On Tue, Jan 8, 2019 at 9:31 PM Fred Cisin via cctalk <cctalk@classiccmp.org> wrote:
> I first encountered it about 60 years ago, in fifth grade. Our textbook > said, "PI is about 3.1416 or 22/7." Our teacher insisted that that > sentence meant "PI is about 3.1416, or exactly 22/7." I argued it. I > pointed out that 22/7 was about 3.1429, and "why would they say 'about > 3.1416' instead of 'about 3.1429' if it were actually 22/7?" I got sent > to the principal's office. My father, who COULD recite a dozen digits of > PI gave me a hard time about "staying out of trouble". Nice to know that clueless schoolteachers are not limited to the UK. I had my fair share of them <mumble> years ago... > About every other semester, I would have a student who had been taught > "exactly 22/7"! One guy admitted that he had just never bothered to > divide it out. Once he did, he understood the concept of > "approximation", did his homework, and found better ones, like 355/113. As an aside, I find the 355/113 approximation useful if I need $\pi$ when doing metalwork and don't have a scientific calculator to hand (e.g. I've just got the HP16C that lives on my workbench). That approximation is good to 6 figures I think, which is way more accurate than I can machine metal to. > > A silly little exercise to get across the concept of approximation was to > get them to divide 1 by 3, write down the result, then clear, and multiply > that result times 3. "What is WRONG with that calculator?" :-) Once they > grasped a comparison to "rounding", "approximation" wasn't so alien. IIRC one of the manuals for the HP15C had a chapter on 'Why this calculator gives the wrong answers'. It covered things like rounding errors. -tony
