New Books

Mathematics and Sports, edited by Joseph A. Gallian, gathers 25 articles that illuminate the power and role of mathematics in the worlds of professional and recreational play.

Divided into sections by the kind of sports, the book offers source materials for classroom use and student projects. Readers will encounter mathematical ideas from an eclectic group of writers, including undergraduate students, graduate students, and professional mathematicians.

Table of Contents

Preface

I Baseball

1. Sabremetrics: The Past, the Present, and the Future (Jim Albert)

2. Surprising Streaks and Playoff Parity: Probability Problems in a Sports Context (Rick Cleary)

3. Did Humidifying the Baseball Decrease the Number of Homers at Coors Field? (Howard Penn)

4. Streaking: Finding the Probability for a Batting Streak (Stanley Rothman and Quoc Le)

II Basketball

5. Bracketology: How can math help? (Tim Chartier, Erich Kreutzer, Amy Langville, and Kathryn Pedings)

6. Down 4 with a Minute to Go (G. Edgar Parker)

7. Jump Shot Mathematics (Howard Penn)

III Football

8. How Deep Is Your Playbook? (Tricia Muldoon Brown and Eric B. Kahn)

9. A Look at Overtime in the NFL (Chris Jones)

10. Extending the Colley Method to Generate Predictive Football Rankings (R. Drew Pasteur)

11. When Perfect Isn’t Good Enough: Retrodictive Rankings in College Football (R. Drew Pasteur)

IV Golf

12.The Science of a Drive (Douglas N. Arnold)

13. Is Tiger Woods a Winner? (Scott M. Berry)

14. G. H. Hardy’s Golfing Adventure (Roland Minton)

15. Tigermetrics (Roland Minton)

V NASCAR

16. Can Mathematics Make a Difference? Exploring Tire Troubles in NASCAR (Cheryll E. Crowe)

VI Scheduling

17. Scheduling a Tournament (Dalibor Froncek)

VII Soccer

18. Bending a Soccer Ball with Math (Tim Chartier)

VIII Tennis

19. Teaching Mathematics and Statistics Using Tennis (Reza Noubary)

20. Percentage Play in Tennis (G. Edgar Parker)

IX Track and Field

21. The Effects of Wind and Altitude in the 400m Sprint with Various IAAF Track Geometries (Vanessa Alday and Michael Frantz)

23. What is the Speed Limit for Men's 100 Meter Dash? (Reza Noubary)

24. May the Best Team Win: Determining the Winner of a Cross Country Race (Stephen Szydlik)

25. Biomechanics of Running and Walking (Anthony Tongen and Roshna E. Wunderlich)

Excerpt

Mathematician Douglas N. Arnold, in his essay "The Science of a Drive," reviews how mathematics elucidates common physical phenomena in the context of a golf drive. He describes the double-pendulum model of a golf swing; the transfer of energy and momentum in the impact between club head and ball; and drag and lift in the flight of a golf ball.

(p. 152)

Once the ball is in flight, its trajectory is completely determined by its launch velocity and launch angle and the forces acting on it. The most important of these forces is, of course, the force of gravity, which is accelerating the ball back down toward the ground at 9.8 meters per second per second. But the forces exerted on the ball by the air it is passing through are important as well. To clarify this, we choose a coordinate system with one axis aligned with the direction of flight of the ball and the others perpendicular to it. Then the forces exerted by the atmosphere on the ball are decomposed into the drag, which is a force impeding the ball in its forward motion, and the lift, which helps the ball fight gravity and stay aloft longer. Drag is the same force you feel pushing on your arm if you stick it out of the window of a moving car. Lift is a consequence of the back spin of the ball, which speeds the air passing over the top of the ball and slows the air passing under it. By Bernoulli’s principle the result is lower pressure above and therefore an upward force on the ball.

About the Editor

Joseph A. Gallian (University of Minnesota Duluth), who has taught courses on mathematics and sports, played a key role in promoting Math Awareness Month (April, 2010): "Mathematics and Sports." Gallian has received numerous MAA awards and served as the Association's President (2007-2008).