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

This challenging problem book by renowned US Olympiad coaches, mathematics teachers, and researchers develops a multitude of problem-solving skills needed to excel in mathematical contests and in mathematical research in number theory. Offering inspiration and intellectual delight, the problems throughout the book encourage students to express their ideas in writing to explain how they conceive problems, what conjectures they make, and what conclusions they reach. Applying specific techniques and strategies, readers will acquire a solid understanding of the fundamental concepts and ideas of number theory The author discloses the mathematics behind a host of problems, including gauging the length of the seam on a baseball, predicting the results of melting polar ice caps, and digging a hole to China. ch. 1. Broad stripes and bright stars -- ch. 2. More stars, honeycombs, and snowflakes -- ch. 3. Slicing things like pizzas and watermelons -- ch. 4. Raindrops keep falling on my head and other goodies -- ch. 5. Raindrops and other goodies revisited -- ch. 6. Which major rivers flow uphill -- ch. 7. A brief look at [pi], e, and some other famous numbers -- ch. 8. Another look at some famous numbers -- ch. 9. Great number sequences : prime, fibonacci, and hailstone -- ch. 10. A fast way to escape -- ch. 11. How to get anywhere in about forty-two minutes -- ch. 12. How fast should you run in the rain -- ch. 13. Great turtle races : pursuit curves -- ch. 14. More great turtle races : logarithmic spirals -- ch. 15. How many people have ever lived -- ch. 16. The great explosion of 2023 -- ch. 17. How to make fairly nice valentines -- ch. 18. Somewhere over the rainbow -- ch. 19. Making mathematical mountains -- ch. 20. How to make mountains out of molehills -- ch. 21. Moving continents from here to there -- ch. 22. Cartography : how to flatten spheres -- ch. 23. Growth and spreading and mathematical analogies -- ch. 24. How long is the seam on a baseball -- ch. 25. Baseball seams, pipe connections, and world travels -- ch. 26. Lengths, areas, and volumes of all kinds of shapes