An edition of How to guard an art gallery and other discrete mathematical adventures (2009)

How to Guard an Art Gallery

And Other Discrete Mathematical Adventures

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Cover of: How to Guard an Art Gallery by T. S. Michael
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An edition of How to guard an art gallery and other discrete mathematical adventures (2009)

How to Guard an Art Gallery

And Other Discrete Mathematical Adventures

by

  • 0 Ratings
  • 0 Want to read
  • 0 Currently reading
  • 0 Have read

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Publish Date
Publisher
Johns Hopkins University Press
Language
English
Pages
257

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Previews available in: English

Subjects
Combinatorial analysis, Algorithms, Computer science, Mathematics, Popular works, Computer science, mathematics

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Edition Availability
Cover of: How to Guard an Art Gallery
How to Guard an Art Gallery: And Other Discrete Mathematical Adventures
2009, Johns Hopkins University Press
Paperback in English
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Libraries near you: WorldCat

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Book Details

Published in

Baltimore, USA

Table of Contents

Contents Page v
Preface Page ix
1. How to Count Pizza Pieces Page 1 1.1. The Pizza-Cutter’s Problem Page 1 1.2. A Recurring Theme Page 4 1.3. Make a Difference Page 7 1.4. How Many Toppings? Page 9 1.5. Proof without Words Page 12 1.6. Count ’em and Sweep Page 14 1.7. Euler’s Formula for Plane Graphs Page 16 1.8. You Can Look It Up Page 20 1.9. Pizza Envy Page 21 1.10. Notes and References Page 22 1.11. Problems Page 24 2. Count on Pick’s Formula Page 33 2.1. The Orchard and the Dollar Page 33 2.2. The Area of the Orchard Page 34 2.3. Twenty-nine Ways to Change a Dollar Page 37 2.4. Lattice Polygons and Pick’s Formula Page 42 2.5. Making Change Page 46 2.6. Pick’s Formula: First Proof Page 48 2.7. Pick’s Formula: Second Proof Page 53 2.8. Batting Averages and Lattice Points Page 56 2.9. Three Dimensions and N-largements Page 58 2.10. Notes and References Page 65 2.11. Problems Page 66 3. How to Guard an Art Gallery Page 73 3.1. The Sunflower Art Gallery Page 73 3.2. Art Gallery Problems Page 75 3.3. The Art Gallery Theorem Page 81 3.4. Colorful Consequences Page 83 3.5. Triangular and Chromatic Assumptions Page 86 3.6. Modern Art Galleries Page 88 3.7. Art Gallery Sketches Page 89 3.8. Right-Angled Art Galleries Page 93 3.9. Guarding the Guards Page 96 3.10. Three Dimensions and the Octoplex Page 102 3.11. Notes and References Page 106 3.12. Problems Page 107 4. Pixels, Lines, and Leap Years Page 113 4.1. Pixels and Lines Page 113 4.2. Lines and Distances Page 116 4.3. Arithmetic Arrays Page 118 4.4. Bresenham’s Algorithm Page 123 4.5. A Touch of Gray: Antialiasing Page 124 4.6. Leap Years and Line Drawing Page 125 4.7. Diophantine Approximations Page 128 4.8. Notes and References Page 134 4.9. Problems Page 135 5. Measure Water with a Vengeance Page 139 5.1. Simon Says: Measure Water Page 139 5.2. A Recipe for Bruce Willis Page 142 5.3. Skew Billiard Tables Page 144 5.4. Big Problems Page 147 5.5. How to Measure Water: An Algorithm Page 148 5.6. Arithmetic Arrays: Climb the Staircase Page 151 5.7. Other Problems to Pour Over Page 155 5.8. Number Theory and Fermat’s Congruence Page 160 5.9. Notes and References Page 164 5.10. Problems Page 165 6. From Stamps to Sylver Coins Page 169 6.1. Sylvester’s Stamps Page 169 6.2. Addition Tables and Symmetry Page 173 6.3. Arithmetic Arrays and Sylvester’s Formula Page 176 6.4. Beyond Sylvester: The Stamp Theorem Page 180 6.5. Chinese Remainders Page 186 6.6. The Tabular Sieve Page 188 6.7. McNuggets and Coin Exchanges Page 190 6.8. Sylver Coinage Page 194 6.9. Notes and References Page 196 6.10. Problems Page 198 7. Primes and Squares: Quadratic Residues Page 207 7.1. Primes and Squares Page 207 7.2. Quadratic Residues Are Squares Page 208 7.3. Errors: Detection amd Correctipn Page 212 7.4. Multiplication Tables, Legendre, and Euler Page 216 7.5. Some Square Roots Page 221 7.6. Marcia and Greg Flip a Coin Page 224 7.7. Round Up at the Gauss Corral Page 226 7.8. It’s the Law: Quadratic Reciprocity Page 232 7.9. Notes and References Page 239 7.10. Problems Page 240 References Page 245 Index Page 251

Edition Notes

Includes bibliographical references and index.

Classifications

Dewey Decimal Class
511/.6
Library of Congress
QA164 .M53 2009, QA164.M53 2009

Contributors

Cover Design
Martha Sewall

The Physical Object

Format
Paperback
Pagination
xi, 257p
Number of pages
257
Dimensions
8.5 x 5.5 x .6 inches
Weight
11.2 ounces

ID Numbers

Open Library
OL23152988M
Internet Archive
howtoguardartgal00mich
ISBN 10
0801892988, 0801892996
ISBN 13
9780801892981, 9780801892998
LCCN
2009000435
OCLC/WorldCat
298325758
Library Thing
9073071
Goodreads
7102997
7332348

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History

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December 31, 2022 Edited by MARC Bot import existing book
December 4, 2022 Edited by ImportBot import existing book
October 13, 2022 Edited by ImportBot import existing book
December 22, 2020 Edited by MARC Bot import existing book
April 28, 2009 Created by ImportBot Imported from Library of Congress MARC record.