Contents -- Preface -- 1 How to Count Pizza Pieces -- 1.1 The Pizza-Cutter's Problem -- 1.2 A Recurring Theme -- 1.3 Make a Difference -- 1.4 How Many Toppings? -- 1.5 Proof without Words -- 1.6 Count 'em and Sweep -- 1.7 Euler's Formula for Plane Graphs -- 1.8 You Can Look It Up -- 1.9 Pizza Envy -- 1.10 Notes and References -- 1.11 Problems -- 2 Count on Pick's Formula -- 2.1 The Orchard and the Dollar -- 2.2 The Area of the Orchard -- 2.3 Twenty-nine Ways to Change a Dollar -- 2.4 Lattice Polygons and Pick's Formula -- 2.5 Making Change -- 2.6 Pick's Formula: First Proof -- 2.7 Pick's Formula: Second Proof -- 2.8 Batting Averages and Lattice Points -- 2.9 Three Dimensions and N-largements -- 2.10 Notes and References -- 2.11 Problems -- 3 How to Guard an Art Gallery -- 3.1 The Sunflower Art Gallery -- 3.2 Art Gallery Problems -- 3.3 The Art Gallery Theorem -- 3.4 Colorful Consequences -- 3.5 Triangular and Chromatic Assumptions -- 3.6 Modern Art Galleries -- 3.7 Art Gallery Sketches -- 3.8 Right-Angled Art Galleries -- 3.9 Guarding the Guards -- 3.10 Three Dimensions and the Octoplex -- 3.11 Notes and References -- 3.12 Problems -- 4 Pixels, Lines, and Leap Years -- 4.1 Pixels and Lines -- 4.2 Lines and Distances -- 4.3 Arithmetic Arrays -- 4.4 Bresenham's Algorithm -- 4.5 A Touch of Gray: Antialiasing -- 4.6 Leap Years and Line Drawing -- 4.7 Diophantine Approximations -- 4.8 Notes and References -- 4.9 Problems -- 5 Measure Water with a Vengeance -- 5.1 Simon Says: Measure Water -- 5.2 A Recipe for Bruce Willis -- 5.3 Skew Billiard Tables -- 5.4 Big Problems -- 5.5 How to Measure Water: An Algorithm -- 5.6 Arithmetic Arrays: Climb the Staircase -- 5.7 Other Problems to Pour Over -- 5.8 Number Theory and Fermat's Congruence -- 5.9 Notes and References -- 5.10 Problems -- 6 From Stamps to Sylver Coins -- 6.1 Sylvester's Stamps.

6.2 Addition Tables and Symmetry -- 6.3 Arithmetic Arrays and Sylvester's Formula -- 6.4 Beyond Sylvester: The Stamp Theorem -- 6.5 Chinese Remainders -- 6.6 The Tabular Sieve -- 6.7 McNuggets and Coin Exchanges -- 6.8 Sylver Coinage -- 6.9 Notes and References -- 6.10 Problems -- 7 Primes and Squares: Quadratic Residues -- 7.1 Primes and Squares -- 7.2 Quadratic Residues Are Squares -- 7.3 Errors: Detection amd Correctipn -- 7.4 Multiplication Tables, Legendre, and Euler -- 7.5 Some Square Roots -- 7.6 Marcia and Greg Flip a Coin -- 7.7 Round Up at the Gauss Corral -- 7.8 It's the Law: Quadratic Reciprocity -- 7.9 Notes and References -- 7.10 Problems -- References -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- J -- K -- L -- M -- N -- O -- P -- Q -- R -- S -- T -- U -- V -- W -- Z.