8 Jan
2019
8 Jan
'19
8:58 p.m.
On Tue, Jan 8, 2019 at 9:31 PM Fred Cisin via cctalk
<cctalk at 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