Wednesday, February 21, 2018
 Article written by Joe Pagano

# Finding a Mall Parking Spot Using Mathematics - Part I

I am always amused when people become fascinated with simple demonstrations of the power of even basic mathematics. We have become mostly a jaded society depending on the technological progress of corporations to give us more and more electronic gadgetry and the like. We have forgotten how all this technological stuff originates: via the harnessing of the knowledge of mathematics and science and their applications in practical ways.

Thus as educator and mathematician, I always enjoy a big smile when I can demonstrate the practicality of knowing even rudimentary mathematics. A good and solid understanding of basic geometry, arithmetic, and algebra can go a long way toward understanding many fundamental laws of nature and even permitting a high degree of general problem solving abilities. People are always amazed when I explain to them how I can tell time at the beach using the sun, or use probability to make general predictions, or to do seemingly amazing human calculator multiplications in my head. Yet all these feats are quite achievable even for the ordinary person.

Having said this, I can move toward the interesting sounding title of this article and explain how basic mathematics can be used for even such an odd sounding thing as finding a parking spot in a busy mall. We all know how frustrating this can be particularly around the holiday shopping season. Now man is a clever animal and if you ask people their method many will quickly volunteer that they have a great system. These systems range from stalking people who leave the mall to circling like hungry sharks waiting to feed on the next open spot.

Personally, I had always had a problem with the methods mentioned above and for this reason, I suppose, one day I thought about the problem and asked myself whether mathematics could solve this problem—or at least come up with a more practical method. Being a mall rat largely because of my wife’s intense love of such locale, I had many opportunities to drop her off in front and then begin the process of “search and destroy,” or more simply put, to wait for parking spots. Being a fan of the two mathematical disciplines of probability and statistics, I decided to see whether using some basic facts within these two areas could help me solve the problem. Thus sitting by the mall waiting for an open spot (mind you the times we would go to the mall were usually on Saturdays when choice spots were rare, and I would always want to park in a particular area near Macy’s where spots were even more limited because of the smaller parking area), I began to make some basic assumptions and to cogitate deeply.

Almost as by happenstance, I pieced together a rudimentary method, did some quick calculations and tested the underlying hypotheses. I surveyed the fully occupied parking area, targeted my preferred area to park, and predicted that within an interval of no more than five minutes one of those preferred spots would become available. Lo and behold within five minutes, a spot opened up. I was amused. Over the next ten or fifteen visits to the mall I tried and tested this method. Success after success after success. I analyzed both the basic assumptions and mathematics used and tested again and again. Always worked. I even demonstrated the method with people in the car. The reaction was always one of amazement when I could tell them within how long a spot would open up. To them, this always seemed like magic; however, a little thoughtful contemplation joined to some basic mathematics was the glue holding the mix together.

In a follow-up article, I will reveal the method and the basic underlying assumptions, as well as the mathematical principles involved (for those who are squeamish about mathematics, fear not; for the explanations will not involve anything beyond the scope of layman mathematics, and my particular strength is the ability to boil down the esoteric and make it understandable). For those who have read this far, I think you realize the broader implications of this: if mathematics can help you find a parking spot in a busy mall, what else can it do? See you in Part II.
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