How to guard an art gallery and other discrete mathematical adventures /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Michael, T. S., 1960-
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Baltimore : Johns Hopkins University Press, 2009.
Colección:Book collections on Project MUSE.
Temas:
Combinatorial analysis.
Algorithms.
Computer science > Mathematics.
Computer algorithms.
Analyse combinatoire.
Algorithmes.
Informatique > Mathématiques.
algorithms.
MATHEMATICS > Combinatorics.
Algorithms
Combinatorial analysis
Computer science > Mathematics
Popular works
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Contents
  • Preface
  • 1 How to Count Pizza Pieces
  • 1.1 The Pizza-Cutterâ€?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 â€?em and Sweep
  • 1.7 Eulerâ€?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 Pickâ€?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 Pickâ€?s Formula
  • 2.5 Making Change
  • 2.6 Pickâ€?s Formula: First Proof2.7 Pickâ€?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 References3.12 Problems
  • 4 Pixels, Lines, and Leap Years
  • 4.1 Pixels and Lines
  • 4.2 Lines and Distances
  • 4.3 Arithmetic Arrays
  • 4.4 Bresenhamâ€?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 Staircase5.7 Other Problems to Pour Over
  • 5.8 Number Theory and Fermatâ€?s Congruence
  • 5.9 Notes and References
  • 5.10 Problems
  • 6 From Stamps to Sylver Coins
  • 6.1 Sylvesterâ€?s Stamps
  • 6.2 Addition Tables and Symmetry
  • 6.3 Arithmetic Arrays and Sylvesterâ€?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 Squares7.2 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 Itâ€?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

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