The above equation, for fixed frequency ν ν , describes an eighth of an ellipse in "mode space" (an eighth because n x , n y , n z are positive). The number of modes with frequency less than ν ν is thus the number of integral points inside the ellipse, which, in the limit of L x , L y , L z → → ∞ ∞ (i.e. for a very large parallelepiped) can be approximated to the volume of the ellipse. Hence, the number of modes N ( ν ν ) with frequency in the range [ 0 , ν ν ] is