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A mathematical tapestry. Demonstrating the beautiful unity of mathematics. (English)
Cambridge: Cambridge University Press (ISBN 978-0-521-76410-0/hbk; 978-0-521-12821-6/pbk). xv, 290~p. (2010).
Over years the authors have published numerous relevant papers, which have now been culminated to this book. The common theme is a number threads running though the whole book and getting finally interwoven to an extraordinary mathematical tapestry: the type of paper folding, number theory, polyhedra, geometry, algebra, combinatorics, group theory, symmetry as well as history. In more detail the book begins with systematic and detailed instructions for paper folding Flexogonen. From the construction of many (polyhedral) models it leads to relationships and insights into number theory, the mathematical structure of polyhedra, combinatorial geometry, group theory and symmetry of geometric structures. The book gives many suggestions for discoveries on ones own and examples of justifications for specific problems. For all this, only basic mathematical skills are required. The book demonstrates the great unity of mathematics. This is supported by a wealth of instructive illustrations which one would wish to see, at least in parts, printed in colour as done on the cover of the book.
Reviewer: Erhard Quaisser (Potsdam)
Classification: A80 G40 K20 F60
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