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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.
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.
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).