MATHEMATICS

  1. You've just bought an expansion franchise for a major league baseball team.
  1. You have the funds to build a new stadium. The contractor tells you it will be cheaper if you keep the outfield dimensions symmetrical. There are two options
    1. The outfield is circular. In fact, the playing field circumscribes a rectangle defined by home plate, the foul lines of 325 feet each, and the opposite corner in dead center.

How far will Mark McGuire have to hit the ball to hit the base of the fence in dead center?

How far would he have to hit it to strike the base of the fence in the power alleys, where the alley is defined by a 45o angle between the third base line and pitcher's mound axis?

(2) The outfield consists of two sides of the square. Then how far must the ball be hit?

  1. You have a choice of locating the team in Washington, DC or in Flagstaff, Az. In which location will the most homers be hit? In Washington, would more homers be hit per game in July than in October, if the Senators reach the playoffs and World Series?

2. Characterize all football scores (under American rules) that are impossible. Are there finitely many? Countably many?