David Gale

Tracking the Automatic ANT (eBook, PDF)

And Other Mathematical Explorations

• Format: PDF

Produktbeschreibung

For those fascinated by the abstract universe of mathematics, David Gale's columns in "The Mathematical Intelligencer" have been a prime source of entertainment, and here his columns are collected for the first time in book form. Encouraged by the magazine's editor, Sheldon Axler, to write on whatever pleased him, Gale ranged far and wide across the field of mathematics, frequently returning to favorite themes: triangles, tilings, games and paradoxes, as well as the particular automaton that gives this collection its title, the "automatic ant." Suitable for everyone having some familiarity with mathematical ideas.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 241
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9781461221920
• Artikelnr.: 44179929

Autorenporträt

David Gale's Mathematical Entertainments columns in the Mathematical Intelligencer, a prime source of entertainment for everyone with an interest in mathematics, are here collected in book form for the first time. Gale has ranged widely over the entire field of mathematics yet returns often to favorite concerns: triangles, tilings, the mysterious properties of sequences given by simple recursions, and the peculiar automaton that gives this collection its title. This book requires some familiarity with mathematical concepts but not great sophistication.

Inhaltsangabe

1 Simple Sequences with Puzzling Properties.- 2 Probability Paradoxes.- 3 Historic Conjectures: More Sequence Mysteries.- 4 Privacy-Preserving Protocols.- 5 Surprising Shuffles.- 6 Hundreds of New Theorems in a Two-Thousand-Year-Old Subject: Where Will It End?.- 7 Pop Math and Protocols.- 8 Six Variations on the Variational Method.- 9 Tiling a Torus: Cutting a Cake.- 10 The Automatic Ant: Compassless Constructions.- 11 Games: Real, Complex, Imaginary.- 12 Coin Weighing: Square Squaring.- 13 The Return of the Ant and the Jeep.- 14 Go.- 15 More Paradoxes. Knowledge Games.- 16 Triangles and Computers.- 17 Packing Tripods.- 18 Further Travels with My Ant.- 19 The Shoelace Problem.- 20 Triangles and Proofs.- 21 Polyominoes.- 22 A Pattern Problem, A Probability Paradox, and A Pretty Proof.- 23 The Sun, the Moon, and Mathematics.- 24 In Praise of Numberlessness.- Appendix 1 A Curious Nim-Type Game.- Appendix 2 The Jeep Once More or Jeeper by the Dozen.- Appendix 3 Nineteen Problems in Elementary Geometry (by Armando Machado).- Appendix 4 The Truth and Nothing But the Truth.