My daughter came home the other day with words that made my Math Geek heart leap for joy. She told me that she is going to start learning “sub-crack-tion”. It seems that in the race between nature and nurture, nurture had just pulled ahead.
Not all my math students are as enthusiastic, however. Math students are known for asking questions like “so when would anyone care about this?” or “when would anyone use this?” In most cases, my background in economics is put to good use as I explain how utility or profit maximization, as well as cost minimization, are computed using derivatives, how integrals can be used in studying the search for a job, a house, or even a spouse, and how linear algebra can be used in modeling the interconnectedness of the many aspects of an economy. However, there is one topic that I don’t use economics to illustrate. When I teach the calculus behind the path taken by an object thrown, I use an example from a basketball game I witnessed many years ago. As the country finishes weeks of the basketball marathon known as “March Madness”, I am reminded of it, and why it is such a compelling example of the calculus behind the parabolic arc formed by an object that has been thrown.
I was what would today be called a “first generation college student” at Georgetown in the early 1980s, where such students were few and far between. I recall being very careful with my money and that I took overloads and honors courses (sometimes in the same semester) so as to squeeze every bit of value out of my tuition dollars. It am therefore still surprised that I agreed to join several friends from my dorm on a road trip to the 1982 NCAA basketball finals in New Orleans. After a twenty four hour drive, I arrived in the city for a weekend of fun and basketball games.
We found ourselves in the final game of the tournament, evenly matched by North Carolina as the ball was traded back and forth by the two teams. Two points for Georgetown, two for North Carolina. Surely, this would run into overtime! However, just as overtime seemed certain, the ball ended up with the other team, without being answered with two points from our team. The ball was immediately passed to a freshman player from the other team, who took the ball and threw it across the court in a perfect parabolic arc, getting the points in the last seconds of the game. It was an amazing sight, and it was as if the thrower knew the equation for such a throw intimately. With only seconds remaining, there was no way for us to recover.
The rest is history. North Carolina won the 1982 NCAA basketball finals. That freshman player, Michael Jordan, went on to become one of the most talented people to ever play the game, repeating that feat many times throughout his career. And I will always have a unique answer to the question of “where will I ever see a parabolic arc like this formed by an object that has been thrown?”
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