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Morrie's Law

\cos(20^\circ)\cos(40^\circ)\cos(80^\circ)={\textstyle{1\over 8}}.

This identity was referred to by Feynman (Gleick 1992). It is a special case of the general identity

2^k\prod_{j=0}^{k-1} \cos(2^j a)={\sin(2^k a)\over\sin a},

with $k=3$ and $a=20^\circ$ (Beyer et al. 1996).


Anderson, E. C. ``Morrie's Law and Experimental Mathematics.'' To appear in J. Recr. Math.

Beyer, W. A.; Louck, J. D.; Zeilberger, D. ``A Generalization of a Curiosity that Feynman Remembered All His Life.'' Math. Mag. 69, 43-44, 1996.

Gleick, J. Genius: The Life and Science of Richard Feynman. New York: Pantheon Books, p. 47, 1992.

© 1996-9 Eric W. Weisstein