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\bf
\centerline
{Math Bite:
A Generalization of a Curiosity that Feynman Remembered All His Life}
\rm
\bigskip
\centerline{ {\it W.A. BEYER({\eighttt  beyer@Lanl.GOV}),
J.D. LOUCK({\eighttt  jimlouck@Lanl.GOV})
and D. ZEILBERGER({\eighttt zeilberg@math.temple.edu})}}
 
{\eightrm If a boy named Morrie Jacobs told him that the cosine of
20 degrees multiplied by the cosine of 40 degrees multiplied by
the cosine of 80 degrees equaled exactly one-eighth, he would remember
that curiosity for the rest of his life, and he would remember that
he was standing in Morrie's father's leather shop when he learned it.}
--- James Gleick [`Genius', p. 47]
 
Morrie Jacobs's identity is the special case $k=3$, $a=20^{o}$, of
the following identity that follows by induction on $k$
using $\sin 2b=2 \sin b \cos b$, with $b=2^{k-1} a$.
$$
          2^k \prod_{j=0}^{k-1} \cos (2^j a) =  {{\sin (2^k a)}\over {\sin a }}
\quad.
$$
 
\bye
 
