The goal of Math-Dunk is not create professional basketball players but instead to expose through sport, the fundamentals of mathematics that can, through perseverance and serendipity, lead to successful careers in areas that have nothing to do with basketball.
Have you ever had a flat tire? Did you ever put air into the tire of your bicycle, or a car? If you had to do it with a hand pump for your bike, you might have noticed that each pump gets a little harder than the previous one as the tire fills toward its capacity. The tire is only so big, but it will expand until it starts to reach its designed limit, and it’s filled with air. If you filled up the tire of a car, the increase in air pressure offsets the weight of the car causing the car to rise in the area in which you’ve filled the tire.
On the much rarer chance you might have had to fill up a basketball that has gone slightly flat. In order to dribble the ball, the ball must be able bounce up from the floor with enough speed to return to the player’s hand. When the ball hits the floor, the air inside is slightly compressed, increasing the pressure. As the ball leaves the floor and returns toward the player’s hand, the ball resumes its shape and the internal pressure returns to its pre-bounce level. If a ball is slightly flat, it will require an extra effort to bounce it high enough to continue the dribble.
If you’ve filled a bike or car tire or a basketball, you were following Boyle’s Law which states; the volume of a fixed amount of a gas is inversely proportional to its pressure at constant temperature. The higher the pressure, within designed limits, the harder the tire or the basketball feels due to the internal pressure from the air inside.
Pretty simple, no?
A man used this part of everyday life which illustrates a basic scientific idea to develop a toy and made millions of dollars from it.