Comparing Pi and Pie
When we were in elementary school, most of us began being exposed to some formulas for calculating values having to do with circles or semicircles, such as the radius, the diameter, the circumference or the area. We may even have been exposed to a more complicated formula for computing the volume of a sphere or ball. Several of those formulas involve using a value which we commonly call Pi. The ones I am thinking of just now are those such as circumference equals Pi times D (for Pi times diameter). Or, more to my thought, Pi R-squared. But a fellow says, pie ain’t square, pies are round! Cakes might be square, but pies are round!
Is the fellow wrong? I’ll agree first off that pies are round. But for the sake of argument, I’m going to hold that Pi R-squared actually works better with round pies than with square ones. I could argue that ordinary pies are round, but they don’t have to be round. For example, fried pies are roughly semi-circular shaped; and, for all I know, a person could bake a pie in a square pan if they wanted to. But, I digress.
Despite the term “squared,” Pi R-squared doesn’t mean that something is square shaped. Pi R-squared actually applies to circles, or semi-circular things, not to square things.
Say that I have a 9-inch pie pan. If I persuade my wife to bake a pie in the pan, that means our pie will have a diameter of nine inches. I could also say that its radius will be half that, or four and a half inches. So, how big around will our pie be? If we slice our pie in half, how will the measurement around the semi-circle compare to the measurements across the straight cut? If we were to do a bit more slicing, cutting our pie into six slices say, then each of our slices will be four and a half inches along the straight sides, but how about the measurement around the curved part?
If we served three of the slices, leaving three still in place in the pan, how will the measure around the semi-circle compare to the measure of a side of a slice. OK, I will admit that even when we are really trying to get each slice equal, so as not to slight anyone with a smaller piece of pie, we don’t usually get out our tape measure to measure around the circular arc of the pie. But we do estimate that measure, just by relying on our “eye” to do so. But, say we decide just for the fun of it to get out our tape measure, and measure around that curve of our three slices of pie. To begin with we might estimate that the measure will be close to three times the measure of a side of our pie slice. That would make the curving edge about 13 and a half inches. But, if we are careful and precise, we will find that the measure is just a bit more than that 13 and a half. Anyway, we are coming up with an estimate of the value of that number we call Pi — just over three times the radius of the circle, or just over three times the measure of a side of our pie slice.
People of many nationalities over the centuries have been relying on various approximations of that valuable number, Pi. One of the common ancient approximations was 3 1/7, or in decimal notation, 3.1428. That one was just a bit too large. Another ancient approximate value was 3 1/8 ( 3.125 ), which was on the small side, and less accurate than 3 1/7.
When I was in elementary school in Pea Ridge, we were using 3.14 as our approximation of Pi when we did our Pi R-squared. So, to get the area of a circle, we would multiply our R times R, and then multiply that result times 3.14. That was not perfect, but then it was pretty close.
Who was it that was talking about things that were “Practically perfect for most every practical purpose!” Was that Mary Poppins? Later; when I was an engineering student at the University of Arkansas, we were trying to use the value of 3.1416 as the value of Pi. That was more accurate than 3.14, but I always found it difficult to be that precise on my slide rule. Those were the days before electronic calculators. Slide rules were the rule then for engineering students.
We had holsters to carry our slide rules. Some were expensive, and very fine. But the invention of scientific calculators and hand held computers has really changed engineering. The slide rule is for the most part a discarded antique.
The Pi part of engineering, however, has not changed. We call it a Constant, even though one could continue calculating more extended and more precise values for Pi as long as we wanted to persist. I understand that some super computers have calculated the value out to 10,000 decimal places. My hand held calculator and my computer spreadsheet program use the value of 3.14159254; which is practically perfect for nearly every practical purpose. I like to say that only God knows the ultimate value of Pi. It never seems to end or to repeat in the sequence of numbers.
Anyway, for my three pieces of pie, 4.5 inches times 3.141592654 equals 14.13716694 inches around the curve, or 4.71238898 inches along the curved edge of each slice. Knowing that, we can be more precise in being sure we get our full slice of pie!
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Editor’s note: This column was originally published Feb. 6, 2008. Jerry Nichols, a native of Pea Ridge and an award-winning columnist, is vice president of Pea Ridge Historical Society. Opinions expressed are those of the writer. He can be contacted by e-mail at joe369@centurytel.net, or call 479-6211621.