TOPICS
Search

Morrie's Law


 cos(20 degrees)cos(40 degrees)cos(80 degrees)=1/8.

An identity communicated to Feynman as a child by a boy named Morrie Jacobs (Gleick 1992, p. 47). Feynman remembered this fact all his life and referred to it in a letter to Jacobs in 1987 (Gleick 1992, p. 450). It is a special case of the general identity

 2^kproduct_(j=0)^(k-1)cos(2^ja)=(sin(2^ka))/(sina),

with k=3 and a=20 degrees (Beyer et al. 1996).


See also

Trigonometry Angles, Trigonometry Angles--Pi/9

Explore with Wolfram|Alpha

References

Anderson, E. C. "Morrie's Law and Experimental Mathematics." J. Recr. Math. 29, 85-88, 1998.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, pp. 47 and 450, 1992.

Referenced on Wolfram|Alpha

Morrie's Law

Cite this as:

Weisstein, Eric W. "Morrie's Law." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/MorriesLaw.html

Subject classifications