# How to Guard an Art Gallery and Other Discrete Mathematical Adventures (Google eBook)

JHU Press, Aug 7, 2009 - Mathematics - 272 pages

What is the maximum number of pizza slices one can get by making four straight cuts through a circular pizza? How does a computer determine the best set of pixels to represent a straight line on a computer screen? How many people at a minimum does it take to guard an art gallery?

Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery.

This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

### What people are saying -Write a review

#### Review: How to Guard an Art Gallery and Other Discrete Mathematical Adventures

User Review  - Ed Smiley - Goodreads

Interesting exploration of algorithms. (Rules of calculation for you non-math types.) Turns out that there is a lot of math in something even as simple as stationing guards or cameras in any polygonal room so that there is line-of-sight to every part of every wall. Read full review

#### Review: How to Guard an Art Gallery and Other Discrete Mathematical Adventures

User Review  - Chris Herdt - Goodreads

Flipped through this at the bookstore. Looks like an entertaining exploration of combinatorics. Read full review

### Contents

 1 How to Count Pizza Pieces 1 2 Count on Picks Formula 33 3 How to Guard an Art Gallery 73 4 Pixels Lines and Leap Years 113 5 Measure Water with a Vengeance 139
 6 From Stamps to Sylver Coins 169 Quadratic Residues 207 References 245 Index 251 Copyright