My kids are both in high school now, hence too advanced in math for this, but here goes for anyone else whose kids are at the right level (and possibly starting the new school year this week). The other day Nyjer Morgan of the Washington Nationals charged the mound after the pitcher threw behind his head. He got there just before the first baseman, who decked him with a devastating clothesline. The question is: Who was closer to the mound and by how much, if we assume for simplicity that they started on, rather than merely near, the bases closest to them (home plate for Morgan, first base for the clothes-liner).
Doing it in my head, I come up with Morgan about 2.5 feet closer, reflecting that the mound is not perfectly centered inside the diamond. [Infield is square, 90 feet per side, hence 2 isosceles right triangles, but mound is only 60'6" from home plate.)
UPDATE: Jim Wetzler corrects me as follows:
“Not sure your geometry is precisely correct. If the diamond is a square with each side 90 feet long, the lines from home to second base and first to third base are 127.27 feet long (by the Pythagorean theorem). So these lines cross at a point 63.64 feet from all the bases. The batter runs 60.5 feet to the mound. The first baseman runs along the hypotenuse of a right triangle whose two legs are (1) the distance from first base to the center of the square (63.64 feet) and (2) the distance from the midpoint of the square to the mound (3.14 feet). By the Pythagorean theorem, the hypotenuse is 63.72 feet. So the first baseman runs 3.2 feet more than the batter.”
My response: Well done. My own mental process (while watching a Mets game) was less rigorous, as I simply rounded off √2 as 1.4 and ignored (though I was aware of) the fact that the first baseman’s trip is made slightly longer by the fact that the mound is off-center. At least the latter simplification was OK, as it only added .08 to the final total.