Math at the US Open

Being a big fan of tennis, I’m trying to catch as much of the US Open as I can. Here are a couple of tennis-inspired math questions.

I. The first problem is about the geometry of Arthur Ashe stadium.

If you’re able to watch the US Open on your computer, take a screenshot of Arthur Ashe stadium at a moment when most of the playing area is visible. Such a view is often shown during baseline rallies. Given that a regulation tennis court is a rectangle 36′ by 78′ (where the width here includes the doubles alleys), can you use your screenshot to:

  1. Figure out how many feet separate the back wall from the baseline?
  2. Determine the height of the back wall?
  3. Determine the height of the umpires tower?
  4. Determine the camera’s exact position?

If you can’t get a screenshot, you can try using the very rough sketch below, but a screenshot would beĀ better. For similar kinds of questions, see my recent blog post Drawn to Math.

Rough sketch of Arthur Ashe stadium.

Very rough sketch of Arthur Ashe stadium.

II. The next question is about the combinatorics of scoring. How many ways are there for the set score to grow from 0-0 to the final score of a set (which could be 6-0, 6-1, 6-2, 6-3, 6-4, 7-5, 7-6, or their opposites). For example, one way the game score can grow (known as a “bagel”) is as follows:

0-0, 1-0, 2-0, 3-0, 4-0, 5-0, 6-0

as current world number ones Caroline Wozniacki and Novak Djokovic both illustrated in their second round matches. (Don’t consider the game scores in your computation. Because of the deuce/advantage system, there are, in principle, infinitely many ways the game score can grow. Also, all sets that reach a score of 6-6 at the US Open are settled with a tiebreaker, so you don’t have to consider scenarios like the marathon 70-68 fifth set between Isner and Mahut at the 2010 Wimbledon!)

For similar kinds of questions, see Lightning Factorial’s Summer Fun problem set in Volume 4, Number 5 of the Girls’ Angle Bulletin.

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