The magic angle is the angle
 |
at which 
.
Equivalently, it is the acute angle for which the
second Legendre polynomial 
vanishes.
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.
The decimal expansion of the magic angle in degrees begins 5, 4, 7, 3, 5, 6, 1, 0, 3, 1, 7, ... (OEIS A210974).
