As we continue the "Why Study Math” series of articles, here we look at the conic section called the parabola. The parabola is obtained by slicing a nap of the cone (see the other articles in this series on this point) with a plane parallel to one of the generators of the cone. In plain English, this means the following: take a cone made out of styrofoam; draw a line from the apex, or point, straight down to the base; on the opposite side of this line, slice the cone with a knife, starting midway down from the top, and such that the cut is made parallel to the line on the opposite side. The resulting cut produces a shape called the parabola.

The parabola is first encountered by students in their study of high school algebra. They learn that the parabola is the curve that is produced by graphing any quadratic or second-degree equation. Unfortunately, students get bogged down by all the methods of solving these equations, and then by the necessity to sketch the graphs; alas they never get to learn the practical applications. This is a common problem in the study of mathematics. Students get lost in the forest and cannot see the trees.

What students are not taught often enough is that parabolas occur frequently in the real world. They just need to open their eyes. For example, the parabola can be seen most visibly when looking up at a suspension bridge. The trace formed by the cables as they suspend from the highest point to the lowest is in the shape of a parabola. During a basketball game, the shots taken by the players trace out a parabola in the air. In fact, this is probably one of the most common applications of the parabola: projectile motion. Any body thrown in space, moving under the force of a gravitational field and without the influence of air resistance, traces out a parabola.

In addition to the applications mentioned above, parabolic surfaces called paraboloids figure in optics and other

technological applications. Reflectors and satellite dishes are in the shape of parabolic surfaces. The headlamps of your car are in this shape as well. In fact the bulb is placed at a special point called the focus of the parabola. An interesting thing to point out is that when you are driving on that dark country road and have your brights on, it is the parabolic surface of your headlamp reflectors that enable you to see further ahead. Remember that when you are trying to see whether deer are crossing ahead. Till next time...

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