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:

- Figure out how many feet separate the back wall from the baseline?
- Determine the height of the back wall?
- Determine the height of the umpires tower?
- 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*.

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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