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Buffon's Needle
---------------
When we are in school we learn that π is used
whenever we talk about circles and spheres. But
does it have a deeper significance? Enter Buffon's
Needle ...
Take a sheet of paper marked with parallel lines
that are spaced a certain distance apart. Then take
a needle whose length must be less than the line
spacing. Drop the needle onto the paper from a
reasonable height and record whether it lands (a)
not touching a line or (b) touching or crossing
a line. Repeat this 100 times and record the
results.
Buffon used the results from his experiment with
a needle to estimate the value of π. He worked
out this formula:
π = 2L/x.p
Where,
L is the length of the needle, x is the line
spacing and p is the proportion of needles
crossing a line (case (b)).
So now we get the notion that π is not just
about circles, but has also has a statistical
significance. In fact π shows up a lot in
statistics. It is a key part of the equation
for the Normal Distribution. So, π does indeed
have a deeper significance.