A Galton Quincunx    (a pictorial of one at the University of Wisconsin:
 
A Galton Quincunx    (a pictorial of one at the University of Wisconsin:
 
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This is, of course, not proportional to the real thing.  The reason there
is a bell shaped distribution is simple:  Each ballbearing fall through the
center slot one at a time, it hits the center pin and there is a 50-50 chance
that it will go to the left or right.  The subseqent rows of pins are offset
to be halfway between the pins of the row above and a constant distance below.
This gives the ballbearing another 50-50 chance at the subsequent row and so
on.  The bell-curve is a result of probability.  The chances of a ballbearing
always bouncing to the left each time is low and therefore the number of
ballbearings in the leftmost slot is small.  The chances of a ballbearing
bouncing to the left and right approximately equal times is higher and
therefore the number of ball bearings near the middle are high.
        This same probability can be done with coins.  drop an N number of
ballbearings down T rows of pins and you get a certain bell curve.  Flip
an N number of coins T times and you will get the same distribution.
        Also, If the pins were not at the spaced exactly the distribution
would not be bell shaped.
 
Bruce Rieber
University of Arizona
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