Have you ever daydreamed about digging a hole to the other side of the world? Robert Banks not only entertains such ideas but, better yet, he supplies the mathematical know-how to turn fantasies into problem-solving adventures. In this sequel to the popular Towing Icebergs, Falling Dominoes (Princeton, 1998), Banks presents another collection of puzzles for readers interested in sharpening their thinking and mathematical skills. The problems range from the wondrous to the eminently practical. In one chapter, the author helps us determine the total number of people who have lived on earth; in another, he shows how an understanding of mathematical curves can help a thrifty lover, armed with construction paper and scissors, keep expenses down on Valentine's Day.
In twenty-six chapters, Banks chooses topics that are fairly easy to analyze using relatively simple mathematics. The phenomena he describes are ones that we encounter in our daily lives or can visualize without much trouble. For example, how do you get the most pizza slices with the least number of cuts? To go from point A to point B in a downpour of rain, should you walk slowly, jog moderately, or run as fast as possible to get least wet? What is the length of the seam on a baseball? If all the ice in the world melted, what would happen to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides?
Covering a broad range of fields, from geography and environmental studies to map- and flag-making, Banks uses basic algebra and geometry to solve problems. If famous scientists have also pondered these questions, the author shares the historical details with the reader. Designed to entertain and to stimulate thinking, this book can be read for sheer personal enjoyment.
Review:
... Banks turns trivial questions into mind-expanding demonstrations of the magical powers of mathematics. Nor does he restrict himself to trivial questions: his shrewd analyses coax secrets out of such weighty topics as global population growth and the melting of polar ice caps. . . . Not a math textbook which teaches readers how to solve set types of problems, this collection of puzzles does something far more important: it teaches us how to delight in unexpected challenges to our numerical imagination. (Booklist)
... [Banks displays] a playful imagination and love of the fantastic that one would not ordinarily associate with a mathematical engineer. . . . Banks's style is entertaining but never condescending. (The Christian Science Monitor)
Table of contents:
Preface ix
Acknowledgments xiii
Chapter 1 Broad Stripes and Bright Stars 3
Chapter 2 More Stars, Honeycombs, and Snowflakes 13
Chapter 3 Slicing Things Like Pizzas and Watermelons 23
Chapter 4 Raindrops Keep Falling on My Head and Other Goodies 34
Chapter 5 Raindrops and Other Goodies Revisited 44
Chapter 6 Which Major Rivers Flow Uphill? 49
Chapter 7 A Brief Look at pi, e, and Some Other Famous Numbers 57
Chapter 8 Another Look at Some Famous Numbers 69
Chapter 9 Great Number Sequences: Prime, Fibonacci, and Hailstone 78
Chapter 10 A Fast Way to Escape 97
Chapter 11 How to Get Anywhere in About Forty-Two Minutes 105
Chapter 12 How Fast Should You Run in the Rain? 114
Chapter 13 Great Turtle Races: Pursuit Curves 123
Chapter 14 More Great Turtle Races: Logarithmic Spirals 131
Chapter 15 How Many People Have Ever Lived? 138
Chapter 16 The Great Explosion of 2023 146
Chapter 17 How to Make Fairly Nice Valentines 153
Chapter 18 Somewhere Over the Rainbow 163
Chapter 19 Making Mathematical Mountains 177
Chapter 20 How to Make Mountains out of Molehills 184
Chapter 21 Moving Continents from Here to There 196
Chapter 22 Cartography: How to Flatten Spheres 204
Chapter 23 Growth and Spreading and Mathematical Analogies 219
Chapter 24 How Long Is the Seam on a Baseball? 232
Chapter 25 Baseball Seams, Pipe Connections, and World Travels 247
Chapter 26 Lengths, Areas, and Volumes of All Kinds of Shapes 256
References 279
Index 285
In twenty-six chapters, Banks chooses topics that are fairly easy to analyze using relatively simple mathematics. The phenomena he describes are ones that we encounter in our daily lives or can visualize without much trouble. For example, how do you get the most pizza slices with the least number of cuts? To go from point A to point B in a downpour of rain, should you walk slowly, jog moderately, or run as fast as possible to get least wet? What is the length of the seam on a baseball? If all the ice in the world melted, what would happen to Florida, the Mississippi River, and Niagara Falls? Why do snowflakes have six sides?
Covering a broad range of fields, from geography and environmental studies to map- and flag-making, Banks uses basic algebra and geometry to solve problems. If famous scientists have also pondered these questions, the author shares the historical details with the reader. Designed to entertain and to stimulate thinking, this book can be read for sheer personal enjoyment.
Review:
... Banks turns trivial questions into mind-expanding demonstrations of the magical powers of mathematics. Nor does he restrict himself to trivial questions: his shrewd analyses coax secrets out of such weighty topics as global population growth and the melting of polar ice caps. . . . Not a math textbook which teaches readers how to solve set types of problems, this collection of puzzles does something far more important: it teaches us how to delight in unexpected challenges to our numerical imagination. (Booklist)
... [Banks displays] a playful imagination and love of the fantastic that one would not ordinarily associate with a mathematical engineer. . . . Banks's style is entertaining but never condescending. (The Christian Science Monitor)
Table of contents:
Preface ix
Acknowledgments xiii
Chapter 1 Broad Stripes and Bright Stars 3
Chapter 2 More Stars, Honeycombs, and Snowflakes 13
Chapter 3 Slicing Things Like Pizzas and Watermelons 23
Chapter 4 Raindrops Keep Falling on My Head and Other Goodies 34
Chapter 5 Raindrops and Other Goodies Revisited 44
Chapter 6 Which Major Rivers Flow Uphill? 49
Chapter 7 A Brief Look at pi, e, and Some Other Famous Numbers 57
Chapter 8 Another Look at Some Famous Numbers 69
Chapter 9 Great Number Sequences: Prime, Fibonacci, and Hailstone 78
Chapter 10 A Fast Way to Escape 97
Chapter 11 How to Get Anywhere in About Forty-Two Minutes 105
Chapter 12 How Fast Should You Run in the Rain? 114
Chapter 13 Great Turtle Races: Pursuit Curves 123
Chapter 14 More Great Turtle Races: Logarithmic Spirals 131
Chapter 15 How Many People Have Ever Lived? 138
Chapter 16 The Great Explosion of 2023 146
Chapter 17 How to Make Fairly Nice Valentines 153
Chapter 18 Somewhere Over the Rainbow 163
Chapter 19 Making Mathematical Mountains 177
Chapter 20 How to Make Mountains out of Molehills 184
Chapter 21 Moving Continents from Here to There 196
Chapter 22 Cartography: How to Flatten Spheres 204
Chapter 23 Growth and Spreading and Mathematical Analogies 219
Chapter 24 How Long Is the Seam on a Baseball? 232
Chapter 25 Baseball Seams, Pipe Connections, and World Travels 247
Chapter 26 Lengths, Areas, and Volumes of All Kinds of Shapes 256
References 279
Index 285