How to Guard an Art Gallery
Subtitle: And Other Discrete Mathematical Adventures
By: T.S. Michael.
Publisher: Johns Hopkins University Press
Published: 2009
Place of publication: Baltimore, USA
Language: eng
Format: Paperback
Number of pages: 257
ISBN-13: 9780801892981; 9780801892998
Subjects: Combinatorial analysis; Algorithms; Computer science -- Mathematics
Description: 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.
Notes: Includes bibliographical references and index.
Table of contents: title: Contents
pagenum: v; title: Preface
pagenum: ix; label: 1
title: How to Count Pizza Pieces
pagenum: 1; label: 1.1
title: The Pizza-Cutter’s Problem
pagenum: 1; label: 1.2
title: A Recurring Theme
pagenum: 4; label: 1.3
title: Make a Difference
pagenum: 7; label: 1.4
title: How Many Toppings?
pagenum: 9; label: 1.5
title: Proof without Words
pagenum: 12; label: 1.6
title: Count ’em and Sweep
pagenum: 14; label: 1.7
title: Euler’s Formula for Plane Graphs
pagenum: 16; label: 1.8
title: You Can Look It Up
pagenum: 20; label: 1.9
title: Pizza Envy
pagenum: 21; label: 1.10
title: Notes and References
pagenum: 22; label: 1.11
title: Problems
pagenum: 24; label: 2
title: Count on Pick’s Formula
pagenum: 33; label: 2.1
title: The Orchard and the Dollar
pagenum: 33; label: 2.2
title: The Area of the Orchard
pagenum: 34; label: 2.3
title: Twenty-nine Ways to Change a Dollar
pagenum: 37; label: 2.4
title: Lattice Polygons and Pick’s Formula
pagenum: 42; label: 2.5
title: Making Change
pagenum: 46; label: 2.6
title: Pick’s Formula: First Proof
pagenum: 48; label: 2.7
title: Pick’s Formula: Second Proof
pagenum: 53; label: 2.8
title: Batting Averages and Lattice Points
pagenum: 56; label: 2.9
title: Three Dimensions and N-largements
pagenum: 58; label: 2.10
title: Notes and References
pagenum: 65; label: 2.11
title: Problems
pagenum: 66; label: 3
title: How to Guard an Art Gallery
pagenum: 73; label: 3.1
title: The Sunflower Art Gallery
pagenum: 73; label: 3.2
title: Art Gallery Problems
pagenum: 75; label: 3.3
title: The Art Gallery Theorem
pagenum: 81; label: 3.4
title: Colorful Consequences
pagenum: 83; label: 3.5
title: Triangular and Chromatic Assumptions
pagenum: 86; label: 3.6
title: Modern Art Galleries
pagenum: 88; label: 3.7
title: Art Gallery Sketches
pagenum: 89; label: 3.8
title: Right-Angled Art Galleries
pagenum: 93; label: 3.9
title: Guarding the Guards
pagenum: 96; label: 3.10
title: Three Dimensions and the Octoplex
pagenum: 102; label: 3.11
title: Notes and References
pagenum: 106; label: 3.12
title: Problems
pagenum: 107; label: 4
title: Pixels, Lines, and Leap Years
pagenum: 113; label: 4.1
title: Pixels and Lines
pagenum: 113; label: 4.2
title: Lines and Distances
pagenum: 116; label: 4.3
title: Arithmetic Arrays
pagenum: 118; label: 4.4
title: Bresenham’s Algorithm
pagenum: 123; label: 4.5
title: A Touch of Gray: Antialiasing
pagenum: 124; label: 4.6
title: Leap Years and Line Drawing
pagenum: 125; label: 4.7
title: Diophantine Approximations
pagenum: 128; label: 4.8
title: Notes and References
pagenum: 134; label: 4.9
title: Problems
pagenum: 135; label: 5
title: Measure Water with a Vengeance
pagenum: 139; label: 5.1
title: Simon Says: Measure Water
pagenum: 139; label: 5.2
title: A Recipe for Bruce Willis
pagenum: 142; label: 5.3
title: Skew Billiard Tables
pagenum: 144; label: 5.4
title: Big Problems
pagenum: 147; label: 5.5
title: How to Measure Water: An Algorithm
pagenum: 148; label: 5.6
title: Arithmetic Arrays: Climb the Staircase
pagenum: 151; label: 5.7
title: Other Problems to Pour Over
pagenum: 155; label: 5.8
title: Number Theory and Fermat’s Congruence
pagenum: 160; label: 5.9
title: Notes and References
pagenum: 164; label: 5.10
title: Problems
pagenum: 165; label: 6
title: From Stamps to Sylver Coins
pagenum: 169; label: 6.1
title: Sylvester’s Stamps
pagenum: 169; label: 6.2
title: Addition Tables and Symmetry
pagenum: 173; label: 6.3
title: Arithmetic Arrays and Sylvester’s Formula
pagenum: 176; label: 6.4
title: Beyond Sylvester: The Stamp Theorem
pagenum: 180; label: 6.5
title: Chinese Remainders
pagenum: 186; label: 6.6
title: The Tabular Sieve
pagenum: 188; label: 6.7
title: McNuggets and Coin Exchanges
pagenum: 190; label: 6.8
title: Sylver Coinage
pagenum: 194; label: 6.9
title: Notes and References
pagenum: 196; label: 6.10
title: Problems
pagenum: 198; label: 7
title: Primes and Squares: Quadratic Residues
pagenum: 207; label: 7.1
title: Primes and Squares
pagenum: 207; label: 7.2
title: Quadratic Residues Are Squares
pagenum: 208; label: 7.3
title: Errors: Detection amd Correctipn
pagenum: 212; label: 7.4
title: Multiplication Tables, Legendre, and Euler
pagenum: 216; label: 7.5
title: Some Square Roots
pagenum: 221; label: 7.6
title: Marcia and Greg Flip a Coin
pagenum: 224; label: 7.7
title: Round Up at the Gauss Corral
pagenum: 226; label: 7.8
title: It’s the Law: Quadratic Reciprocity
pagenum: 232; label: 7.9
title: Notes and References
pagenum: 239; label: 7.10
title: Problems
pagenum: 240; title: References
pagenum: 245; title: Index
pagenum: 251