Trash to Treasure, Peach Basket to NBA Basketball

Prelude—Measuring the Volume of a Basketball

You’ve heard the old saying, “One man’s trash is another man’s treasure.” Did I get it right?

Well, if peach baskets were left behind in the trash in the late 19th century, then one man picked up two of them, nailed them to a wall, and that’s the beginning of the game where players toss the ball in a basket (peach basket in 1891).

Dr. James Naismith was the man’s name. He did not patent his idea. He made no money for his clever invention.

What he did, however, was created one of the most popular sports games in modern history.

During the summer, I have had some very bright students who needed to see simple applications of math in the real world. What better examples are there in this world than sports examples.

I told the class to calculate the volume of a prolate spheroid. They grimaced, and said, “What?” I answered, “OK, I will say it another way, a football.”

One of the students who was born in Nigeria immediately asked could he do the mathematics of the soccer ball.  I said, “No.” Then, on August 3, 2009, I changed my mind.

Here is what happened:

I went to class. I announced, “Today, I am going to show you how to build a model for a calculation of the volume of a soccer ball or basketball." I asked, “Does anyone have a basketball?”

To my surprise, one student sitting on the front row said he had a basketball in his truck. I quipped, “You keep a basketball in your truck?” He answered, “Yeah.” I said, “Go get it.” He smiled, “OK.”

It gets more interesting as we move along. I pulled out my Olympus digital recorder and camera.

I said, “Go make a video of a couple of guys measuring the basketball.” It was during tonight’s class that we got creative.

A portion of my lecture went like this

I know you are trying to figure out how to measure the radius of the basketball. I will give you the steps to the process. Measure the circumference of the basketball. Now, use the formula for the circumference of a circle, say, 6.28r, where r is the radius.

The next step is to take your measure, say, 30 inches and set it equal to 6.28r. Solve for r.

Note that the upper semicircle, centered at the origin, (0,0) can be represented by y^2 = (r^2 – x^2), if you take the positive branch of the square root of y. We calculated the radius to be about 4.77. If the upper semicircle is rotated around the x axis, we get a three dimensional spheroid.

Note that the diameter of the two-dimensional circle goes from -4.77 to 4.77. Using the Disc Method, we construct R(x), which is the difference function of the equation of the upper semicircle and the x axis, which has an equation y=0.

Now integrate the square of R(x), using the limits of integration from -4.77 to 4.77. Don’t forget to check your anti-derivative by differentiating it to see if you get the original function.

The students left the class tonight with a different attitude. We loaded their sample video on YouTube. I challenged them to create a more creative video for the completed project which is due on August 12, 2009, at 6 pm.

Now back to the peach basket. The man who developed the game which used a soccer ball in the early days, was a clergyman who became a medical doctor. He specialized in sports physiology. He not only played the game, he had a brain!

As I think about the minister’s contribution, I am reminded of the phrase "from trash to treasure."  

So many young men played ball near trash cans, near Newkirk Street in Brooklyn, New York, where I lived as a graduate student and teacher in New York City. Many more made hoops out of small milk crates, transformed so that the ball would go through it.

I have watched children play with broken hoops, in vacant lots, and in driveways. Some hoops leaned, others were unstable. Most of all, the young people and old ones, too, were enjoying a game that started with a peach basket and transformed to a game that is treasured by millions.

The main lesson to be learned from this story is that the man who developed the game of basketball during the earlier stages was a man of character, a clergyman; he was a medical doctor and scientist; and he was a man who contributed a “priceless sport” to the world, yet he charged no price to do so.

Dr. James Naismith had the elements of a great man. The game Naismith developed is a forerunner to NBA basketball.

The moral of the story: Go and find somebody’s trash and transform it to a treasure!

Next, go buy yourself a peach, maybe a Georgia peach, and treasure the sweet taste as you remember the superior contributions of a man who has touched the lives of millions.

We salute Dr. James Naismith, the clergyman, scientist, sportsman and educator. We honor him as a pioneer in Sports and the STEM professions.