The Magic of Numbers

The Magic of Numbers by Walter McIntyre

Contrary to how you may have learned math, the story of numbers is one of magic. Numbers fill our lives in ways we never think of. From IP addresses to the television channel you watch, numbers allow us to differentiate between categories and events.

To see the real magic behind our numbers, try this experiment. Solve this equation (4+15)/(29*16). Now solve this equation without converting it to our modern numbering system, (IV+XIV)/(XXIX*XVI). The Roman numerals were for documentation and it was not possible to perform operations with them. The Romans used Arabic numbers, similar to what we use today for commerce, where operations were needed. Aren’t you glad you were taught math in our modern numbering system rather that Roman numerals? Imagine how much harder long division would have been.

Here is another piece of number magic. The constant pi is equal to 3.14 (plus an infinite number of places after the decimal point). But what is pi and where did it come from? Performing this next experiment in number magic back in Jr. Hi. would have made your journey through geometry a lot easier.

Get a dinner plate and a sewing measuring tape. Measure the circumference of the plate as exactly as you can. Also, do an exact measurement of the plate’s diameter. If you multiple the diameter by 3.14 (pi), you will get the exact same number as the circumference. If you do the same experiment with any round object, no matter how big or small, you will always get the same result. Isn’t is comforting to know that some things in the universe are constant?

I know this sounds crazy, but a few years back I had a vehicle that calculated instantaneous and trip miles per gallon. I noticed an increase in my vehicle’s fuel economy that did not agree with what I was seeing at the pump. It was 3.5 miles to the gallon better than reality (my fuel economy was worse than calculated by the vehicle’s computer).

I measured the diameter of my tires, ground to top of the tire, put the appropriate air pressure in them and measured their diameter again. The difference was 0.38 inches. I used pi and to determine the distance covered by one revolution of my tires before and after increasing the air pressure. The calculated difference in fuel economy was 3.48 miles to the gallon.

Basically, my vehicle’s computer assumed a specific diameter of the tires and was not programmed to adjust to changes in diameter. I know that you are thinking this was a waste of time and effort, but if the engineer who programmed your vehicle’s computer had not know how to use pi, or if pi were not a constant as in the experiment above, the fuel economy display on your dashboard would not be possible.

Who says there isn’t magic in the world?