Tracking the Automatic Ant: And Other Mathematical Explorations

ISBN-13: 9781461274537 / Angielski / Miękka / 2011 / 241 str.

David Gale

Opis

For those fascinated by the abstract universe of mathematics, David Gale's columns in The Mathematical Intelligencer have been a prime source of entertainment. Here Gale's 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 but frequently returned to favorite themes: triangles, tilings, the mysterious properties of sequences given by simple recursions, games and paradoxes, and the particular automaton that gives this collection its title, the "automatic ant." The level is suitable for those with some familiarity with mathematical ideas, but great sophistication is not needed.

Spis treści

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.

O autorze

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.