Power play

the long version

Power Play is a country walk through the magical world of numbers. Powers of numbers exhibit fascinating patterns, some of which indicate a deep and complex structure. This book collects many of them. The book can be enjoyed by anyone, regardless of technical background. The chapters are supplemented by notes, exercises and solutions directed to those who have some background in mathematics. Strict amateurs who ignore the exercises and notes will find that a background in high school algebra will carry them through. Many of the exercises can be done by high school students. Teachers at all levels will find resource material for both mainstream and enrichment mathematics. Mathematicians will find a handy compilation of results and references to the literature for material strewn over many books and journals of the last fifty years. While this book could be read as one listens to a symphony, there are exercises (with solutions) and references to the literature for those who would like to probe deeper. There is a great deal of enrichment material here, as well as exercises on basic mathematics that are more interesting than standard textbook fare.