- Hardcover: 465 pages
- Publisher: Cambridge University Press (12 Jun 1997)
- Language English
- ISBN-10: 0521554322
- ISBN-13: 978-0521554329
- Product Dimensions: 25.4 x 18.6 x 2.8 cm
- Average Customer Review: 5.0 out of 5 stars See all reviews (1 customer review)
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Amazon Bestsellers Rank:
2,182,071 in Books (See Top 100 in Books)
- #53 in Books > Science & Nature > Mathematics > Geometry & Topology > Euclidean Geometry
- See Complete Table of Contents
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Product Description
Review
'The topic itself … is easily visualised and it has a long history as part of our culture, interacting with philosophy, art and chemistry. Cromwell's treatment admirably exploits all these opportunities, with many interesting digressions and a lively historical commentary … popular exposition at a high level.' Sir Michael Atiyah, Times Higher Educational Supplement
'… plenty to fascinate.' New Scientist
'… Peter Cromwell has done us a great service by writing this handsome, scholarly and beautifully illustrated book.' Peter Giblin, The London Mathematical Society Newsletter
'This remarkable book goes far beyond the superficial, providing a solid and fascinating account of the history and mathematics of polyhedra, especially regular polyhedra. It is likely to become the classic book on the topic.' MAA Online
' … a fascinating book … the book holds many surprises and will find rich use among students of both mathematics and computer science.' Choice
' … a well got-up book with an abundant and beautiful material of illustration. The study of polyhedra, as the author explicitly states, 'is currently enjoying something of a renaissance'. This work itself will surely help this renaissance, and may be an enjoyable reading for a very wide audience.' Acta. Sci. Math.
' … the book should have a wide and appreciative audience of all ages.' The Times Higher Education Supplement
' … this book contains a thorough treatment of all that is known about polyhedra … A very interesting and detailed account.' European Mathematical Society
' … well-illustrated throughout with line diagrams, as well as several colour plates of the author's own superb models. The writing is clear and entertaining, and reassuringly anticipates many of the reader's questions.' Thomas Bending, The Mathematical Gazette
'… plenty to fascinate.' New Scientist
'… Peter Cromwell has done us a great service by writing this handsome, scholarly and beautifully illustrated book.' Peter Giblin, The London Mathematical Society Newsletter
'This remarkable book goes far beyond the superficial, providing a solid and fascinating account of the history and mathematics of polyhedra, especially regular polyhedra. It is likely to become the classic book on the topic.' MAA Online
' … a fascinating book … the book holds many surprises and will find rich use among students of both mathematics and computer science.' Choice
' … a well got-up book with an abundant and beautiful material of illustration. The study of polyhedra, as the author explicitly states, 'is currently enjoying something of a renaissance'. This work itself will surely help this renaissance, and may be an enjoyable reading for a very wide audience.' Acta. Sci. Math.
' … the book should have a wide and appreciative audience of all ages.' The Times Higher Education Supplement
' … this book contains a thorough treatment of all that is known about polyhedra … A very interesting and detailed account.' European Mathematical Society
' … well-illustrated throughout with line diagrams, as well as several colour plates of the author's own superb models. The writing is clear and entertaining, and reassuringly anticipates many of the reader's questions.' Thomas Bending, The Mathematical Gazette
Product Description
Polyhedra have cropped up in many different guises throughout recorded history. In modern times, polyhedra and their symmetries have been cast in a new light by combinatorics and group theory. This book 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 presenting a rigorous treatment of the mathematics involved. It is attractively illustrated with dozens of diagrams to illustrate ideas that might otherwise prove difficult to grasp. Historians of mathematics as well as those more interested in the mathematics itself, will find this unique book fascinating.
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First Sentence
One of the most basic applications of mathematics is the determination of area and volume. Read the first page
Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
One of the most basic applications of mathematics is the determination of area and volume. Read the first page
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Front Cover | Copyright | Table of Contents | Excerpt | Index | Back Cover
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Customer Reviews
Most Helpful Customer Reviews
5 of 5 people found the following review helpful
Format:Paperback
This book achieves a good balance between very basic definitions of polyhedra, starting with how they were discovered and used in as far back as Ancient Greek civilisation, and then explaining how they can be classified and explored using different mathematical algorithms and axioms. From the cube to the ridiculously complex stellations of the icosahedron, and beyond, this book is ideal for those wishing to explore polyhedra in much more detail, and maybe even do some exploring of their own!
Most Helpful Customer Reviews on Amazon.com (beta)
Amazon.com:
7 reviews
15 of 15 people found the following review helpful
The _Best_ Polyhedra Book
13 Aug 2000
Format:Paperback
I've read many books on polyhedra, and this is the best I have seen. It covers the history and mathematics of many different polyhedra; the Platonic and Archimedean solids are just the beginning. Kepler's rhombic polyhedra, stellated polyhedra, Miller's solid, etc. -- it's all here. The diagrams are exceptional. I teach high school geometry, and have found this book to be an essential resource in class. The level of detail is quite high, making the book useful as a straight-through read (for someone who is really into math) or a book to flip around in (for those who find heavy math intimidating, but still like polyhedra). Includes helpful tips for model-making. Buy it!
6 of 6 people found the following review helpful
A good treatment of the subject
8 Sep 2007
Format:Paperback|Amazon Verified Purchase
I really like this book. It would be easy to say it's the best book on the subject that I've seen, but that doesn't say too much, because it's just about the only book I've ever seen devoted exclusively to this subject. So let me say instead that if you are at all interested in the geometric objects known as polyhedra, you will probably find something interesting in this book.
The author deals with the classical geometry of polyhedra, but not exclusively with that aspect. He covers the symmetry properties, best explained in terms of group theory concepts, and introduces and explains the notation of Schoenflies for describing symmetry groups (one of the two most common notations, and the one most used by people interested in things like molecular structure). This makes the book useful as well for those who want to learn about symmetry, and in fact this book is in many ways better for this purpose than many books I have seen with "symmetry" in their titles.
There is one thing with which I find fault: the index is inadequate. I had looked to see whether the book had a section describing the polyhedra known as Johnson solids, and found no reference to either "Norman Johnson" (after whom they are named) or "Johnson solids" in the index. But later, on scanning through the book, I found a very good treatment, explaining Johnson's terminology and with good illustrations of the Johnson solids and related polyhedra. The index made the book appear to be less adequate than it is. If this book ever goes into a second edition, it needs someone to make a new index.
The author deals with the classical geometry of polyhedra, but not exclusively with that aspect. He covers the symmetry properties, best explained in terms of group theory concepts, and introduces and explains the notation of Schoenflies for describing symmetry groups (one of the two most common notations, and the one most used by people interested in things like molecular structure). This makes the book useful as well for those who want to learn about symmetry, and in fact this book is in many ways better for this purpose than many books I have seen with "symmetry" in their titles.
There is one thing with which I find fault: the index is inadequate. I had looked to see whether the book had a section describing the polyhedra known as Johnson solids, and found no reference to either "Norman Johnson" (after whom they are named) or "Johnson solids" in the index. But later, on scanning through the book, I found a very good treatment, explaining Johnson's terminology and with good illustrations of the Johnson solids and related polyhedra. The index made the book appear to be less adequate than it is. If this book ever goes into a second edition, it needs someone to make a new index.
12 of 15 people found the following review helpful
Comprehensive masterpiece!
25 July 2001
Format:Paperback
This is the best book about polyhedra! But it's not always easy to read. He has chosen to take a chronological approach. That means that sometimes you have to look around a bit.
I picked up the book wanting to understand two things.
1. What are the exact definition of the Platonic and Archimedian solids, i.e., how to destinguish the Platonic from the the Deltahedra and the 13 Archimedian from their isomeric forms and the pyramids.
3. What's the reason behind the names for the Kepler-Poinsot solids. Why is the great stellated dodecahedron called the great stellated dodecahedron?
Cromwell answers the first question beautifully in Chapter 2. The second question is first discussed in Chapter 4, but I was still confused. It was only in Chapter 7 that it started to make sense.
I believe the book will answer most of your questions, but you may have to look around for it.
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