PDF Ebook Shapes, Space and Symmetry, by Alan Holden
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Shapes, Space and Symmetry, by Alan Holden
PDF Ebook Shapes, Space and Symmetry, by Alan Holden
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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.
- Sales Rank: #7851254 in Books
- Published on: 1973-09
- Original language: English
- Number of items: 1
- Binding: Paperback
- 200 pages
Most helpful customer reviews
20 of 21 people found the following review helpful.
An excellent introduction to Archimedean Star Polyhedra
By Donald Rogers
This well-made and inexpensive book is brim-full of pictures of Alan Holden's models of polyhedra. It is a book for the hobbyist and the enthusiastic closet Pythagorean, more than it is for the professional mathematician. It is especially useful as an introduction to Archimedean star polyhedra, which are surely as beautiful as anything in geometry, and which were not fully catalogued until the 1950s.
If you find this material as compellingly fascinating as I do, you may want to follow up this book with these two:
"Polyhedron Models," by Magnus Wenninger, has a more thorough and systematic treatment of the Archimedean star polyhedra than Holden's book. These include some incredibly complicated models of "snub" star polyhedra -- spectacular stuff that is not included here. (On the other hand, Wenninger's book costs a good deal more.)
"Regular Polytopes," by H.S.M. Coxeter, is an elegantly written introduction to polyhedra in 3 and 4 dimensions. Coxeter himself wrote the first systematic treatment of the Archimedean star-polyhedra, and helped to discover the last few in the process. This book's illustrations are nowhere near as nice as the other ones', but this is balanced by its more rigorous mathematical treatment of the theme. Somebody needs to come up with a better way (using computer graphics?) to illustrate higher-dimensional polyhedra. In the meantime, this inexpensive book is the best I know on the subject.
33 of 35 people found the following review helpful.
Little Gem
By Andrew MacDonald
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.
65 of 68 people found the following review helpful.
A beautiful, simple and elegant book on polyhedra
By Hop David
A friend of mine lent me this book in 1975. (I still haven't given it back). Although this 200 page book is very simply and clearly written, I have never been able to sit down and read it from start to finish. Each part I read makes me stop and contemplate. After 24 years I still find new things in it! The book starts out describing the five Platonic solids. Next it explores the dualities: between the octahedron and cube, between the dodecahedron and icosohedron, and between the tetrahedron with itself. Holden talks about solids discovered by Kepler and Poinsot, space filling solids other than the cube, Nolids, lattices and a whole lot more. He also describes how to make your own models with cardboard and Elmers' glue. Doug Kendall's photographs of Holden's models are very pleasing. This is my favorite book.
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