April is
Mathematics Awareness Month

The theme for 2010 is

Mathematics and Sports

COD students can join in the fun by reading any of the following sports-related math articles here:

• Binomial Baseball
  "Programmable calculators can be used to play simulated baseball games. [] The use of random numbers to determine hits and outs introduces the student to the Monte Carlo method in a familiar context."
• Designing A Baseball Cover
  "Problems in design, even those of a rather frivolous nature, can produce some very interesting mathematics. Consider the 130-year-old problem of designing the cover for a baseball. Early experimental work on this problem involved the freehand drawing of plane figures. We will use geometric insight and calculus to give a relatively easy solution of the problem in space. Next, a differential equation will be derived that gives a mathematical solution with plane figures, in the style of the early efforts. Finally, we will see how well trial and error have worked, by looking at the cover design that is currently used in the manufacture of major league baseballs."
• Building Home Plate: Field of Dreams, or Reality?
  "In the moview Field of Dreams, Kevin Costner's character, Ray Kinsella, considers building a baseball park in the middle of his cornfield. [] An assistant coach for my nine-year-old son's baseball team, I was interesting to read in the official league rules the following specifications for home plate:"
• A Mathematician Catches a Baseball
  "In the game of baseball, what strategy does an outfielder employ to catch a fly ball? Recently, Michael McBeath and Dennis Shaffer, who are psychologists, and Mary Kaiser, a researcher at NASA, proposed a new model to explain how this task is accomplished. The model, called the linear optical trajectory (LOT) model, was developed and tested empirically by the three researchers, and it received national attention during the 1995 baseball season. In this paper, seeking to clarify what is written, we develop equations relating the motion of a fly ball to the motion of an outfielder utilizing the LOT strategy. In the process, we provide a mathematical foundation on which the LOT model can rest."
• How To Make A Bank Shot
• Tennis Ball Paradox
• Geometric Series From Tennis
• A Progression of Projectiles: Examples from Sports
  "The interplay between theory and application makes elementary differential equations an attractive course. For many students, this is the time when their knowledge of calculus and linear algebra is consolidated, and this is their first chance to translate physical situations directly into mathematical equations for analysis. For a course succeeding at so many levels, it is difficult to contemplate major reform. But tecnology has changed the way mathematics is learned and practiced, and our courses must reflect the increased emphasis on numerical methods and nonlinear models."
• Designs, Geometry, and a Golfer's Dilemma
  "I was taken off guard the other day when my father-in-law, John, posed to me a very simply stated problem. He plays golf. In fact, John plays a lot of golf. When you play as much golf as he does, you become bored playing with the same people over and over again. So here's the problem: John regularly plays with a group of 16 people. Three days a week for the entire summer, they go out in 4 groups of 4 players each to hit the course. Is there some way they can arrange the players int he groups each day so that everybody plays with everybody else in some sort of regular way? As my father-in-law said, 'We want to mix it up as much as possible.'"
• How To Kick A Field Goal
  "Before a record crowd of 100,963, third-ranked California faced sixth-ranked Ohio State in the Rose Bowl of January 2, 1950. With only1:55 remaining on the clock, the two teams were deadlocked in a 14-14 tie. Ohio State's drive for the goal had stalled at the California 6-yeard line; it was now fourth down. Ohio State coach Wes Fesler decided to try for a field goal to take the lead. However, confusion with substitutes caused Ohio State to draw a 5-yeard delay-of-game penalty. The field goal attempt was successful despite this seeminly foolish mistake, and Ohio State went on to win the game 17-14. According to the New York Times:
  
  Fesler, in his post-game comment, said that he had deliberately sent in two substitutes just before the crucial field goal to draw a five-yard penalty and puch the ball back from California's sex-yard line to the eleve, 'to give us a better angle.'
  
  Did Fesler make the right call? Is it really possible to improve the chances of scoring a field goal by backing up?"
• Basketball, Beta and Bayes (also, see Putnam Proof Without Words and Path Progression of a Freethrow Shooter's Progress )
  "Problem B1 on the 2002 Putnam competition reads as follows:
  
  PUTNAM PROBLEM (PP): Shanille O'Keale shoots free throws on a basketball court. She hits the first, misses the second, and thereafter the probability that she hits the next shot is equal to the proportion of the shots she has hit so far. What is the probability that she hits exactly 50 out of her first 100 shots?
  
  The answer is 1/99, as the reader may enjoy showing. Indeed, the probability that Shanille hits K of her next 98 shots is 1/99 for all k with 0 <= k <= 98; we will prove this later as a corollary to a more general result."
• New Angles on an Old Game
  "A standard exercise in calculus shows that the trajectory of a projectile, subject only to gravity, is a parabola. If we think of the projectile as a basketball, two additional interesting questions can be asked."
• Hammer Juggling, Rotational Instability and Eigenvalues
  "Get a hammer. Seriously, get a hammer. As an experiment, hold the hammer in front of you with its head pointing up. Toss it upward (CAREFULLY!), end-over-end, and catch it after one revolution. The orientation of the hammer when you catch it will be the same as when you tossed it.
  As a second experiment, hold the hammer in front of you with its head pointing sideways, to the right. Toss the hammer upward, end-over-end, and catch it after one revolution. This time, the orientation changes--the head pointed to the right when you tossed it, but points to the left when you catch it!"
  

The American Mathematical Society, the American Statistical Association, the Mathematical Association of America, and the Society for Industrial and Applied Mathematics announce that the theme for Mathematics Awareness Month, April 2010, is Mathematics and Sports. The applet above requires the free Flash Player 10 plug-in, available from Adobe.