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A MATHEMATICAL TAPESTRY

Demonstrating the Beautiful Unity of Mathematics

This easy-to-read book demonstrates how a simple geometric idea reveals fascinat-

ing connections and results in number theory, polyhedral geometry, combinatorial

geometry, and group theory. Using a systematic paper-folding procedure, it is

possible to construct a regular polygon with any number of sides. This remarkable

algorithm has led to interesting proofs of certain results in number theory, has

been used to answer combinatorial questions involving partitions of space, and has

enabled the authors to obtain the formula for the volume of a regular tetrahedron in

around three steps, using nothing more complicated than basic arithmetic and the

most elementary plane geometry. All of these ideas, and more, reveal the beauty

of mathematics and the interconnectedness of its various branches.

Detailed instructions, including clear illustrations, enable the reader to gain

hands-on experience constructing these models and to discover for themselves the

patterns and relationships they unearth.

peter hilton

is Distinguished Professor Emeritus in the Department of Math-

ematical Sciences at the State University of New York (SUNY), Binghamton.

jean pedersen

is Professor of Mathematics and Computer Science at Santa

Clara University, California.

sylvie donmoyer

is a professional artist and freelance illustrator (www.

scientiﬁc-illustrator.com).

A MATHEMATICAL TAPESTRY

Demonstrating the Beautiful Unity of Mathematics

PETER HILTON

State University of New York, Binghamton

JEAN PEDERSEN

Santa Clara University, California

With illustrations by

SYLVIE DONMOYER