I will show how in joint work with Richard Montgomery and Susan Holmes,
we analyzed the natural process of flipping a coin which is caught in the
hand. We prove that vigorously-flipped coins are biased to come up the
same way they started.
The amount of bias depends on a single parameter, the angle between the
normal to the coin and the angular momentum vector. Measurements of this
parameter based on high-speed photography are reported. For natural flips, the chance of
coming up as started is about .51.
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