Morrie's Law

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

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

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

with

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

References

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.