Huygens' principle

The sharp difference in how a wave's influence fades, depending only on the parity of the spatial dimension.

Huygens' principle states that in three (and every odd) spatial dimension $\ge3$ , a wave solution depends only on the boundary of the backward cone's base ball -- a sharp leading and trailing edge -- while in two (and every even) spatial dimension it depends on the whole ball, giving a sharp leading edge but a slowly-decaying trailing edge (the 'diffusion of waves').