This easy-to-read book demonstrates how a simple geometric idea reveals fascinating connections and results in number theory, the mathematics of polyhedra, 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, ...

Combinatorial Games: Tic-Tac-Toe Theory (Encyclopedia of Mathematics and its Applications)

Traditional game theory has been successful at developing strategy in games of incomplete information: when one player knows something that the other does not. But it has little to say about games of complete information, for example tic-tac-toe, solitaire and hex. This is the subject of combinatorial game theory.

This second edition of Alexander Sofier’s Geometric Etudes in Combinatorial Mathematics provides supplementary reading materials to students of all levels interested in pursuing mathematics, especially in algebra, geometry, and combinatorial geometry.
Within the text, the author outlines an introduction to graph theory and combinatorics while exploring topics such as the pigeonhole principle, Borsuk problem, and theorems of Helly and Szokefalvi—Nagy.

Applications of Combinatorial Mathematics

In the last thirty years, combinatorial mathematics has found itself at the heart of many technological applications. The aims of the conference on which this book is based were to stimulate combinatorial mathematicians to pursue new lines of research of potential and practical importance,
and to uncover the breadth of applications to the subject.