Teaching Approximations (was Re: Microcode, which is a no-go for

[Tony Duell]

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