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"Pi Day" Hits The Tennis Court





March 14, 2012



2012 Daily Tennis News Wire -
And, because π is so famous, it actually has its own day -- "pi day." Which, for obvious reasons, is March 14.(3.14, get it?). Mathematicians sometimes celebrate by having a piece of pie. They also urge people to go out and look for items related to π.

So, in honor of pi day, we're going to have a look around the tennis court.

The first thing is obvious: The tennis ball. It's round. That means that you need to know π to determine its circumference, its surface area (a big deal in determining air resistance!), and its volume. Also such things as its inertia. And, since tennis balls spin in flight, you need to use π to calculate their stability and the curvature of their flight.

And when you swing at the ball, your arm pivots around a particular point (your shoulder). That means that the course of the racquet follows along an arc of a circle (modified, to be sure, by the movement of the elbow and wrist. But those too pivot around a particular point. Thus the motion of the racquet is the sum of three circular paths).

There is also a relationship between π and the ball's rise and fall under gravity, but it runs through calculus and that eiπ+1=0 relationship above; we won't go into that except to mention it.

But it is worth mentioning that the head of a tennis racquet is an ellipse -- a shape which, just like a circle, is measured in terms of π. Think that doesn't matter? The people who are designing the racquet to get the largest possible "sweet spot" would disagree....

There is another important point about racquet design, and that's stress on the strings. A badly-formed racquet head will stress the strings very unevenly, meaning that the strings are more likely to break at some places than others. It doesn't really matter to the user where the strings break, of course -- but if there is a spot subject to breakage, that means that strings will break more often, and that obviously does matter to the user. So racquet designers need to construct careful mathematical models, involving π, of the shapes of their racquets.

That's about it for uses of π in the equipment, since the court is rectangular (although the author can't help but wonder what it would be like to play on a circular or elliptical court). But the downward curve of the net between the posts and the center is calculated using the hyperbolic trigonometric functions, which involve e and π although not i. For that matter, net posts are circular. The strings of the net are set in a square array, but you need to use π to figure out if a ball can possibly go through the gaps in the net. The camera lenses which record the match are circular. So are the eyes with which you watch it. When players fly from tournament to tournament, they fly along a great circle arc -- and the length of that great circle determines the flight distance, and hence their frequent flyer miles. And you need π to measure that. So π affects players even when they're between tournaments. Pie may not be good for your tennis game -- but without π, you wouldn't be playing.


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