise, rare for a mathematics book. But the real substance lies in the photographs of polyhedra models. These are contructed in such a way that it is always easy to see the details of the solid: faces of different shapes are made of different shades of paper, complicated models are shown in intermediate stages of construction, polyhedra to be compared (such as duals) are shown as individuals and interpenetrating. The great icosidodecahedron photo on page 112 (or its companion that might go by the same name on page 98) is almost worth the price of the book by itself.
This is not a rigorous treatment of the subject, but it is a beautiful one.

33 people found this helpful

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Top reviews from other countries

artofpets

Cook designs

Reviewed in Canada on June 27, 2019

Verified Purchase

Drawing

Thomas Dana Lloyd

extremely useful illustrations.

Reviewed in the United Kingdom on August 28, 2015

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Must read for anyone trying to understand topology, extremely useful illustrations.

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