An Approximation? Exactly!

Soon there will be nothing left of my education. Not because I’ve forgotten what I was taught, mind you, but exactly because of what I was taught. I’m thinking here of Rutherford’s model not being what an atom is actually like, and of the whole conspiracy to hide the key linguistic fact that the-French-qui-is-not-the-same-as-the-English-who.

“What now?” you sigh. “Pi,” I reply. OK. Let’s do this.

Pi, perhaps the first mathematical constant I ever heard of, is the ratio of any circle’s circumference to its diameter. Or as Sesame Street’s singing monsters might present it:

π = around/through

Pi’s decimal form goes on, apparently forever, with no pattern to it.

By the start of the 20th century, about 500 digits of pi were known.
With computation advances, thanks to computers,
we now know more than the first six billion digits of pi.

A measly six billion? Pshaw. That was in the olden days: 1999. As of about a year ago, scientists had computed a hundred trillion digits of pi. Goodness knows what AI will do with that in the next two months.

Anyway, pi is a little more than 3. How much more? Well, for the math we were doing, the two-decimal version (3.14) usually sufficed; if we needed to get fancier/closer, we went to 5 decimal places (3.14159). But if we wanted to be exact, we used the fraction form: 22/7. There. Done. Exact, even if not neatly divisible.

Imagine my surprise, then, when looking at websites for this coming Saturday’s celebration of Pi Day: the 22nd of July, or 22/7. What the heck was this about Pi Approximation Day? Clearly that name applied more accurately to the other Pi Day: March 14, or 3.14. After all, using 22/7 was to represent pi exactly, right?

Wrong. Pi is smaller than 22/7. Only just, mind you, but still. Here again I find the school system going out of its way to teach a misleadingly simplified version. It drives me crazy.

Of course, there’s another reason these little discrepancies between “what I was taught” and “what was known at the time to be true” might drive me crazy. Maybe, just maybe, the problem lies not in what I was taught, but in what I remember being taught. Just as 22/7 only approximates pi, maybe my memory only approximates the truth. Especially in math.

But here’s the thing: Based on the number of YouTube videos debunking the idea that pi is 22/7 (here and here [“Do you know that pi ≠ 22/7?”] and here [“popular and fundamental myths in mathematics”] and here [“Your school lied to you”] . . .), a whole whack of people share my memory. How many people? I don’t know. Maybe as many as the number of digits of pi that were known as of 1999. Exactly as many? Oh no. It’s just an approximation.

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14 Responses to An Approximation? Exactly!

  1. Tom Watson says:

    Wow! I’m lost. Approximately, that is!

  2. barbara carlson says:

    AAAARRRGGG… stop!

    • Isabel Gibson says:

      Barbara – What? No more pi videos?

      • barbara carlson says:

        I see using just the ?/ in 22/7 = the old ./. division sign — no longer on keyboards.

        Also all these numbers! Reminds me of the time my parents’ bank was robbed. My father was certain his accounts were now at zero.
        My mother assured him the robbers only took cash, not numbers.
        He was somewhat reassured.

        The whole economy is just numbers. Soon cash will be verboten.

        • Isabel Gibson says:

          Barbara – Yeah, there’s probably a more-cumbersome way to insert that old-fashioned division sign – and that’s progress! I like your father’s concept of money in banks. It makes a lot of sense . . .

  3. Judith Umbach says:

    Possibly, our teachers did say that 22/7 is only a useful approximation, as we were drilled in how to use it. Most memories seem to omit the quibbles. Or maybe the teachers, with their one or two math courses in an ed degree didn’t know about the exact measure either. All I really know is that approximate math has stood me in good stead throughout a not-very-mathematical career.

    • Isabel Gibson says:

      Judith – IKR? Impossible to disentangle at this remove in time, and not of any great significance. My math has also been sufficient. (I sympathize a bit with the 40-ish Peggy Sue who time-travelled back to high school and informed her math teacher that she happened to know she would have no use for algebra.)

  4. Jim Taylor says:

    I don’t really care how many decimal points they can calculate pi to, because pi is the ratio of the circumference over the diameter. How can they measure circ/diam so precisely that they can calculate pi to several trillion decimal points? The quotient can only be as precise as the input measurements, right?

    Jim T

  5. Is there any reason in the real world for working on the pi decimals? What drives some people to such non-ends? The same crowd who are destroying Mt. Everest — or their cousins? In what sense (there’s that nasty concept of reason popping up) are those strings of numbers meaningful? Is someone with a computer boasting, “Look at me, Ma!”
    “Yikes!, Junior. Get a real job!”

    • Isabel Gibson says:

      Laurna – It’s a good point. I don’t understand all the motivations, but the article I linked to in Jim T’s comment takes a stab at addressing this.

  6. Jim Taylor says:

    Okay, I checked with my cousin-the-mathematics-prof, who assured me that pi is in fact real, but it not based on measurements of circumferences and diameters. Take that, Aristotle! It is, however, determined by a formula, whose closest approximation seems to be pi/4 = 1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11… and so on to infinity…

    Or, if you want a simpler formulation and if my high-school algebra still works, pi = 4 times (1 – 1/3 + 1/5 – 1/7 + 1/9 – 1/11…) Which explains why you can keep adding decimals to infinity, because you keep adding real fractions to infinity.

    How much this helps to make sure that your wheels do not thump when you drive down the highway, I’m not sure.

    Jim T

    • Isabel Gibson says:

      Jim T – Good to know I am only 2 degrees of separation from a math prof – just in case. Thanks to your cousin for the explanation of the calculation. We’ll leave the questions of why it works and why someone thought to do it to the next class.

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