This is the highest value of n such that the n-body problem is exactly solvable, and the potential energy of a spring is proportional to this power of displacement.
The magic angle can be obtained by solving a Legendre polynomial with this degree found in the z component of a magnetic dipole's B field. A central force and a potential with this degree with respect to distance are the only ones whose bound orbits are all closed orbits, according to Bertrand's theorem. In a potential well dependent on this power of position, all of the energy levels are (*) equally spaced. In a system with this many bodies, an additional, much smaller body can stably fit in one of five Lagrange points. This is the highest value of n such that the n-body problem is exactly solvable, and the potential energy of a spring is proportional to this power of displacement. For 10 points, what cardinal number corresponds to a law stating the entropy of the universe always increases?
The magic angle can be obtained by solving a Legendre polynomial with this degree found in the z component of a magnetic dipole's B field.
two [accept quadratic] 