Many anisotropic interactions contain the angular factor . They therefore vanish when their relevant axis makes the magic angle with a fixed direction. In solid-state
nuclear magnetic resonance, magic-angle spinning uses this cancellation to average
orientation-dependent broadening.
Andrew, E. R.; Bradbury, A.; and Eades, R. G. "Nuclear Magnetic Resonance Spectra from a Crystal Rotated at High Speed."
Nature182, 1659, 1958. https://doi.org/10.1038/1821659a0.Sloane,
N. J. A. Sequence A210974 in "The
On-Line Encyclopedia of Integer Sequences."
.
Equivalently, it is the acute angle for which the
second Legendre polynomial 
vanishes.
. They therefore vanish when their relevant axis makes the magic angle with a fixed direction. In solid-state
nuclear magnetic resonance, magic-angle spinning uses this cancellation to average
orientation-dependent broadening.
