Message-Id: <l03102801b24438e00880@[209.142.17.67]>
Date: Fri, 9 Oct 1998 14:06:13 -0800
To: pinhole@exploratorium.edu
From: Ronald Wong <ronwong@inreach.com>
Subject: pi and the 22/7
A little bit of history (BSHC - Before Scientific Hand Calculators):
When computer programmers needed to use the value of pi in their programs,
they would use the ratio of 355/113 rather than 22/7. The difference was an
error of around 8 millionth of a percent versus the 4 hundreth of a percent
that one would get using the ratio 22/7.
It was easy to remember the ratio. You just took the last three digits of
the number 113355 and divided it by the first three digits. Voila!
Of course, you wouldn't have to do this if you knew pi to 7 or more
significant figures and I know that many of you do - "May I have a large
container of coffee?" will satisfy the needs of most people for instance.
In the past, computer programmers, engineers, and some physicists couldn't
be bothered. If their work wouldn't tolerate an error of 0.000008 %, they
looked it up or recalled a mnemonic that would produce a higher degree of
accuracy. A popular one among physicists yields a value with 15 significant
figures.
Today there is the handy, dandy scientific calculator which gives pi to 11
significant figures (usually, one more than that displayed). If your
calculator isn't scientific (it doesn't have a pi-key) just remember 113355.
The convenient turn of the digits reminds me of another fortunate twist
which also involves pi.
How many seconds are there in a year?
Luckily,there is pi.
The error in using pi times the "lucky" power of ten rather than a more
precise value is less than half of one percent. For back-of-the-envelope
type of work this is just fine. Engineers, physicists and astronomers use
it all the time.
Or maybe they use to. Nowadays one can quickly compute the value to nine
significant figures using a simple calculator and the current number of
days in the year. Of course, you have to know the number of days in the
year to nine significant figures but then...don't we all?
ron