Slicing Pizzas, Racing Turtles, and Further Adventures in Applied Mathematics

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Princeton University Press, May 2, 2012 - Mathematics - 304 pages
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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.

 

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Contents

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 π e and Some Other Famous Numbers
57
Chapter 8 Another Look at Some Famous Numbers
69
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
How to Flatten Spheres
204
Chapter 23 Growth and Spreading and Mathematical Analogies
219

Prime Fibonacci and Hailstone
78
Chapter 10 A Fast way to Escape
97
Chapter 11 How to Get Anywhere in about FortyTwo Minutes
105
Chapter 12 How Fast should you Run in the Rain?
114
Pursuit Curves
123
Logarithmic Spirals
131
Chapter 15 How Many People have Ever Lived?
138
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
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About the author (2012)

Robert B. Banks (1922-2002) was the author of "Towing Icebergs, Falling Dominoes, and Other Adventures in Applied Mathematics" (Princeton). He was professor of engineering at Northwestern University and dean of engineering at the University of Illinois at Chicago.

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