Everyone has heard about the guy who attempts to measure pi
by throwing pins on flags and estimating the probability that it
lies entirely in one stripe (Buffon's problem).
Here I would like to add a few more serious techniques for finding Pi,
just in case you find yourself stranded on a desert island
without a computer or a copy of Pi to a Million Digits
(one of my all time favorites for light reading).
Of course if the island is perfectly circular the problem is trivial.
Literary Methods
First you can count the number of letters in the words of the
following:
- Now I know a number. (only 4 decimal places)
- May I draw a circle? (only 4 decimal places)
- Now I must a while endeavour to reckon right the ratio.
(10 decimal places)
- Sir. I send a story excelling
in sacred truth and rigid spelling.
Numerical sprites elucidate
for me the lesson's full weight.
If nature gain
not you complain
tho Dr Johnson fulminate. (30 decimal places)
The last is has the nice feature of having a decimal point in the right place.
It is also almost optimal since it is followed by 50288,
and it is hard to come up with pronounceable word with zero letters
(and the poem has grown wierd enough as it is).
Scientific Methods
There are various experiments one can perform that will
easily return pi.
- Paint a spot on the edge of a large circular wheel.
Spin the wheel and measure the number of rotations per second.
Next run with the wheel and let someone observe from the side
the sinusoidal patern made by the spot and measure its angular
frequency. Find pi by dividing.
- Find a black body, measure its spectrum and fit
it to Planck's distribution. This will give you Planck's
constant h. Find two superconductors and
a nonsuperconductor, make a Josephson junction
and apply a DC field. Measuring the frequency of the oscillatory
supercurrent will allow one to measure h-bar which
is h time 2 pi. Division gives 2 pi.
(It has been suggested that by using the known value of pi
this experiment becomes a physical measurement of 2.)
Less Scientific Methods
- S. Ramanujan reports that family deities can inspire you to
know pi to hundreds of decimal places.